dEMWEx {RelDists}

The Exponentiated Modifien Weibull Extension distribution

Description

Density, distribution function, quantile function, random generation and hazard function for the Exponentiated Modifien Weibull Extension distribution with parameters mu, sigma, nu and tau.

Usage

dEMWEx(x, mu, sigma, nu, tau, log = FALSE)

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

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

rEMWEx(n, mu, sigma, nu, tau)

hEMWEx(x, mu, sigma, nu, tau)

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.

Details

The Exponentiated Modifien Weibull Extension Distribution with parameters mu, sigma, nu and tau has density given by

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

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

Value

dEMWEx gives the density, pEMWEx gives the distribution function, qEMWEx gives the quantile function, rEMWEx generates random deviates and hEMWEx gives the hazard function.

Author(s)

Johan David Marin Benjumea, [e-mail]

References

Almalki SJ, Nadarajah S (2014). “Modifications of the Weibull distribution: A review.” Reliability Engineering & System Safety, 124, 32–55. doi:10.1016/j.ress.2013.11.010.

Sarhan AM, Apaloo J (2013). “Exponentiated modified Weibull extension distribution.” Reliability Engineering & System Safety, 112, 137–144.

Examples

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

## The probability density function 
curve(dEMWEx(x, mu = 49.046, sigma =3.148, nu=0.00005, tau=0.1), from=0, to=100,
      col = "red", las = 1, ylab = "f(x)")

## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pEMWEx(x, mu = (1/4), sigma =1, nu=1, tau=2), from = 0, to = 1, 
      ylim = c(0, 1), col = "red", las = 1, ylab = "F(x)")
curve(pEMWEx(x, mu = (1/4), sigma =1, nu=1, tau=2, lower.tail = FALSE), 
      from = 0, to = 1, 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 = qEMWEx(p = p, mu = 49.046, sigma =3.148, nu=0.00005, tau=0.1), y = p, 
     xlab = "Quantile", las = 1, ylab = "Probability")
curve(pEMWEx(x, mu = 49.046, sigma =3.148, nu=0.00005, tau=0.1), from = 0, add = TRUE, 
      col = "red")

## The random function
hist(rEMWEx(1000, mu = (1/4), sigma =1, nu=1, tau=2), freq = FALSE, xlab = "x", 
     las = 1, main = "")
curve(dEMWEx(x, mu = (1/4), sigma =1, nu=1, tau=2),  from = 0, add = TRUE, 
      col = "red", ylim = c(0, 0.5))

## The Hazard function(
par(mfrow=c(1,1))
curve(hEMWEx(x, mu = 49.046, sigma =3.148, nu=0.00005, tau=0.1), from = 0, to = 80, 
      col = "red", ylab = "Hazard function", las = 1)

par(old_par) # restore previous graphical parameters