OW: The Odd Weibull Distribution

In ousuga/reldist: Reliability and survival distributions

Description

Density, distribution function, quantile function, random generation and hazard function for the odd weibull distribution with parameters alpha, theta and lambda.

Usage

dOW(x, alpha, theta, lambda, log = FALSE)

pOW(q, alpha, theta, lambda, lower.tail = TRUE, log.p = FALSE)

qOW(p, alpha, theta, lambda, lower.tail = TRUE, log.p = FALSE)

rOW(n, alpha, theta, lambda)

hOW(x, alpha, theta, lambda)

Arguments

x,q	vector of quantiles.
alpha	parameter one.
theta	parameter two.
lambda	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 generalized power weibull with parameters alpha, theta and lambda has density given by

f(x) = alpha*theta*lambda*x^(theta-1)*exp(alpha*(x^theta))*(exp(alpha*(x^theta))-1)^(lambda-1)*(1+(exp(alpha*(x^theta))-1)^lambda)^-2

for x > 0.

Value

dOW gives the density, pOW gives the distribution function, qOW gives the quantile function, rOW generates random deviates and hOW gives the hazard function.

Examples

## The probability density function
curve(dOW(x, alpha = 2, theta = 3, lambda = 0.2), from = 0, to = 4, ylim = c(0, 2), col = "red", las = 1, ylab = "The probability density function")

## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pOW(x, alpha = 2, theta = 3, lambda = 0.2), from = 0, to = 4, ylim = c(0, 1), col = "red", las = 1, ylab = "The cumulative distribution function")
curve(pOW(x, alpha = 2, theta = 3, lambda = 0.2, lower.tail = FALSE), from = 0, to = 4,  ylim = c(0, 1), col = "red", las = 1, ylab = "The Reliability function")

## The quantile function
p <- seq(from = 0, to = 0.998, length.out = 100)
plot(x = qOW(p, alpha = 2, theta = 3, lambda = 0.2), y = p, xlab = "Quantile", las = 1, ylab = "Probability")
curve(pOW(x, alpha = 2, theta = 3, lambda = 0.2), from = 0, add = TRUE, col = "red")

## The random function
hist(rOW(n = 10000, alpha = 2, theta = 3, lambda = 0.2), freq = FALSE, ylim = c(0, 2),xlab = "x", las = 1, main = "")
curve(dOW(x, alpha = 2, theta = 3, lambda = 0.2),  from = 0, ylim = c(0, 2), add = T, col = "red")

## The Hazard function
curve(hOW(x, alpha = 2, theta = 3, lambda = 0.2), from = 0, to = 2.5, ylim = c(0, 3), col = "red", ylab = "The hazard function", las = 1)

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