Kw-CWG: Kumaraswamy Complementary Weibull Geometric Probability...

In elfDistr: Kumaraswamy Complementary Weibull Geometric (Kw-CWG) Probability Distribution

Description

Density, distribution function, quantile function and random generation for the Kumaraswamy Complementary Weibull Geometric (Kw-CWG) probability distribution.

Usage

dkwcwg(x, alpha, beta, gamma, a, b, log = FALSE)

pkwcwg(q, alpha, beta, gamma, a, b, lower.tail = TRUE, log.p = FALSE)

qkwcwg(p, alpha, beta, gamma, a, b, lower.tail = TRUE, log.p = FALSE)

rkwcwg(n, alpha, beta, gamma, a, b)

Arguments

x, q	vector of quantiles.
alpha, beta, gamma, a, b	Parameters of the distribution. 0 < alpha < 1, and the other parameters mustb e positive.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X ≤ x] otherwise, P[X > x].
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

Probability density function

f(x) = α^a β γ a b (γ x)^{β - 1} \exp[-(γ x)^β] \cdot \frac{\{1 - \exp[-(γ x)^β]\}^{a-1}}{\{ α + (1 - α) \exp[-(γ x)^β] \}^{a+1}} \cdot

\cdot \bigg\{ 1 - \frac{α^a[1 - \exp[-(γ x)^β]]^a}{\{ α + (1 - α) \exp[-(γ x)^β] \}^a} \bigg\}

Cumulative density function

F(x) = 1 - \bigg\{ 1 - \bigg[ \frac{α (1 - \exp[-(γ x)^β]) }{ α + (1 - α) \exp[-(γ x)^β] } \bigg]^a \bigg\}^b

Quantile function

Q(u) = γ^{-1} \bigg\{ \log\bigg[\frac{ α + (1 - α) √[a]{1 - √[b]{1 - u} } }{ α (1 - √[a]{1 - √[b]{1 - u} } ) }\bigg] \bigg\}^{1/β}, 0 < u < 1

References

Afify, A.Z., Cordeiro, G.M., Butt, N.S., Ortega, E.M. and Suzuki, A.K. (2017). A new lifetime model with variable shapes for the hazard rate. Brazilian Journal of Probability and Statistics

elfDistr documentation built on Oct. 8, 2019, 1:05 a.m.