NTLKwIEx

NTLKwIEx provides statistical tools for the New Topp-Leone Kumaraswamy Inverse Exponential (NTLKwIEx) distribution, a flexible five-parameter lifetime distribution. The package lets you:

evaluate the density, the cumulative distribution function and the quantiles;
simulate random samples;
estimate the parameters by maximum likelihood;
plot the theoretical curves and compare a fitted density with your data.

The distribution

With $K(x) = e^{-\theta/x}$ for $x > 0$, the cumulative distribution function is

$$F(x;\theta,\alpha,a,b,m) = \left[,1-\left(1-K(x)^{,a,\alpha^{K(x)}}\right)^{2b}\right]^{m}, \qquad \theta,\ \alpha,\ a,\ b,\ m > 0 .$$

The theory, the properties and applications of the distribution are presented in the articles listed in the References section.

Installation

Install the released version from CRAN:

install.packages("NTLKwIEx")

Or the development version from GitHub:

# install.packages("pak")
# pak::pak("Otodji/NTLKwIEx")
install.packages("NTLKwIEx", repos = c('https://otodji.r-universe.dev', 'https://cloud.r-project.org'))

Functions

Function	Purpose
`P_NTLKwIEx(x, teta, alpha, a, b, m)`	Probability density function
`C_NTLKwIEx(x, teta, alpha, a, b, m)`	Cumulative distribution function
`Q_NTLKwIEx(p, teta, alpha, a, b, m)`	Quantile for a probability `p`
`R_NTLKwIEx(n, teta, alpha, a, b, m)`	Random sample of size `n`
`E_NTLKwIEx(data)`	Maximum likelihood estimation of the five parameters
`Sim_NTLKwIEx(data)`	Histogram of the data with the fitted density overlaid
`Plot_PNTLKwIEx(teta, alpha, a, b, m, min_x, max_x)`	Plot of the density
`Plot_CNTLKwIEx(teta, alpha, a, b, m, min_x, max_x)`	Plot of the cumulative distribution function

The package also ships the dataset ConductorFailureTimes: failure times (in hours) of 59 conductors from an accelerated life test.

Examples

library(NTLKwIEx)

Density, distribution function and quantiles

# Density and cumulative probability at x = 2
P_NTLKwIEx(2, teta = 2, alpha = 0.5, a = 1, b = 1, m = 2)
#> [1] 0.3427294
C_NTLKwIEx(2, teta = 2, alpha = 0.5, a = 1, b = 1, m = 2)
#> [1] 0.5029632

# Median of the distribution
Q_NTLKwIEx(0.5, teta = 2, alpha = 0.5, a = 1, b = 1, m = 2)
#> [1] 1.99138

Random samples

set.seed(123)
R_NTLKwIEx(5, teta = 2, alpha = 0.5, a = 1, b = 1, m = 2)
#> [1] 1.466277 3.349205 1.748319 4.542187 6.319556

Plotting the density

Plot_PNTLKwIEx(teta = 2, alpha = 0.5, a = 1, b = 1, m = 2,
               min_x = 0.1, max_x = 10)

Fitting the distribution to data

E_NTLKwIEx() returns the maximum likelihood estimates in the order teta, alpha, a, b, m.

data(ConductorFailureTimes)

estimates <- E_NTLKwIEx(ConductorFailureTimes)
setNames(estimates, c("teta", "alpha", "a", "b", "m"))
#>         teta        alpha            a            b            m 
#> 2.078874e+01 1.213560e-06 1.108665e+00 1.446496e+00 8.543094e-01

Sim_NTLKwIEx() draws the histogram of the data and overlays the fitted density:

Sim_NTLKwIEx(ConductorFailureTimes)

References

If you use this package, please cite the articles that introduce the distribution:

Atchadé, M. N., Otodji, T., & Djibril, A. (2024). https://doi.org/10.1063/5.0179458
Atchadé, M. N., Otodji, T., Djibril, A., & N’bouké, M. (2023). https://doi.org/10.1515/phys-2023-0151

The citation of the package itself is given by:

citation("NTLKwIEx")

Authors

Mintodê Nicodème Atchadé
Théophile Otodji (maintainer) — ORCID 0009-0003-0389-9007

Bug reports

Please report bugs and suggestions on the issue tracker.

License

GPL-2