Cumulative Distribution Function (CDF) of the NTLKwIEx distribution

Description

This function calculates the Cumulative density function (CDF) of the NTLKwIEx distribution.

Usage

C_NTLKwIEx(x, teta, alpha, a, b, m)

Arguments

Details

It takes parameters x, teta, alpha, a, b, and m, and returns the CDF value at x based on these parameters. The formula used for the calculation is provided in the documentation header. The Cumulative Distribution Function (CDF) of the NTLKwIEx distribution is defined as:

F(x;a,b,m,\alpha,\theta) = \left[ 1-\left(1-K(x,\xi)^{a \alpha^{K(x,\xi)}}\right)^{2b} \right]^{m}

where \alpha , a , b, m, \theta > 0.

Value

Value of the CDF for the NTLKwIEx distribution evaluated at x

Dataset: ConductorFailureTimes

Description

This dataset contains failure times measured in hours from an accelerated life test with 59 conductors.

Usage

data(ConductorFailureTimes)

Format

A numeric vector of failure times.

Details

This dataset contains failure times (measured in hours) obtained from an accelerated life test involving 59 conductors. The data are presented as a numeric vector.

References

Nasiri, B., et al. (2010). "Bayesian analysis of the accelerated life model with Type-II censoring." Journal of Statistical Planning and Inference, 140(6), 1565-1572.

Schafft, H. A., et al. (1987). "Reproducibility of the accelerated test for electric cable insulation." IEEE Transactions on Electrical Insulation, 22(5), 739-746.

Estimate parameters with constraints

Description

This function estimates the parameters of the NTLKwIEx distribution while adhering to parameter constraints. It employs the maximum likelihood estimation method and returns estimated values for each parameter based on a given dataset and the specified constraints.

Usage

E_NTLKwIEx(data)

Arguments

Value

Numeric vector of estimated parameters.

Probability Density Function (PDF) of the NTLKwIEx distribution

Description

The Probability Density Function (PDF) of the NTLKwIEx distribution is defined as:

Usage

P_NTLKwIEx(x, teta, alpha, a, b, m)

Arguments

Details

f(x, \theta, \alpha, a, b, m) =2abm\frac{\theta}{x^{2}}\left( -\frac{\theta}{x}log\left( \alpha \right)+ exp\left( \dfrac{\theta}{x}\right)\right)exp\left\lbrace -\frac{\theta}{x}\left(1+a\alpha^{exp\left(-\frac{\theta}{x}\right)}\right)\right\rbrace \left\lbrace 1-exp\left( -a\frac{\theta}{x}\alpha^{exp\left(-\frac{\theta}{x}\right)} \right)\right\rbrace^{2b-1}\left\lbrace 1-\left\lbrace 1-exp\left( -\frac{a\theta}{x} \alpha^{exp\left(-\frac{\theta}{x}\right) }\right)\right\rbrace ^{2b} \right\rbrace^{m-1}

Value

Value of the PDF for the NTLKwIEx distribution evaluated at x

Graphical representation of the Cumulative Distribution Function (CDF) of the NTLKwIEx distribution

Description

This function generates a plot of the Cumulative Distribution Function (CDF) of the NTLKwIEx distribution over a specified range of x values.

Usage

Plot_CNTLKwIEx(teta, alpha, a, b, m, min_x, max_x)

Arguments

Value

A plot of the CDF of the NTLKwIEx distribution

Graphical representation of the probability density function (PDF) of the NTLKwIEx distribution

Description

This function generates a graph of the probability density function (PDF) of the NTLKwIEx distribution over a specified range of x values.

Usage

Plot_PNTLKwIEx(teta, alpha, a, b, m, min_x, max_x)

Arguments

Value

A graph of the PDF of the NTLKwIEx distribution

Quantile Value of the NTLKwIEx distribution

Description

This function calculates the quantile value of the NTLKwIEx distribution for a given probability p.

Usage

Q_NTLKwIEx(p, teta, alpha, a, b, m)

Arguments

Value

The quantile value corresponding to the probability p for the NTLKwIEx distribution

Random Sampling from the NTLKwIEx distribution

Description

This function generates random samples from the NTLKwIEx distribution based on the given parameters.

Usage

R_NTLKwIEx(n, teta, alpha, a, b, m)

Arguments

Value

A vector of n random samples from the NTLKwIEx distribution

Estimate parameters with constraints

Description

This function generates a histogram that depicts the distribution of the provided input data. Additionally, it estimates the parameters of a distribution that would correspond to the given data. By overlaying the estimated density function onto the histogram, Sim_NTLKwIEx enables an immediate comparison between the empirical distribution and the estimated one. Sim_NTLKwIEx proves to be a valuable tool for initial data exploration, streamlining trend identification, and understanding key features. Its usage comes recommended for tasks that require a swift exploratory analysis of data distributions.

Usage

Sim_NTLKwIEx(data)

Arguments

Value

Numeric vector of estimated parameters.

Examples

Sim_NTLKwIEx(c(38.181,	38.542,	38.928,	39.334,35.8))