Type:	Package
Title:	Parametric Mortality Models, Life Tables and HMD
Version:	2.1.3
Maintainer:	Marius D. Pascariu <mpascariu@outlook.com>
Description:	Fit the most popular human mortality 'laws', and construct full and abridge life tables given various input indices. A mortality law is a parametric function that describes the dying-out process of individuals in a population during a significant portion of their life spans. For a comprehensive review of the most important mortality laws see Tabeau (2001) <doi:10.1007/0-306-47562-6_1>. Practical functions for downloading data from various human mortality databases are provided as well.
License:	MIT + file LICENSE
LazyData:	TRUE
Depends:	R (≥ 3.0.0)
Imports:	minpack.lm (≥ 1.2), RCurl (≥ 1.95), pbapply (≥ 1.3-4), tidyr (≥ 0.8.1), rvest (≥ 1.0.3), httr (≥ 1.4.5), methods
Suggests:	testthat, knitr, rmarkdown
URL:	https://github.com/mpascariu/MortalityLaws
BugReports:	https://github.com/mpascariu/MortalityLaws/issues
Encoding:	UTF-8
RoxygenNote:	7.3.2
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2025-04-15 18:19:16 UTC; dump_
Author:	Marius D. Pascariu [aut, cre, cph], Vladimir Canudas-Romo [ctb]
Repository:	CRAN
Date/Publication:	2025-04-16 07:40:02 UTC

MortalityLaws: Parametric Mortality Models, Life Tables and HMD

Description

Fit the most popular human mortality 'laws', and construct full and abridge life tables given various input indices. A mortality law is a parametric function that describes the dying-out process of individuals in a population during a significant portion of their life spans. For a comprehensive review of the most important mortality laws see Tabeau (2001) doi:10.1007/0-306-47562-6_1. Practical functions for downloading data from various human mortality databases are provided as well.

Details

To learn more about the package, start with the vignettes: browseVignettes(package = "MortalityLaws")

Author(s)

Maintainer: Marius D. Pascariu mpascariu@outlook.com (ORCID) [copyright holder]

Other contributors:

• Vladimir Canudas-Romo [contributor]

See Also

Useful links:

• https://github.com/mpascariu/MortalityLaws

• Report bugs at https://github.com/mpascariu/MortalityLaws/issues

AHMD sample Data object generated by the ReadAHMD() function.

Description

AHMD sample Data object generated by the ReadAHMD() function.

Usage

AHMD_sample

Format

An object of class ReadAHMD of length 5.

Value

A sample of demographic data in a data.frame

AIC function for MortalityLaw

Description

AIC function for MortalityLaw

Usage

## S3 method for class 'MortalityLaw'
AIC(object, ...)

Arguments

Value

model AIC value

region codes

Description

region codes

Usage

AUSregions()

Value

a vector

Country codes

Description

Country codes

Usage

CANregions()

Value

a vector

CHMD sample Data object generated by the ReadCHMD() function.

Description

CHMD sample Data object generated by the ReadCHMD() function.

Usage

CHMD_sample

Format

An object of class ReadCHMD of length 5.

Value

A sample of demographic data in a data.frame

HMD sample Data object generated by the ReadHMD() function.

Description

HMD sample Data object generated by the ReadHMD() function.

Usage

HMD_sample

Format

An object of class ReadHMD of length 5.

Value

A sample of demographic data in a data.frame

Country codes

Description

Country codes

Usage

HMDcountries()

Value

a vector

HMD Indices

Description

HMD Indices

Usage

HMDindices()

Value

a vector

Heligman-Pollard Mortality Law - 8 parameters - 1980

Description

Heligman-Pollard Mortality Law - 8 parameters - 1980

Usage

HP(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

HP(x = 0:100)

Heligman-Pollard 2 Mortality Law - 8 parameters

Description

Heligman-Pollard 2 Mortality Law - 8 parameters

Usage

HP2(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

HP2(x = 0:100)

Heligman-Pollard 3 Mortality Law - 9 parameters

Description

Heligman-Pollard 3 Mortality Law - 9 parameters

Usage

HP3(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

HP3(x = 0:100)

Heligman-Pollard 4 Mortality Law - 9 parameters

Description

Heligman-Pollard 4 Mortality Law - 9 parameters

Usage

HP4(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

HP4(x = 0:100)

JMD sample Data object generated by the ReadJMD() function.

Description

JMD sample Data object generated by the ReadJMD() function.

Usage

JMD_sample

Format

An object of class ReadJMD of length 5.

Value

A sample of demographic data in a data.frame

region codes

Description

region codes

Usage

JPNregions()

Value

the vector

Compute Life Tables from Parameters of a Mortality Law

Description

Compute Life Tables from Parameters of a Mortality Law

Usage

LawTable(x, par, law, sex = NULL, lx0 = 1e+05, ax = NULL)

Arguments

Details

The "life table" is also called "mortality table" or "actuarial table". This shows, for each age, what the probability is that a person of that age will die before his or her next birthday, the expectation of life across different age ranges or the survivorship of people from a certain population.

Value

The output is of the "LifeTable" class with the components:

Author(s)

Marius D. Pascariu

See Also

LifeTable MortalityLaw

Examples

# Example 1 --- Makeham --- 4 tables ----------
x1 = 45:100
L1 = "makeham"
C1 = matrix(c(0.00717, 0.07789, 0.00363,
              0.01018, 0.07229, 0.00001,
              0.00298, 0.09585, 0.00002,
              0.00067, 0.11572, 0.00078),
            nrow = 4, dimnames = list(1:4, c("A", "B", "C")))

LawTable(x = 45:100, par = C1, law = L1)

# WARNING!!!

# It is important to know how the coefficients have been estimated. If the
# fitting of the model was done over the [x, x+) age-range, the LawTable
# function can be used to create a life table only for age x onward.

# What can go wrong?

# ** Example 1B - is OK.
LawTable(x = 45:100, par = c(0.00717, 0.07789, 0.00363), law = L1)

# ** Example 1C - Not OK, because the life expectancy at age 25 is
# equal with life expectancy at age 45 in the previous example.
LawTable(x = 25:100, par = c(0.00717, 0.07789, 0.00363), law = L1)

# Why is this happening?

# If we have a model that covers only a part of the human mortality curve
# (e.g. adult mortality), in fitting the x vector is scaled down, meaning
# age (x) becomes (x - min(x) + 1). And, the coefficients are estimated on
# a scaled x in ordered to obtain meaningful estimates. Otherwise the
# optimization process might not converge.

# What can we do about it?

# a). Know which mortality laws are rescaling the x vector in the fitting
# process. If these models are fitted with the MortalityLaw() function, you
# can find out like so:
A <- availableLaws()$table
A[, c("CODE", "SCALE_X")]

# b). If you are using one of the models that are applying scaling,
# be aware over what age-range the coefficients have been estimated. If they
# have been estimated using, say, ages 50 to 80, you can use the
# LawTable() to build a life tables from age 50 onwards.


# Example 2 --- Heligman-Pollard -- 1 table ----
x2 = 0:110
L2 = "HP"
C2 = c(0.00223, 0.01461, 0.12292, 0.00091,
       2.75201, 29.01877, 0.00002, 1.11411)

LawTable(x = x2, par = C2, law = L2)

# Because "HP" is not scaling down the x vector, the output is not affected
# by the problem described above.

# Check
LawTable(x = 3:110, par = C2, law = L2)
# Note the e3 = 70.31 in both tables

Compute Life Tables from Mortality Data

Description

Construct either a full or abridged life table with various input choices like: death counts and mid-interval population estimates (Dx, Ex) or age-specific death rates (mx) or death probabilities (qx) or survivorship curve (lx) or a distribution of deaths (dx). If one of these options is specified, the other can be ignored. The input data can be an object of class: numerical vector, matrix or data.frame.

Usage

LifeTable(x, Dx = NULL, Ex = NULL,
             mx = NULL,
             qx = NULL,
             lx = NULL,
             dx = NULL,
             sex = NULL,
             lx0 = 1e5,
             ax  = NULL)

Arguments

Details

The "life table" is also called "mortality table" or "actuarial table". This shows, for each age, what the probability is that a person of that age will die before his or her next birthday, the expectation of life across different age ranges or the survivorship of people from a certain population.

Value

The output is of the "LifeTable" class with the components:

Author(s)

Marius D. Pascariu

See Also

LawTable convertFx

Examples

# Example 1 --- Full life tables with different inputs ---

y  <- 1900
x  <- as.numeric(rownames(ahmd$mx))
Dx <- ahmd$Dx[, paste(y)]
Ex <- ahmd$Ex[, paste(y)]

LT1 <- LifeTable(x, Dx = Dx, Ex = Ex)
LT2 <- LifeTable(x, mx = LT1$lt$mx)
LT3 <- LifeTable(x, qx = LT1$lt$qx)
LT4 <- LifeTable(x, lx = LT1$lt$lx)
LT5 <- LifeTable(x, dx = LT1$lt$dx)

LT1
LT5
ls(LT5)

# Example 2 --- Compute multiple life tables at once ---

LTs = LifeTable(x, mx = ahmd$mx)
LTs
# A warning is printed if the input contains missing values.
# Some of the missing values can be handled by the function.

# Example 3 --- Abridged life table ------------

x  <- c(0, 1, seq(5, 110, by = 5))
mx <- c(.053, .005, .001, .0012, .0018, .002, .003, .004,
        .004, .005, .006, .0093, .0129, .019, .031, .049,
        .084, .129, .180, .2354, .3085, .390, .478, .551)
LT6 <- LifeTable(x, mx = mx, sex = "female")
LT6

# Example 4 --- Abridged life table w using my own 'ax' ------------
# In this examples we are using the ages (x) and death rates (mx) from
# example 3. Note that 'ax' must have the same length as the 'x' vector
# otherwise an error message will be returned.

my_ax <- c(0.1, 1.5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
           2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1)

LT7 <- LifeTable(x = x, mx = mx, ax = my_ax)

Check LifeTable input

Description

Check LifeTable input

Usage

LifeTable.check(input)

Arguments

Value

A list of life table validated data

LifeTable.core

Description

LifeTable.core

Usage

LifeTable.core(x, Dx, Ex, mx, qx, lx, dx, sex, lx0, ax)

Arguments

Value

A data.frame containing life table results

Fit Mortality Laws

Description

Fit parametric mortality models given a set of input data which can be represented by death counts and mid-interval population estimates (Dx, Ex) or age-specific death rates (mx) or death probabilities (qx). Using the argument law one can specify the model to be fitted. So far more than 27 parametric models have been implemented; check the availableLaws function to learn about the available options. The models can be fitted under the maximum likelihood methodology or by selecting a loss function to be optimised. See the implemented loss function by running the availableLF function.

Usage

MortalityLaw(x, Dx = NULL, Ex = NULL, mx = NULL, qx = NULL,
                law = NULL,
                opt.method = "LF2",
                parS = NULL,
                fit.this.x = x,
                custom.law = NULL,
                show = FALSE, ...)

Arguments

Details

Depending on the complexity of the model, one of following optimization strategies is employed:

1. Nelder-Mead method: approximates a local optimum of a problem with n variables when the objective function varies smoothly and is unimodal. For details see optim;

2. PORT routines: provides unconstrained optimization and optimization subject to box constraints for complicated functions. For details check nlminb;

3. Levenberg-Marquardt algorithm: damped least-squares method. For details check nls.lm.

Value

The output is of the "MortalityLaw" class with the components:

Author(s)

Marius D. Pascariu

See Also

availableLaws availableLF LifeTable ReadHMD

Examples

# Example 1: --------------------------
# Fit Makeham Model for Year of 1950.

x  <- 45:75
Dx <- ahmd$Dx[paste(x), "1950"]
Ex <- ahmd$Ex[paste(x), "1950"]

M1 <- MortalityLaw(x = x, Dx = Dx, Ex = Ex, law = 'makeham')

M1
ls(M1)
coef(M1)
summary(M1)
fitted(M1)
predict(M1, x = 45:95)
plot(M1)


# Example 2: --------------------------
# We can fit the same model using a different data format
# and a different optimization method.
x  <- 45:75
mx <- ahmd$mx[paste(x), ]
M2 <- MortalityLaw(x = x, mx = mx, law = 'makeham', opt.method = 'LF1')
M2
fitted(M2)
predict(M2, x = 55:90)

# Example 3: --------------------------
# Now let's fit a mortality law that is not defined
# in the package, say a reparameterized Gompertz in
# terms of modal age at death
# hx = b*exp(b*(x-m)) (here b and m are the parameters to be estimated)

# A function with 'x' and 'par' as input has to be defined, which returns
# at least an object called 'hx' (hazard rate).
my_gompertz <- function(x, par = c(b = 0.13, M = 45)){
  hx  <- with(as.list(par), b*exp(b*(x - M)) )
  return(as.list(environment()))
}

M3 <- MortalityLaw(x = x, Dx = Dx, Ex = Ex, custom.law = my_gompertz)
summary(M3)
# predict M3 for different ages
predict(M3, x = 85:130)


# Example 4: --------------------------
# Fit Heligman-Pollard model for a single
# year in the dataset between age 0 and 100 and build a life table.

x  <- 0:100
mx <- ahmd$mx[paste(x), "1950"] # select data
M4 <- MortalityLaw(x = x, mx = mx, law = 'HP', opt.method = 'LF2')
M4
plot(M4)

LifeTable(x = x, qx = fitted(M4))

Download the Australian Human Mortality Database (AHMD)

Description

Download detailed mortality and population data for different provinces and territories in Australia, in a single object from the Australian Human Mortality Database.

Usage

ReadAHMD(what, regions = NULL, interval = "1x1", save = FALSE, show = TRUE)

Arguments

Details

(Description taken from the AHMD website).

The Australian Human Mortality Database (AHMD) was created to provide detailed Australian mortality and population data to researchers, students, journalists, policy analysts, and others interested in the history of human longevity. The project is an achievement of the Mortality, Ageing & Health research team in the ANU School of Demography under the supervision of Associate Professor Vladimir Canudas-Romo, in collaboration with demographers at the Max Plank Institute for Demographic Research (Rostock, Germany) and the Department of Demography, University of California at Berkeley.

The AHMD is a "satellite" of the Human Mortality Database (HMD), an international database which currently holds detailed data for multiple countries or regions. Consequently, the AHMD's underlying methodology corresponds to the one used for the HMD.

The AHMD gathers all required data (deaths counts, births counts, population size, exposure-to-risk, death rates) to compute life tables for Australia, its states and its territories. One of the great advantages of the database is to include data that is validated and corrected, when required, and rendered comparable, if possible, for the period ranging from 1971 thru 2016. For comparison purposes, various life tables published by governmental organizations are also available for download in PDF format.

Value

A ReadAHMD object that contains:

Author(s)

Marius D. Pascariu

See Also

ReadHMD ReadCHMD

Examples

# Download demographic data for Australian Capital Territory and
# Tasmania regions in 5x1 format

# Death counts. We don't want to export data outside R.
AHMD_Dx <- ReadAHMD(what = "Dx",
                    regions = c('ACT', 'TAS'),
                    interval  = "5x1",
                    save = FALSE)
AHMD_Dx

# Download life tables for female population in all the states and export data.
LTF <- ReadAHMD(what = "LT_f", interval  = "5x1", save = FALSE)
LTF

Download the Canadian Human Mortality Database (CHMD)

Description

Download detailed mortality and population data for different provinces and territories in Canada, in a single object from the Canadian Human Mortality Database.

Usage

ReadCHMD(what, regions = NULL, interval = "1x1", save = FALSE, show = TRUE)

Arguments

Details

(Description taken from the CHMD website).

The Canadian Human Mortality Database (CHMD) was created to provide detailed Canadian mortality and population data to researchers, students, journalists, policy analysts, and others interested in the history of human longevity. The project is an achievement of the Mortality and Longevity research team at the Department of Demography, Universite de Montreal, under the supervision of Professor Robert Bourbeau, in collaboration with demographers at the Max Plank Institute for Demographic Research (Rostock, Germany) and the Department of Demography, University of California at Berkeley. Nadine Ouellette, researcher at the Institut national d'etudes demographiques in Paris and member of the Mortality and Longevity research team at the Universite de Montreal, is in charge of computing all CHMD life tables and updating the CHMD web site.

The CHMD is a "satellite" of the Human Mortality Database (HMD), an international database which currently holds detailed data for multiple countries or regions. Consequently, the CHMD's underlying methodology corresponds to the one used for the HMD.

The CHMD gathers all required data (deaths counts, births counts, population size, exposure-to-risk, death rates) to compute life tables for Canada, its provinces and its territories. One of the great advantages of the database is to include data that is validated and corrected, when required, and rendered comparable, if possible, for the period ranging from 1921 thru 2011. For comparison purposes, various life tables published by governmental organizations are also available for download in PDF format.

Value

A ReadCHMD object that contains:

Author(s)

Marius D. Pascariu

See Also

ReadHMD ReadAHMD

Examples

# Download demographic data for Quebec and Saskatchewan regions in 1x1 format

# Death counts. We don't want to export data outside R.
CHMD_Dx <- ReadCHMD(what = "Dx",
                    regions = c('QUE', 'SAS'),
                    interval  = "1x1",
                    save = FALSE)

# Download life tables for female population. To export data use save = TRUE.
LTF <- ReadCHMD(what = "LT_f",
                regions = c('QUE', 'SAS'),
                interval  = "1x1",
                save = FALSE)

Download The Human Mortality Database (HMD)

Description

Download detailed mortality and population data for different countries and regions in a single object from the Human Mortality Database.

Usage

ReadHMD(
  what,
  countries = NULL,
  interval = "1x1",
  username,
  password,
  save = FALSE,
  show = TRUE
)

Arguments

Details

The Human Mortality Database (HMD) was created to provide detailed mortality and population data to researchers, students, journalists, policy analysts, and others interested in the history of human longevity. The project began as an outgrowth of earlier projects in the Department of Demography at the University of California, Berkeley, USA, and at the Max Planck Institute for Demographic Research in Rostock, Germany (see history). It is the work of two teams of researchers in the USA and Germany (see research teams), with the help of financial backers and scientific collaborators from around the world (see acknowledgements). The Center on the Economics and Development of Aging (CEDA) French Institute for Demographic Studies (INED) has also supported the further development of the database in recent years.

Value

A ReadHMD object that contains:

Author(s)

Marius D. Pascariu

Examples

## Not run: 


# Download demographic data for 3 countries in 1x1 format
age_int  <- 1  # age interval: 1,5
year_int <- 1  # year interval: 1,5,10
interval <- paste0(age_int, "x", year_int)  # --> 1x1
# And the 3 countries: Sweden Denmark and USA. We have to use the HMD codes
cntr  <- c('SWE', 'DNK', 'USA')

# Download death counts. We don't want to export data outside R.
HMD_Dx <- ReadHMD(what = "Dx",
                  countries = cntr,
                  interval  = interval,
                  username  = "user@email.com",
                  password  = "password",
                  save = FALSE)
HMD_Dx

# Download life tables for female population and export data.
LTF <- ReadHMD(what = "LT_f",
               countries = cntr,
               interval  = interval,
               username  = "user@email.com",
               password  = "password",
               save = TRUE)
LTF

## End(Not run)

Function to Download Data for a one Country

Description

Function to Download Data for a one Country

Usage

ReadHMD.core(what, country, interval, username, password, link)

Arguments

Value

A data.frame containing demographic data

Download the Japanese Mortality Database (JMD)

Description

Download detailed mortality and population data of the 47 prefectures in Japan, in a single object. The source of data is the Japanese Mortality Database.

Usage

ReadJMD(what, regions = NULL, interval = "1x1", save = FALSE, show = TRUE)

Arguments

Details

(Description taken from the JMD website).

The Japanese Mortality Database is a comprehensively-reorganized mortality database that is optimized for mortality research and consistent with the Human Mortality Database. This database is provided as a part of the research project "Demographic research on the causes and the socio-economic consequence of longetivity extension in Japan" (2011-2013), "Demographic research on longevity extension, population aging, and their effects on the social security and socio-economic structures in Japan" (2014-2016), and "Comprehensive research from a demographic viewpoint on the longevity revolution" (2017-2019) at the National Institute of Population and Social Security Research.

The Japanese Mortality Database is designed to provide the life tables to all the people who are interested in Japanese mortality including domestic and foreign mortality researchers for the purpose of mortality research. Especially because we have structured it to conform with the HMD, our database is suitable for international comparison, we put emphasis on the compatibility with the HMD more than our country's particular characteristics. Therefore, the life tables by JMD do not necessarily exhibit the same values as ones by the official life tables prepared and released by the Statistics and Information Department, Minister's Secretariat, Ministry of Health, Labor and Welfare according to the different base population or the methods for estimating the tables. When doing things other than mortality research, if life table that statistically displays our country's mortality situation is necessary, please use the official life table that has been prepared by the Statistics and Information Department, Minister's Secretariat, Ministry of Health, Labor and Welfare.

At the present time, we offer the data for All Japan and by prefecture. The project team is studying the methodology for estimating life tables along with data preparation. Therefore, the data may be updated when a new methodology is adopted. Please refer to "Methods" for further information.

Value

A ReadJMD object that contains:

Author(s)

Marius D. Pascariu

See Also

ReadHMD ReadCHMD

Examples

# Download demographic data for Fukushima and Tokyo regions in 1x1 format

# Death counts. We don't want to export data outside R.
JMD_Dx <- ReadJMD(what = "Dx",
                  regions = c('Fukushima', 'Tokyo'),
                  interval  = "1x1",
                  save = FALSE)
JMD_Dx

# Download life tables for female population in all the states and export data.
LTF <- ReadJMD(what = "LT_f", interval  = "5x5", save = FALSE)
LTF

Depending on the chosen mortality law, additional details need to be specified in order to be able to fit the models taking into account it's particularities.

Description

Depending on the chosen mortality law, additional details need to be specified in order to be able to fit the models taking into account it's particularities.

Usage

addDetails(law, custom.law = NULL, parS = NULL)

Arguments

Value

A list of model specifications

What age(s) are we looking at?

Description

What age(s) are we looking at?

Usage

ageMsg(what, x)

Arguments

Value

A scalar or character indicating age groups

MortalityLaws Test Data

Description

Dataset containing altered death rates (mx), death counts (Dx) and exposures (Ex) for the female population living in England & Wales in four different years: 1850, 1900, 1950 and 2010. The data-set is provided for testing purposes only. Download the actual data free of charge from https://www.mortality.org. Once a username and a password are created on the website the function ReadHMD can be used for downloading.

Usage

ahmd

Format

An object of class list of length 3.

Source

Human Mortality Database

See Also

ReadHMD

Examples

head(ahmd$mx)

Check Data Availability in HMD

Description

The function returns information about available data in the Human Mortality Database, HMD (period life tables etc.), with the range of years covered by the life tables.

Usage

availableHMD(link = "https://www.mortality.org/Data/DataAvailability")

Arguments

Value

A tibble.

Author(s)

Marius D. Pascariu

See Also

ReadHMD

Examples

availableHMD()

Check Available Loss Function

Description

The function returns information about the implemented loss function used by the optimization procedure in the MortalityLaw function.

Usage

availableLF()

Value

A list of class availableLF with the components:

Author(s)

Marius D. Pascariu

See Also

MortalityLaw

Examples

availableLF()

Check Available Mortality Laws

Description

The function returns information about the parametric models that can be called and fitted in the MortalityLaw function. For a comprehensive review of the most important mortality laws, Tabeau (2001) is a good starting point.

Usage

availableLaws(law = NULL)

Arguments

Value

The output is of the "availableLaws" class with the components:

Author(s)

Marius D. Pascariu

References

1. Gompertz, B. (1825). On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies. Philosophical Transactions of the Royal Society of London, 115, 513-583.

2. Makeham, W. (1860). On the Law of Mortality and Construction of Annuity Tables. The Assurance Magazine and Journal of the Institute of Actuaries, 8(6), 301-310. doi:10.1017/S204616580000126X

3. Thiele, T. (1871). On a Mathematical Formula to express the Rate of Mortality throughout the whole of Life, tested by a Series of Observations made use of by the Danish Life Insurance Company of 1871. Journal of the Institute of Actuaries and Assurance Magazine, 16(5), 313-329. doi:10.1017/S2046167400043688

4. Oppermann, L. H. F. (1870). On the graduation of life tables, with special application to the rate of mortality in infancy and childhood. The Insurance Record Minutes from a meeting in the Institute of Actuaries, 42.

5. Wittstein, T. and D. Bumsted. (1883). The Mathematical Law of Mortality. Journal of the Institute of Actuaries and Assurance Magazine, 24(3), 153-173.

6. Steffensen, J. (1930). Infantile mortality from an actuarial point of view. Skandinavisk Aktuarietidskrift 13, 272-286. doi:10.1080/03461238.1930.10416902

7. Perks, W. (1932). On Some Experiments in the Graduation of Mortality Statistics. Journal of the Institute of Actuaries, 63(1), 12-57. doi:10.1017/S0020268100046680

8. Harper, F. S. (1936). An actuarial study of infant mortality. Scandinavian Actuarial Journal 1936 (3-4), 234-270. doi:10.1080/03461238.1936.10405113

9. Weibull, W. (1951). A statistical distribution function of wide applicability. Journal of applied mechanics 103, 293-297. doi:10.1115/1.4010337

10. Beard, R. E. (1971). Some aspects of theories of mortality, cause of death analysis, forecasting and stochastic processes. Biological aspects of demography 999, 57-68.

11. Vaupel, J., Manton, K.G., and Stallard, E. (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16(3): 439-454. doi:10.2307/2061224

12. Siler, W. (1979), A Competing-Risk Model for Animal Mortality. Ecology, 60: 750-757. doi:10.2307/1936612

13. Heligman, L., & Pollard, J. (1980). The age pattern of mortality. Journal of the Institute of Actuaries, 107(1), 49-80. doi:10.1017/S0020268100040257

14. Rogers A and Planck F (1983). MODEL: A General Program for Estimating Parametrized Model Schedules of Fertility, Mortality, Migration, and Marital and Labor Force Status Transitions. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-83-102

15. Martinelle S. (1987). A generalized Perks formula for old-age mortality. Stockholm, Sweden, Statistiska Centralbyran, 1987. 55 p. (R&D Report, Research-Methods-Development, U/STM No. 38)

16. Carriere J.F. (1992). Parametric models for life tables. Transactions of the Society of Actuaries. Vol.44

17. Kostaki A. (1992). A nine-parameter version of the Heligman-Pollard formula. Mathematical Population Studies. Vol. 3 277-288. doi:10.1080/08898489209525346

18. Thatcher AR, Kannisto V and Vaupel JW (1998). The force of mortality at ages 80 to 120. Odense Monographs on Population Aging Vol. 5, Odense University Press, 1998. 104, 20 p. Odense, Denmark

19. Tabeau E. (2001). A Review of Demographic Forecasting Models for Mortality. In: Tabeau E., van den Berg Jeths A., Heathcote C. (eds) Forecasting Mortality in Developed Countries. European Studies of Population, vol 9. Springer, Dordrecht. doi:10.1007/0-306-47562-6_1

20. Finkelstein M. (2012) Discussing the Strehler-Mildvan model of mortality Demographic Research, Vol. 26(9), 191-206. doi:10.4054/DemRes.2012.26.9

See Also

MortalityLaw

Examples

availableLaws()

Beard Model - 1971

Description

Beard Model - 1971

Usage

beard(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

beard(x = 50:100)

Makeham-Beard Model - 1971

Description

Makeham-Beard Model - 1971

Usage

beard_makeham(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

beard_makeham(x = 0:100)

Bring or Rename Starting Parameters in the Law Functions

Description

Bring or Rename Starting Parameters in the Law Functions

Usage

bring_parameters(law, par = NULL)

Arguments

Value

Vector or initial model parameters

Carriere Mortality Law - 1992

Description

Carriere1 = weibull + invweibull + gompertz

Usage

carriere1(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

carriere1(x = 0:100)

Carriere Mortality Law - 1992

Description

Carriere2 = weibull + invgompertz + gompertz

Usage

carriere2(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

carriere2(x = 0:100)

Function to check input data in MortalityLaw

Description

Function to check input data in MortalityLaw

Usage

check.MortalityLaw(input)

Arguments

Value

No return value, called for side effects

Check input ReadAHMD

Description

Check input ReadAHMD

Usage

check_input_ReadAHMD(x)

Arguments

Value

No return value, called for checking stuff

Check input ReadHMD

Description

Check input ReadHMD

Usage

check_input_ReadCHMD(x)

Arguments

Value

No return value, called for input validation

Check input ReadHMD

Description

Check input ReadHMD

Usage

check_input_ReadHMD(x)

Arguments

Value

No return value, called for validating input data

Check input ReadAHMD

Description

Check input ReadAHMD

Usage

check_input_ReadJMD(x)

Arguments

Value

No return value, called for validating input data

Select an optimizing method

Description

Select an optimizing method

Usage

choose_optim(input)

Arguments

Value

A list of model specification corresponding to the best fitted model

Find ax[1:2] indicators using Coale-Demeny coefficients Here we adjust the first two values of ax to account for infant mortality more accurately

Description

Find ax[1:2] indicators using Coale-Demeny coefficients Here we adjust the first two values of ax to account for infant mortality more accurately

Usage

coale.demeny.ax(x, mx, ax, sex)

Arguments

Value

A vector of coefficients

Find ax indicator

Description

Find ax indicator

Usage

compute.ax(x, mx, qx)

Arguments

Value

ax - the point in the age internal where 50 have already occurred

Convert Life Table Indicators

Description

Easy conversion between the life table indicators. This function is based on the LifeTable function and methods behind it.

Usage

convertFx(x, data, from, to, ...)

Arguments

Value

A matrix or array containing life table indicators.

Author(s)

Marius D. Pascariu

See Also

LifeTable

Examples

# Data ---
x  <- 0:110
mx <- ahmd$mx

# mx to qx
qx <- convertFx(x, data = mx, from = "mx", to = "qx")
# mx to dx
dx <- convertFx(x, data = mx, from = "mx", to = "dx")
# mx to lx
lx <- convertFx(x, data = mx, from = "mx", to = "lx")


# There are 28 possible combinations --------------------------------
# Let generate all of them.
from <- c("mx", "qx", "dx", "lx")
to   <- c("mx", "qx", "dx", "lx", "Lx", "Tx", "ex")
K    <- expand.grid(from = from, to = to) # all possible cases/combinations

for (i in 1:nrow(K)) {
  In  <- as.character(K[i, "from"])
  Out <- as.character(K[i, "to"])
  N <- paste0(Out, "_from_", In)
  cat(i, " Create", N, "\n")
  # Create the 28 sets of results
  assign(N, convertFx(x = x, data = get(In), from = In, to = Out))
}

Data formats

Description

Data formats

Usage

data_format()

Value

a vector

deviance function for MortalityLaw

Description

deviance function for MortalityLaw

Usage

## S3 method for class 'MortalityLaw'
deviance(object, ...)

Arguments

Value

model deviance value

df.residual function for MortalityLaw

Description

df.residual function for MortalityLaw

Usage

## S3 method for class 'MortalityLaw'
df.residual(object, ...)

Arguments

Value

model residual value

dx to lx

Description

Function to convert dx into lx and back

Usage

dx_lx(ux, out = c("dx", "lx"))

Arguments

Value

A vector containing dx or lx values

Function that identifies the case/problem we have to solve

Description

Function that identifies the case/problem we have to solve

Usage

find.my.case(Dx = NULL, Ex = NULL, mx = NULL, qx = NULL, lx = NULL, dx = NULL)

Arguments

Value

A list containing problem solving details

Gamma-Gompertz Model as in Vaupel et al. (1979)

Description

Gamma-Gompertz Model as in Vaupel et al. (1979)

Usage

ggompertz(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

ggompertz(x = 50:120)

Gompertz Mortality Law - 1825

Description

Gompertz Mortality Law - 1825

Usage

gompertz(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

gompertz(x = 45:90)

Gompertz Mortality Law - informative parameterization

Description

Gompertz Mortality Law - informative parameterization

Usage

gompertz0(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

gompertz0(x = 45:90)

Summary function - display head and tail in a single data.frame The original code for this function was first written for 'psych' R package here we have modified it a bit

Description

Summary function - display head and tail in a single data.frame The original code for this function was first written for 'psych' R package here we have modified it a bit

Usage

head_tail(x, hlength = 4, tlength = 4, digits = 4, ellipsis = TRUE)

Arguments

Value

Print table's head and tail

Inverse-Gompertz Mortality Law - informative parameterization

Description

m - is a measure of location because it is the mode of the density, m > 0 sigma - represents the dispersion of the density about the mode, sigma > 0

Usage

invgompertz(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

invgompertz(x = 15:25)

Inverse-Weibull Mortality Law

Description

The Inverse-Weibull proves useful for modelling the childhood and teenage years, because the logarithm of h(x) is a concave function. m > 0 is a measure of location sigma > 0 is measure of dispersion

Usage

invweibull(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

invweibull(x = 1:20)

Kannisto Mortality Law - 1998

Description

Kannisto Mortality Law - 1998

Usage

kannisto(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

kannisto(x = 85:120)

Kannisto-Makeham Mortality Law - 1998

Description

Kannisto-Makeham Mortality Law - 1998

Usage

kannisto_makeham(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

kannisto_makeham(x = 85:120)

Kostaki Model - 1992

Description

Kostaki Model - 1992

Usage

kostaki(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

kostaki(x = 0:100)

logLik function for MortalityLaw

Description

logLik function for MortalityLaw

Usage

## S3 method for class 'MortalityLaw'
logLik(object, ...)

Arguments

Value

model log-Likelohood value

Make HTTP request

Description

Make HTTP request

Usage

make_http_request(url)

Arguments

Value

url response

Makeham Mortality Law - 1860

Description

Makeham Mortality Law - 1860

Usage

makeham(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

makeham(x = 45:90)

Makeham Mortality Law - informative parameterization

Description

Makeham Mortality Law - informative parameterization

Usage

makeham0(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

makeham0(x = 45:90)

Martinelle Model - 1987

Description

Martinelle Model - 1987

Usage

martinelle(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

martinelle(x = 0:100)

mx to qx

Description

Function to convert mx into qx and back, using the constant force of mortality assumption (CFM).

Usage

mx_qx(x, nx, ux, out = c("qx", "mx"))

Arguments

Value

A vector of rates

Function to be Optimize

Description

Function to be Optimize

Usage

objective_fun(par, x, Dx, Ex, mx, qx, law, opt.method, custom.law)

Arguments

Value

The optimal value

Opperman Mortality Law - 1870

Description

Opperman Mortality Law - 1870

Usage

opperman(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

opperman(x = 1:25)

Perks Model - 1932

Description

Perks Model - 1932

Usage

perks(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

perks(x = 50:100)

Plot Function for MortalityLaw

Description

Plot Function for MortalityLaw

Usage

## S3 method for class 'MortalityLaw'
plot(x, ...)

Arguments

Value

generate a plot

Author(s)

Marius D. Pascariu

See Also

MortalityLaw

Examples

# See complete example in MortalityLaw help page

Predict function for MortalityLaw

Description

Predict function for MortalityLaw

Usage

## S3 method for class 'MortalityLaw'
predict(object, x, ...)

Arguments

Value

A vector of predicted hazard rates

Author(s)

Marius D. Pascariu

See Also

MortalityLaw

Examples

# Extrapolate old-age mortality with the Kannisto model
# Fit ages 80-94 and extrapolate up to 120.

Mx <- ahmd$mx[paste(80:94), "1950"]
M1 <- MortalityLaw(x = 80:94, mx  = Mx, law = 'kannisto')
fitted(M1)
predict(M1, x = 80:120)

# See more examples in MortalityLaw function help page.

Print LifeTable

Description

Print LifeTable

Usage

## S3 method for class 'LifeTable'
print(x, ...)

Arguments

Value

Print data on the console

Print MortalityLaw

Description

Print MortalityLaw

Usage

## S3 method for class 'MortalityLaw'
print(x, ...)

Arguments

Value

Print data on console

Print ReadCHMD

Description

Print ReadCHMD

Usage

## S3 method for class 'ReadAHMD'
print(x, ...)

Arguments

Value

Print data on console

Print ReadCHMD

Description

Print ReadCHMD

Usage

## S3 method for class 'ReadCHMD'
print(x, ...)

Arguments

Value

Print data on the console

Print ReadHMD

Description

Print ReadHMD

Usage

## S3 method for class 'ReadHMD'
print(x, ...)

Arguments

Value

Print data on the console

Print ReadJMD

Description

Print ReadJMD

Usage

## S3 method for class 'ReadJMD'
print(x, ...)

Arguments

Value

Print info on the console

Print availableLF

Description

Print availableLF

Usage

## S3 method for class 'availableLF'
print(x, ...)

Arguments

Value

print info on the console

Print availableLaws

Description

Print availableLaws

Usage

## S3 method for class 'availableLaws'
print(x, ...)

Arguments

Value

print info on the console

Print summary.MortalityLaw

Description

Print summary.MortalityLaw

Usage

## S3 method for class 'summary.MortalityLaw'
print(x, ...)

Arguments

Value

Print data on console

Quadratic Model

Description

Quadratic Model

Usage

quadratic(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

quadratic(x = 0:100)

Rogers-Planck Model - 1983

Description

Rogers-Planck Model - 1983

Usage

rogersplanck(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

rogersplanck(x = 0:100)

Print message when saving an object

Description

Print message when saving an object

Usage

saveMsg()

Value

No return value, called for side effects

Save Output in the working directory

Description

Save Output in the working directory

Usage

saveOutput(out, show, prefix)

Arguments

Value

No return value, called for side effects

Scaling method for x vector

Description

Scaling method for x vector

Usage

scale_x(x)

Arguments

Value

scalar

Siler Mortality Law - 1979

Description

Siler Mortality Law - 1979

Usage

siler(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

siler(x = 0:100)

Strehler-Mildvan Model - 1960

Description

Strehler-Mildvan Model - 1960

Usage

strehler_mildvan(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

strehler_mildvan(x = 30:85)

Extracting the last n characters from a string

Description

Extracting the last n characters from a string

Usage

substrRight(x, n)

Arguments

Value

A character vector of length n

Summary MortalityLaw

Description

Summary MortalityLaw

Usage

## S3 method for class 'MortalityLaw'
summary(object, ..., digits = max(3L, getOption("digits") - 3L))

Arguments

Value

A list of model diagnosis

Thiele Mortality Law - 1871

Description

Thiele Mortality Law - 1871

Usage

thiele(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

thiele(x = 0:100)

Educate mx or qx on how to behave above age 100 if it gets in trouble (with NA's, zero's and Inf)

Description

Educate mx or qx on how to behave above age 100 if it gets in trouble (with NA's, zero's and Inf)

Usage

uxAbove100(x, ux, omega = 100, verbose = FALSE)

Arguments

Value

A vector of rates

Van der Maen Model - 1943

Description

Van der Maen Model - 1943

Usage

vandermaen(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

vandermaen(x = 0:100)

Van der Maen 2 Model - 1943

Description

Van der Maen 2 Model - 1943

Usage

vandermaen2(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

vandermaen(x = 0:100)

Weibull Mortality Law - 1939

Description

Note that if sigma > m, then the mode of the density is 0 and hx is a non-increasing function of x, while if sigma < m, then the mode is greater than 0 and hx is an increasing function. m > 0 is a measure of location sigma > 0 is measure of dispersion

Usage

weibull(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

weibull(x = 1:20)

Wittstein Mortality Law - 1883

Description

Wittstein Mortality Law - 1883

Usage

wittstein(x, par = NULL)

Arguments

Value

A list of rates and model parameters

Examples

wittstein(x = 0:100)