dEMWEx function

The Exponentiated Modifien Weibull Extension distribution

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

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.

Returns

dEMWEx gives the density, pEMWEx gives the distribution function, qEMWEx gives the quantile function, rEMWEx

generates random deviates and hEMWEx gives the hazard function.

Details

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

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

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

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

References

Rdpack::insert_ref(key="almalki2014modifications",package="RelDists")

Rdpack::insert_ref(key="sarhan2013exponentiated",package="RelDists")

Author(s)

Johan David Marin Benjumea, johand.marin@udea.edu.co