Kumaraswamy exponential distribution: Compute the Rényi, Havrda and Charvat, and Arimoto entropies of the Kumaraswamy exponential distribution

Description

Compute the Rényi, Havrda and Charvat, and Arimoto entropies of the Kumaraswamy exponential distribution.

Usage

re_kexp(lambda, a, b, delta)
hce_kexp(lambda, a, b, delta)
ae_kexp(lambda, a, b, delta)

Value

The functions re_kexp, hce_kexp, and ae_kexp provide the Rényi entropy, Havrda and Charvat entropy, and Arimoto entropy, respectively, depending on the selected parametric values of the Kumaraswamy exponential distribution and $\delta$.

Arguments

a: The strictly positive shape parameter of the Kumaraswamy distribution ($a > 0$).
b: The strictly positive shape parameter of the Kumaraswamy distribution ($b > 0$).
lambda: The strictly positive parameter of the exponential distribution ($\lambda > 0$).
delta: The strictly positive parameter ($\delta > 0$) and ($\delta \ne 1$).

Author

Muhammad Imran, Christophe Chesneau and Farrukh Jamal

R implementation and documentation: Muhammad Imran <imranshakoor84@yahoo.com>, Christophe Chesneau <christophe.chesneau@unicaen.fr> and Farrukh Jamal farrukh.jamal@iub.edu.pk.

Details

The following is the probability density function of the Kumaraswamy exponential distribution: $$ f(x)=ab\lambda e^{-\lambda x}\left(1-e^{-\lambda x}\right)^{a-1}\left\{ 1-\left(1-e^{-\lambda x}\right)^{a}\right\} ^{b-1}, $$ where $x > 0$, $a > 0$, $b > 0$ and $\lambda > 0$.

References

Cordeiro, G. M., & de Castro, M. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81(7), 883-898.

Examples

Run this code

delta <- c(1.5, 2, 3)
re_kexp(1.2, 1.2, 1.4, delta)
hce_kexp(1.2, 1.2, 1.4, delta)
ae_kexp(1.2, 1.2, 1.4, delta)

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