| Type: | Package |
| Title: | Probabilistic Hazard Assessment |
| Version: | 0.1.0 |
| Maintainer: | Emrah Altun <emrahaltun123@gmail.com> |
| Description: | Computes the probability density and cumulative distribution functions of fourteen distributions used for the probabilistic hazard assessment. Estimates the model parameters of the distributions using the maximum likelihood and reports the goodness-of-fit statistics. The recurrence interval estimations of earthquakes are computed for each distribution. |
| License: | GPL-3 |
| Imports: | VGAM, invgamma, pracma, rmutil, methods, graphics |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 7.1.2 |
| Depends: | R (≥ 2.10) |
| NeedsCompilation: | no |
| Packaged: | 2023-06-22 11:47:12 UTC; emrah |
| Author: | Emrah Altun [aut, cre, cph], Gamze Ozel [ctb] |
| Repository: | CRAN |
| Date/Publication: | 2023-06-22 19:00:12 UTC |
Cumulative distribution function of the Birnbaum-Saunders-Generalized Pareto distribution
Description
Cumulative distribution function of the Birnbaum-Saunders-Generalized Pareto distribution
Usage
cdfbsgdp(par, x)
Arguments
par |
parameter vector of the Birnbaum-Saunders-Generalized Pareto distribution. First parameter is the shape, second parameter is the scale parameter. Third parameter is the lower bound parameter. |
x |
vector of observations or single value |
Value
return the value of the cdf of the Birnbaum-Saunders-Generalized Pareto distribution
References
Altun, E., Ozel, G. A novel approach to probabilistic hazard assessment: BSGPD model. (Under Review)
Examples
cdfbsgdp(c(0.5,2,0.5),3)
Cumulative distribution function of the exponentiated exponential distribution
Description
Cumulative distribution function of the exponentiated exponential distribution
Usage
cdfeexp(par, x)
Arguments
par |
parameter vector of the exponentiated exponential distribution. First parameter is the shape, second is the scale parameter. |
x |
vector of observations or single value |
Value
return the value of the pdf of the exponentiated exponential distribution
References
Gupta, R. D., & Kundu, D. (1999). Theory & methods: Generalized exponential distributions. Australian & New Zealand Journal of Statistics, 41(2), 173-188.
Examples
cdfeexp(c(0.5,0.3),2)
Cumulative distribution function of the exponentiated Rayleigh distribution
Description
Cumulative distribution function of the exponentiated Rayleigh distribution
Usage
cdfer(par, x)
Arguments
par |
parameter vector of the exponentiated Rayleigh distribution. First parameter is the scale, second is the shape parameter. |
x |
vector of observations or single value |
Value
return the value of the pdf of the exponentiated Rayleigh distribution
References
Vodă, V. G. (1976). Inferential procedures on a generalized Rayleigh variate. I. Aplikace matematiky, 21(6), 395-412.
Examples
cdfer(c(0.5,0.3),2)
Cumulative distribution function of the exponentiated Weibull distribution
Description
Cumulative distribution function of the exponentiated Weibull distribution
Usage
cdfew(par, x)
Arguments
par |
parameter vector of the exponentiated Weibull distribution. First parameter is the shape, second is the scale parameter and third parameter is shape parameter. |
x |
vector of observations or single value |
Value
return the value of the pdf of the exponentiated Weibull distribution
References
Mudholkar, G. S., & Srivastava, D. K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE transactions on reliability, 42(2), 299-302.
Examples
cdfew(c(0.5,0.3,0.6),2)
Cumulative distribution function of the Gamma distribution
Description
Cumulative distribution function of the Gamma distribution
Usage
cdfgamma(par, x)
Arguments
par |
parameter vector of the gamma distribution. First parameter is the shape and second is the scale parameter |
x |
vector of quantiles |
Value
return the value of the cdf of the gamma distribution
References
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
Examples
cdfgamma(c(2,3),5)
Cumulative distribution function of the generalized gamma distribution
Description
Cumulative distribution function of the generalized gamma distribution
Usage
cdfggamma(par, x)
Arguments
par |
parameter vector of the generalized gamma distribution. First parameter is the dispersion, second is the location parameter and third is the family parameter. |
x |
vector of observations or single value |
Value
return the value of the pdf of the generalized gamma distribution
References
Stacy, E. W. (1962). A generalization of the gamma distribution. The Annals of mathematical statistics, 1187-1192.
Examples
pdfggamma(c(2,5,3),3)
Cumulative distribution function of the gumbel distribution
Description
Cumulative distribution function of the gumbel distribution
Usage
cdfgumbel(par, x)
Arguments
par |
parameter vector of the gumbel distribution. First parameter is the location, second is the scale parameter. |
x |
vector of observations or single value |
Value
return the value of the pdf of the gumbel distribution
References
Gumbel, E. J. (1941). The return period of flood flows. The annals of mathematical statistics, 12(2), 163-190.
Examples
pdfgumbel(c(0.5,0.3),2)
Cumulative distribution function of the inverse gamma distribution
Description
Cumulative distribution function of the inverse gamma distribution
Usage
cdfinvgamma(par, x)
Arguments
par |
parameter vector of the inverse gamma distribution. First parameter is the shape, second is the rate parameter. |
x |
vector of observations or single value |
Value
return the value of the pdf of the inverse gamma distribution
References
Cook, J. D. (2008). Inverse gamma distribution. online: http://www. johndcook. com/inverse gamma. pdf, Tech. Rep.
Examples
cdfinvgamma(c(2,5,3),3)
Cumulative distribution function of the inverse Weibull distribution
Description
Cumulative distribution function of the inverse Weibull distribution
Usage
cdfiwweibull(par, x)
Arguments
par |
parameter vector of the inverse Weibull distribution. First parameter is the shape and second is the scale parameter |
x |
vector of quantiles |
Value
return the value of the cdf of the inverse Weibull distribution
References
Mudholkar, G. S., & Kollia, G. D. (1994). Generalized Weibull family: a structural analysis. Communications in statistics-theory and methods, 23(4), 1149-1171.
Examples
cdfiwweibull(c(2,3),5)
Cumulative distribution function of the Levy distribution
Description
Cumulative distribution function of the Levy distribution
Usage
cdflevy(par, x)
Arguments
par |
parameter vector of the Levy distribution. First parameter is the location, second is the scale parameter. |
x |
vector of observations or single value |
Value
return the value of the pdf of the Levy distribution
References
Nolan, J. P. (2003). Modeling financial data with stable distributions. In Handbook of heavy tailed distributions in finance (pp. 105-130). North-Holland.
Examples
cdflevy(c(0.5,0.3),2)
Cumulative distribution function of the log-normal distribution
Description
Cumulative distribution function of the log-normal distribution
Usage
cdflnormal(par, x)
Arguments
par |
parameter vector of the log-normal distribution. First parameter is the shape and second is the scale parameter |
x |
vector of quantiles |
Value
return the value of the cdf of the log-normal distribution
References
Heyde, C. C. (1963). On a property of the lognormal distribution. Journal of the Royal Statistical Society: Series B (Methodological), 25(2), 392-393.
Examples
cdflnormal(c(2,3),5)
Cumulative distribution function of the Pareto distribution
Description
Cumulative distribution function of the Pareto distribution
Usage
cdfpareto(par, x)
Arguments
par |
parameter vector of the Pareto distribution. First parameter is the shape and second is the scale parameter |
x |
vector of quantiles |
Value
return the value of the cdf of the Pareto distribution
References
Arnold, B. C. (1983). Pareto Distributions, International Cooperative Publishing House.
Examples
cdfpareto(c(2,5),2)
Cumulative distribution function of the Rayleigh distribution
Description
Cumulative distribution function of the Rayleigh distribution
Usage
cdfrayleigh(par, x)
Arguments
par |
scale parameter vector of the Rayleigh distribution. |
x |
vector of quantiles |
Value
return the value of the cdf of the Rayleigh distribution
References
Siddiqui, M. M. (1964). Statistical inference for Rayleigh distributions. Journal of Research of the National Bureau of Standards, Sec. D, 68(9), 1005-1010.
Examples
cdfrayleigh(c(2),5)
Cumulative distribution function of the Weibull distribution
Description
Cumulative distribution function of the Weibull distribution
Usage
cdfweibull(par, x)
Arguments
par |
parameter vector of the Weibull distribution. First parameter is the shape and second is the scale parameter |
x |
vector of quantiles |
Value
return the value of the cdf of the weibull distribution
References
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
Examples
cdfweibull(c(2,3),5)
Earthquake dataset
Description
The elapsed time (year) between the earthquakes with 6.5 and 7 magnitudes in Turkey occured between the years of 1990-2021
Usage
data_earthquake_6.5_7
Format
A numeric vector
Earthquake dataset
Description
The elapsed time (year) between the earthquakes with 6 and 6.5 magnitudes in Turkey occured between the years of 1990-2021
Usage
data_earthquake_6_6.5
Format
A numeric vector
Earthquake dataset
Description
The elapsed time (year) between the earthquakes having the magnitudes higher than 7 in Turkey occured between the years of 1990-2021
Usage
data_earthquake_7
Format
A numeric vector
Probabilistic estimation of earthquake recurrence interval using exponentiated exponential distribution
Description
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
Usage
expexpcp(fit, r, te)
Arguments
fit |
Fit is the fitexpexp object. See ?fitexpexp for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
Value
A numeric value
References
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
Examples
fit=fitexpexp(c(1,1),data=data_earthquake_7)
expexpcp(fit,r=2,te=5)
Probabilistic estimation of earthquake recurrence interval using exponentiated Rayleigh distribution
Description
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
Usage
expraycp(fit, r, te)
Arguments
fit |
Fit is the fitexprayleigh object. See ?fitexprayleigh for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
Value
A numeric value
References
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
Examples
fit=fitexprayleigh(c(0.5,0.5),data=data_earthquake_7)
expraycp(fit,r=2,te=5)
Probabilistic estimation of earthquake recurrence interval using exponentiated Weibull distribution
Description
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
Usage
expweicp(fit, r, te)
Arguments
fit |
Fit is the fitexpweibull object. See ?fitexpweibull for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
Value
A numeric value
References
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
Examples
fit=fitexpweibull(c(1,1,1),data=data_earthquake_7)
expweicp(fit,r=2,te=5)
Fitting the Birnbaum-Saunders-Generalized Pareto distribution
Description
Fitting the Birnbaum-Saunders-Generalized Pareto distribution
Usage
fitbsgpd(starts, data)
Arguments
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
Value
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
Examples
library(VGAM)
data=ERPeq::rbsgpd(500,5,0.7,0.2)
fitbsgpd(starts =c(1,1),data=data)
Fitting the exponentiated exponential distribution
Description
Fitting the exponentiated exponential distribution
Usage
fitexpexp(starts, data)
Arguments
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
Value
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
Examples
data=rexpexp(500,2,3)
fitexpexp(starts =c(2,2),data=data)
Fitting the exponentiated exponentiated Rayleigh distribution
Description
Fitting the exponentiated exponentiated Rayleigh distribution
Usage
fitexprayleigh(starts, data)
Arguments
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
Value
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
Examples
data=rexprayleigh(500,2,3)
fitexprayleigh(starts =c(2,2),data=data)
Fitting the exponentiated Weibull distribution
Description
Fitting the exponentiated Weibull distribution
Usage
fitexpweibull(starts, data)
Arguments
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
Value
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
Examples
data=rexpweibull(500,2,3,5)
fitexpweibull(starts =c(2,2,2),data=data)
Fitting the gamma distribution
Description
Fitting the gamma distribution
Usage
fitgamma(starts, data)
Arguments
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
Value
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
Examples
datagamma=rgamma(500,2,2)
fitgamma(starts =c(2,2),data=datagamma)
Fitting the generalized gamma distribution
Description
Fitting the generalized gamma distribution
Usage
fitggamma(starts, data)
Arguments
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
Value
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
Examples
library(rmutil)
data=rggamma(500,2,2,2)
fitggamma(starts =c(1,1,1),data=data)
Fitting the Gumbel distribution
Description
Fitting the Gumbel distribution
Usage
fitgumbel(starts, data)
Arguments
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
Value
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
Examples
library(VGAM)
data=rgumbel(500,2,0.5)
fitgumbel(starts =c(2,2),data=data)
Fitting the inverse gamma distribution
Description
Fitting the inverse gamma distribution
Usage
fitinvgamma(starts, data)
Arguments
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
Value
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
Examples
library(invgamma)
data=rinvgamma(500,2,0.5)
fitinvgamma(starts =c(2,2),data=data)
Fitting the gamma distribution
Description
Fitting the gamma distribution
Usage
fitiweibull(starts, data)
Arguments
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
Value
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
Examples
set.seed(7)
data=rgamma(500,shape=1,scale=1)
fitiweibull(starts =c(0.5,0.5),data=data)
Fitting the Levy distribution
Description
Fitting the Levy distribution
Usage
fitlevy(starts, data)
Arguments
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
Value
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
Examples
library(VGAM)
data=ERPeq::rlevy(100,2,0.1)
fitlevy(starts =c(0.1),data=data)
Fitting the log-normal distribution
Description
Fitting the log-normal distribution
Usage
fitlnormal(starts, data)
Arguments
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
Value
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
Examples
data=rlnorm(500,2,0.5)
fitlnormal(starts =c(2,2),data=data)
Fitting the Pareto distribution
Description
Fitting the Pareto distribution
Usage
fitpareto(starts, data)
Arguments
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
Value
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
Examples
library(VGAM)
data=VGAM::rpareto(500,5,2)
fitpareto(starts =c(2),data=data)
Fitting the Rayleigh distribution
Description
Fitting the Rayleigh distribution
Usage
fitrayleigh(starts, data)
Arguments
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
Value
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
Examples
library(VGAM)
data=rrayleigh(500,2)
fitrayleigh(starts =c(2),data=data)
Fitting the Weibull distribution
Description
Fitting the Weibull distribution
Usage
fitweibull(starts, data)
Arguments
starts |
A vector defining the starting values for the Nelder-Mead algorithm. |
data |
A vector containing the observations |
Value
List the estimated parameters of the distribution with standard errors and goodness-of-fit statistics.
Examples
dataweibull=rweibull(500,2,2)
fitweibull(starts =c(2,2),data=dataweibull)
Probabilistic estimation of earthquake recurrence interval using gamma distribution
Description
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
Usage
gammacp(fit, r, te)
Arguments
fit |
Fit is the fitgamma object. See ?fitgamma for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
Value
A numeric value
References
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
Examples
fit=fitgamma(c(1,1),data=data_earthquake_6_6.5)
gammacp(fit,r=2,te=5)
Probabilistic estimation of earthquake recurrence interval using generalized gamma distribution
Description
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
Usage
ggammacp(fit, r, te)
Arguments
fit |
Fit is the fitggamma object. See ?fitggamma for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
Value
A numeric value
References
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
Examples
fit=fitggamma(c(1,1,1),data=data_earthquake_6_6.5)
ggammacp(fit,r=2,te=5)
Probabilistic estimation of earthquake recurrence interval using Gumbel distribution
Description
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
Usage
gumbelcp(fit, r, te)
Arguments
fit |
Fit is the fitgumbel object. See ?fitgumbel for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
Value
A numeric value
References
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
Examples
fit=fitgumbel(c(1,1),data=data_earthquake_7)
gumbelcp(fit,r=2,te=5)
Probabilistic estimation of earthquake recurrence interval using inverse gamma distribution
Description
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
Usage
invgammacp(fit, r, te)
Arguments
fit |
Fit is the fitinvgamma object. See ?fitinvgamma for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
Value
A numeric value
References
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
Examples
fit=fitinvgamma(c(1,1),data=data_earthquake_7)
invgammacp(fit,r=2,te=5)
Probabilistic estimation of earthquake recurrence interval using inverse Weibull distribution
Description
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
Usage
iweibullcp(fit, r, te)
Arguments
fit |
Fit is the fitiwebull object. See ?fitiwebull for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
Value
A numeric value
References
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
Examples
fit=fitiweibull(c(1,1),data=data_earthquake_6.5_7)
iweibullcp(fit,r=2,te=5)
Probabilistic estimation of earthquake recurrence interval using Levy distribution
Description
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
Usage
levycp(fit, r, te)
Arguments
fit |
Fit is the fitlevy object. See ?fitlevy for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
Value
A numeric value
References
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
Examples
fit=fitlevy(c(1),data=data_earthquake_7)
levycp(fit,r=2,te=5)
Probabilistic estimation of earthquake recurrence interval using log-normal distribution
Description
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
Usage
lnormalcp(fit, r, te)
Arguments
fit |
Fit is the fitlnormal object. See ?fitlnormal for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
Value
A numeric value
References
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
Examples
fit=fitlnormal(c(1,1),data=data_earthquake_6.5_7)
lnormalcp(fit,r=2,te=5)
Probabilistic estimation of earthquake recurrence interval using Pareto distribution
Description
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
Usage
paretocp(fit, r, te)
Arguments
fit |
Fit is the fitpareto object. See ?fitpareto for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
Value
A numeric value
References
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
Examples
library(VGAM)
data=VGAM::rpareto(200,2,5)
fit=fitpareto(c(0.5),data=data)
paretocp(fit,r=2,te=5)
Probability density function of the Birnbaum-Saunders-Generalized Pareto distribution
Description
Probability density function of the Birnbaum-Saunders-Generalized Pareto distribution
Usage
pdfbsgdp(par, x)
Arguments
par |
parameter vector of the Birnbaum-Saunders-Generalized Pareto distribution. First parameter is the shape, second parameter is the scale parameter. Third parameter is the lower bound parameter. |
x |
vector of observations or single value |
Value
return the value of the pdf of the Birnbaum-Saunders-Generalized Pareto distribution.
References
Altun, E., Ozel, G. A novel approach to probabilistic hazard assessment: BSGPD model. (Under Review)
Examples
pdfbsgdp(c(2,0.5,0.5),1)
Probability density function of the exponentiated exponential distribution
Description
Probability density function of the exponentiated exponential distribution
Usage
pdfeexp(par, x)
Arguments
par |
parameter vector of the exponentiated exponential distribution. First parameter is the shape, second is the scale parameter. |
x |
vector of observations or single value |
Value
return the value of the pdf of the exponentiated exponential distribution
References
Gupta, R. D., & Kundu, D. (1999). Theory & methods: Generalized exponential distributions. Australian & New Zealand Journal of Statistics, 41(2), 173-188. Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
Examples
pdfeexp(c(0.5,0.3),2)
Probability density function of the exponentiated Rayleigh distribution
Description
Probability density function of the exponentiated Rayleigh distribution
Usage
pdfer(par, x)
Arguments
par |
parameter vector of the exponentiated Rayleigh distribution. First parameter is the scale, second is the shape parameter. |
x |
vector of observations or single value |
Value
return the value of the pdf of the exponentiated Rayleigh distribution
References
Vodă, V. G. (1976). Inferential procedures on a generalized Rayleigh variate. I. Aplikace matematiky, 21(6), 395-412.
Examples
pdfer(c(0.5,0.3),2)
Probability density function of the exponentiated Weibull distribution
Description
Probability density function of the exponentiated Weibull distribution
Usage
pdfew(par, x)
Arguments
par |
parameter vector of the exponentiated Weibull distribution. First parameter is the shape, second is the scale parameter and third parameter is shape parameter. |
x |
vector of observations or single value |
Value
return the value of the pdf of the exponentiated Weibull distribution
References
Mudholkar, G. S., & Srivastava, D. K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE transactions on reliability, 42(2), 299-302.
Examples
pdfew(c(0.5,0.3,0.6),2)
Probability density function of the Gamma distribution
Description
Probability density function of the Gamma distribution
Usage
pdfgamma(par, x)
Arguments
par |
parameter vector of the gamma distribution. First parameter is the shape and second is the scale parameter |
x |
vector of observations or single value |
Value
return the value of the pdf of the gamma distribution
References
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
Examples
pdfgamma(c(2,3),5)
Probability density function of the generalized gamma distribution
Description
Probability density function of the generalized gamma distribution
Usage
pdfggamma(par, x)
Arguments
par |
parameter vector of the generalized gamma distribution. First parameter is the dispersion, second is the location parameter and third is the family parameter. |
x |
vector of observations or single value |
Value
return the value of the pdf of the generalized gamma distribution
References
Stacy, E. W. (1962). A generalization of the gamma distribution. The Annals of mathematical statistics, 1187-1192.
Examples
pdfggamma(c(2,5,3),3)
Probability density function of the gumbel distribution
Description
Probability density function of the gumbel distribution
Usage
pdfgumbel(par, x)
Arguments
par |
parameter vector of the gumbel distribution. First parameter is the location, second is the scale parameter. |
x |
vector of observations or single value |
Value
return the value of the pdf of the gumbel distribution
References
Gumbel, E. J. (1941). The return period of flood flows. The annals of mathematical statistics, 12(2), 163-190.
Examples
pdfgumbel(c(0.5,0.3),2)
Probability density function of the inverse gamma distribution
Description
Probability density function of the inverse gamma distribution
Usage
pdfinvgamma(par, x)
Arguments
par |
parameter vector of the inverse gamma distribution. First parameter is the shape, second is the rate parameter. |
x |
vector of observations or single value |
Value
return the value of the pdf of the inverse gamma distribution
References
Cook, J. D. (2008). Inverse gamma distribution. online: http://www. johndcook. com/inverse gamma. pdf, Tech. Rep.
Examples
pdfinvgamma(c(2,5,3),3)
Probability density function of the inverse Weibull distribution
Description
Probability density function of the inverse Weibull distribution
Usage
pdfiweibull(par, x)
Arguments
par |
parameter vector of the inverse Weibull distribution. First parameter is the shape and second is the scale parameter |
x |
vector of observations or single value |
Value
return the value of the pdf of the inverse Weibull distribution
References
Mudholkar, G. S., & Kollia, G. D. (1994). Generalized Weibull family: a structural analysis. Communications in statistics-theory and methods, 23(4), 1149-1171.
Examples
pdfiweibull(c(2,3),5)
Probability density function of the Levy distribution
Description
Probability density function of the Levy distribution
Usage
pdflevy(par, x)
Arguments
par |
parameter vector of the Levy distribution. First parameter is the location, second is the scale parameter. |
x |
vector of observations or single value |
Value
return the value of the pdf of the Levy distribution
References
Nolan, J. P. (2003). Modeling financial data with stable distributions. In Handbook of heavy tailed distributions in finance (pp. 105-130). North-Holland.
Examples
pdflevy(c(0.5,0.3),2)
Probability density function of the log-normal distribution
Description
Probability density function of the log-normal distribution
Usage
pdflnormal(par, x)
Arguments
par |
parameter vector of the log-normal distribution. First parameter is the shape and second is the scale parameter |
x |
vector of observations or single value |
Value
return the value of the pdf of the log-normal distribution
References
Heyde, C. C. (1963). On a property of the lognormal distribution. Journal of the Royal Statistical Society: Series B (Methodological), 25(2), 392-393.
Examples
pdflnormal(c(2,3),5)
Probability density function of the Pareto distribution
Description
Probability density function of the Pareto distribution
Usage
pdfpareto(par, x)
Arguments
par |
parameter vector of the Pareto distribution. First parameter is the scale and second is the shape parameter |
x |
vector of observations or single value |
Value
return the value of the pdf of the Pareto distribution
References
Arnold, B. C. (1983). Pareto Distributions, International Cooperative Publishing House.
Examples
pdfpareto(c(2,5),3)
Probability density function of the Rayleigh distribution
Description
Probability density function of the Rayleigh distribution
Usage
pdfrayleigh(par, x)
Arguments
par |
scale parameter vector of the Rayleigh distribution. |
x |
vector of observations or single value |
Value
return the value of the pdf of the Rayleigh distribution
References
Siddiqui, M. M. (1964). Statistical inference for Rayleigh distributions. Journal of Research of the National Bureau of Standards, Sec. D, 68(9), 1005-1010.
Examples
pdfrayleigh(c(2),5)
Probability density function of the Weibull distribution
Description
Probability density function of the Weibull distribution
Usage
pdfweibull(par, x)
Arguments
par |
parameter vector of the weibull distribution. First parameter is the shape and second is the scale parameter |
x |
vector of observations or single value |
Value
return the value of the pdf of the weibull distribution
References
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
Examples
pdfweibull(c(2,3),5)
Probabilistic estimation of earthquake recurrence interval using Rayleigh distribution
Description
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
Usage
rayleighcp(fit, r, te)
Arguments
fit |
Fit is the fitrayleigh object. See ?fitrayleigh for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
Value
A numeric value
References
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
Examples
fit=fitrayleigh(c(1),data=data_earthquake_7)
rayleighcp(fit,r=2,te=5)
Generate random observations from Birnbaum-Saunders-Generalized Pareto distribution
Description
Generate random observations from Birnbaum-Saunders-Generalized Pareto distribution
Usage
rbsgpd(n, beta, alpha, gamma)
Arguments
n |
number of observations to be generated from the Birnbaum-Saunders-Generalized Pareto |
beta |
lower bound parameter of the |
alpha |
scale parameter of the Birnbaum-Saunders-Generalized Pareto distribution |
gamma |
shape parameter of the Birnbaum-Saunders-Generalized Pareto distribution |
Value
return the random sample generated from scale parameter of the Birnbaum-Saunders-Generalized Pareto distribution distribution
References
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
Examples
rbsgpd(100,2,3,5)
Generate random observations from exponentiated exponential distribution
Description
Generate random observations from exponentiated exponential distribution
Usage
rexpexp(n, alpha, lambda)
Arguments
n |
number of observations to be generated |
alpha |
shape parameter of the exponentiated exponential distribution |
lambda |
scale parameter of the exponentiated exponential distribution |
Value
return the random sample generated from exponentiated exponential distribution
References
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
Examples
rexpexp(100,2,3)
Generate random observations from exponentiated Rayleigh distribution
Description
Generate random observations from exponentiated Rayleigh distribution
Usage
rexprayleigh(n, alpha, beta)
Arguments
n |
number of observations to be generated |
alpha |
shape parameter of the exponentiated Rayleigh distribution |
beta |
scale parameter of the exponentiated Rayleigh distribution |
Value
return the random sample generated from exponentiated exponential distribution
References
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
Examples
rexprayleigh(100,2,3)
Generate random observations from exponentiated Weibull distribution
Description
Generate random observations from exponentiated Weibull distribution
Usage
rexpweibull(n, alpha, beta, theta)
Arguments
n |
number of observations to be generated |
alpha |
shape parameter of the exponentiated Weibull distribution |
beta |
scale parameter of the exponentiated Weibull distribution |
theta |
shape parameter of the exponentiated Weibull distribution |
Value
return the random sample generated from exponentiated Weibull distribution
References
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
Examples
rexpweibull(100,2,3,2)
Generate random observations from Levy distribution
Description
Generate random observations from Levy distribution
Usage
rlevy(n, mu, c)
Arguments
n |
number of observations to be generated |
mu |
location parameter of the Levy distribution |
c |
scale parameter of the Levy distribution |
Value
return the random sample generated from Levy distribution
References
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 21. Wiley, New York.
Examples
rlevy(500,2,3)
Probabilistic estimation of earthquake recurrence interval using Weibull distribution
Description
Computes the probability of an earthquake within a specified time "r" and elapsed time "te".
Usage
weibullcp(fit, r, te)
Arguments
fit |
Fit is the fitweibull object. See ?fitweibull for details. |
r |
The specified time in which the probability of an earthquake is desired to be calculated. |
te |
Elapsed time since the last earthquake |
Value
A numeric value
References
Pasari, S. and Dikshit, O. (2014). Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure and Applied Geophysics, 171, 1251-1281.
Examples
fit=fitweibull(c(1,1),data=data_earthquake_6_6.5)
weibullcp(fit,r=2,te=5)