dWGEE {RelDists}

The Weighted Generalized Exponential-Exponential distribution

Description

Density, distribution function, quantile function, random generation and hazard function for the Weighted Generalized Exponential-Exponential distribution with parameters mu, sigma and nu.

Usage

dWGEE(x, mu, sigma, nu, log = FALSE)

pWGEE(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)

qWGEE(p, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)

rWGEE(n, mu, sigma, nu)

hWGEE(x, mu, sigma, nu)

Arguments

x, q

vector of quantiles.

mu

parameter.

sigma

parameter.

nu

parameter.

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.

Details

The Weighted Generalized Exponential-Exponential Distribution with parameters mu, sigma and nu has density given by

f(x)= \sigma \nu \exp(-\nu x) (1 - \exp(-\nu x))^{\sigma - 1} (1 - \exp(-\mu \nu x)) / 1 - \sigma B(\mu + 1, \sigma),

for x > 0, \mu > 0, \sigma > 0 and \nu > 0.

Value

dWGEE gives the density, pWGEE gives the distribution function, qWGEE gives the quantile function, rWGEE generates random deviates and hWGEE gives the hazard function.

Author(s)

Johan David Marin Benjumea, [e-mail]

References

Mahdavi A (2015). “Two Weighted Distributions Generated by Exponential Distribution.” Journal of Mathematical Extension, 9(1), 1–12.

Mahdavi A (2015). “Two weighted distributions generated by exponential distribution.” Journal of Mathematical Extension, 9, 1–12.

Examples

old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters

## The probability density function 
curve(dWGEE(x, mu = 5, sigma = 0.5, nu = 1), from = 0, to = 6, 
ylim = c(0, 1), col = "red", las = 1, ylab = "The probability density function")

## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pWGEE(x, mu = 5, sigma = 0.5, nu = 1), from = 0, to = 6, 
ylim = c(0, 1), col = "red", las = 1, ylab = "The cumulative distribution function")
curve(pWGEE(x, mu = 5, sigma = 0.5, nu = 1, lower.tail = FALSE), 
from = 0, to = 6, ylim = c(0, 1), col = "red", las = 1, ylab = "The Reliability function")

## The quantile function
p <- seq(from = 0, to = 0.99999, length.out = 100)
plot(x = qWGEE(p = p, mu = 5, sigma = 0.5, nu = 1), y = p, 
xlab = "Quantile", las = 1, ylab = "Probability")
curve(pWGEE(x, mu = 5, sigma = 0.5, nu = 1), from = 0, add = TRUE, 
col = "red")

## The random function
hist(rWGEE(1000, mu = 5, sigma = 0.5, nu = 1), freq = FALSE, xlab = "x", 
ylim = c(0, 1), las = 1, main = "")
curve(dWGEE(x, mu = 5, sigma = 0.5, nu = 1),  from = 0, add = TRUE, 
col = "red", ylim = c(0, 1))

## The Hazard function(
par(mfrow=c(1,1))
curve(hWGEE(x, mu = 5, sigma = 0.5, nu = 1), from = 0, to = 6, 
ylim = c(0, 1.4), col = "red", ylab = "The hazard function", las = 1)

par(old_par) # restore previous graphical parameters