SZMW: The Sarhan and Zaindins Modified Weibull Distribution

In ousuga/reldist: Reliability and survival distributions

Description

Density, distribution function, quantile function, random generation and hazard function for Sarhan and Zaindins modified weibull distribution with parameters alpha, beta and gamma.

Usage

dSZMW(x, alpha, beta, gamma, log = FALSE)

pSZMW(q, alpha, beta, gamma, lower.tail = TRUE, log.p = FALSE)

qSZMW(p, alpha, beta, gamma, lower.tail = TRUE, log.p = FALSE)

rSZMW(n, alpha, beta, gamma)

hSZMW(x, alpha, beta, gamma)

Arguments

x,q	vector of quantiles.
alpha	parameter one.
beta	parameter two.
gamma	parameter three.
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 Sarhan and Zaindins modified weibull with parameters alpha, beta and gamma has density given by

f(x)=(alpha+beta*gamma*x^(gamma-1))*exp(-alpha*x-beta*x^gamma)

for x>0.

Value

dSZMW gives the density, pSZMW gives the distribution function, qSZMW gives the quantile function, rSZMW generates random deviates and hSZMW gives the hazard function.

Examples

## The probability density function
curve(dSZMW(x, alpha = 2, beta = 1.5, gamma = 0.2), from = 0, to = 2, ylim = c(0, 1.7), col = "red", las = 1, ylab = "The probability density function")

## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pSZMW(x, alpha = 2, beta = 1.5, gamma = 0.2), from = 0, to = 2, ylim = c(0, 1), col = "red", las = 1, ylab = "The cumulative distribution function")
curve(pSZMW(x, alpha = 2, beta = 1.5, gamma = 0.2, lower.tail = FALSE), from = 0, to = 2, 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 = qSZMW(p = p, alpha = 2, beta = 1.5, gamma = 0.2), y = p, xlab = "Quantile", las = 1, ylab = "Probability")
curve(pSZMW(x, alpha = 2, beta = 1.5, gamma = 0.2), from = 0, add = TRUE, col = "red")

## The random function
hist(rSZMW(n = 1000, alpha = 2, beta = 1.5, gamma = 0.2), freq = FALSE, xlab = "x", las = 1, main = "")
curve(dSZMW(x, alpha = 2, beta = 1.5, gamma = 0.2),  from = 0, add = TRUE, col = "red")

## The Hazard function
curve(hSZMW(x, alpha = 2, beta = 1.5, gamma = 0.2), from = 0, to = 3, ylim = c(0, 8), col = "red", ylab = "The hazard function", las = 1)

ousuga/reldist documentation built on May 24, 2019, 5:54 p.m.