AdequacyModel (version 1.0.8)

kwbs: Pseudo-Random Numbers - Kumaraswamy Birnbaum-Saunders Distribution

Description

Generates pseudorandom numbers from Kumaraswamy Birnbaum-Saunders Distribution.

Usage

rkwbs(n, alpha, beta, a, b)

Arguments

n

Amount of generated numbers;

alpha

Shape parameter of the Kumaraswamy Birnbaum-Saunders distribution;

beta

Scale parameter Kumaraswamy Birnbaum-Saunders distribution;

a

Shape parameter Kumaraswamy Birnbaum-Saunders distribution;

b

Shape parameter Kumaraswamy Birnbaum-Saunders distribution.

Details

The additional parameters introduced by the Kumaraswamy generalization are sought as a manner to furnish a more flexible distribution. The Kw-BS distribution is expected to have immediate application in reliability and survival studies. The BS distribution arises as the basic exemplar for $a = b = 1$. The exponentiated Birnbaum-Saunders (EBS) distribution corresponds to $b = 1$. The Kw-BS is a particular case of the Mc-BS distribution when $a = c$; see Cordeiro et al. (2011).

$$F(x; \alpha, \beta, a, b) = 1 - {1 - \Phi(\nu)^a}^b$$ where $\beta > 0$ is a scale parameter and the other positive parameters $\alpha$, $a$, and $b$ are shape parameters in that $\nu = \alpha^{-1}\rho(x/\beta)$, $\rho(z) = z^{1/2} - z^{-1/2}$ and $\Phi(\cdotp)$ denotes the standard normal distribution function.

References

Saulo, H.; Leao, J. and Bourguignon, M. The Kumaraswamy Birnbaum-Saunders Distribution. Journal of Statistical Theory and Practice 6, 745-759.

Cordeiro, G. M., and M. Castro. 2011. A new family of generalized distributions. J. Stat. Comput. Simulation, 81(7), 883-898.

Cordeiro, G.M. Lemonte, A.J. and Ortega, E.M.M. (2013). An extended fatigue life distribution. Statistics 47, 626-653.

Examples

a = 2.0
b = 2.5
alpha = 1.0
beta = 1.0
rkwbs(5, alpha, beta, a, b)