RelDists (version 1.0.0)

dBGE: The Beta Generalized Exponentiated distribution

Description

Density, distribution function, quantile function, random generation and hazard function for the Beta Generalized Exponentiated distribution with parameters mu, sigma, nu and tau.

Usage

dBGE(x, mu, sigma, nu, tau, log = FALSE)
pBGE(q, mu, sigma, nu, tau, lower.tail = TRUE, log.p = FALSE)
qBGE(p, mu, sigma, nu, tau, lower.tail = TRUE, log.p = FALSE)
rBGE(n, mu, sigma, nu, tau)
hBGE(x, mu, sigma, nu, tau)

Value

dBGE gives the density, pBGE gives the distribution function, qBGE gives the quantile function, rBGE

generates random deviates and hBGE gives the hazard function.

Arguments

x, q

vector of quantiles.

mu

parameter.

sigma

parameter.

nu

parameter.

tau

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.

Author

Johan David Marin Benjumea,

Details

The Beta Generalized Exponentiated Distribution with parameters mu, sigma, nu and tau has density given by

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

for \(x > 0\), \(\mu > 0\), \(\sigma > 0\), \(\nu > 0\) and \(\tau > 0\).

References

almalki2014modificationsRelDists

barreto2010betaRelDists

Examples

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

## The probability density function 
curve(dBGE(x, mu = 1.5, sigma =1.7, nu=1, tau=1), from = 0, to = 3, 
      col = "red", las = 1, ylab = "f(x)")

## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pBGE(x, mu = 1.5, sigma =1.7, nu=1, tau=1), from = 0, to = 6, 
      ylim = c(0, 1), col = "red", las = 1, ylab = "F(x)")
curve(pBGE(x, mu = 1.5, sigma =1.7, nu=1, tau=1, lower.tail = FALSE), 
      from = 0, to = 6, ylim = c(0, 1), col = "red", las = 1, ylab = "R(x)")

## The quantile function
p <- seq(from = 0, to = 0.99999, length.out = 100)
plot(x = qBGE(p = p, mu = 1.5, sigma =1.7, nu=1, tau=1), y = p, 
     xlab = "Quantile", las = 1, ylab = "Probability")
curve(pBGE(x, mu = (1/4), sigma =1, nu=1, tau=2), from = 0, add = TRUE, 
      col = "red")

## The random function
hist(rBGE(1000, mu = 1.5, sigma =1.7, nu=1, tau=1), freq = FALSE, xlab = "x", 
     ylim = c(0, 1), las = 1, main = "")
curve(dBGE(x, mu = 1.5, sigma =1.7, nu=1, tau=1),  from = 0, add = TRUE, 
      col = "red", ylim = c(0, 0.5))

## The Hazard function(
par(mfrow=c(1,1))
curve(hBGE(x, mu = 0.9, sigma =0.5, nu=1, tau=1), from = 0, to = 2, 
      col = "red", ylab = "Hazard function", las = 1)

par(old_par) # restore previous graphical parameters