KMW: The Kumaraswamy modified Weibull distribution

Description Usage Arguments Details Value Examples

Description

Density, distribution function, quantile function, random generation and hazard function for the kumaraswamy modified weibull distribution with parameters alpha, theta, lambda, a and b.

Usage

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dKMW(x, alpha, theta, lambda, a, b, log = FALSE)

pKMW(q, alpha, theta, lambda, a, b, lower.tail = TRUE, log.p = FALSE)

qKMW(p, alpha, theta, lambda, a, b, lower.tail = TRUE, log.p = FALSE)

rKMW(n, alpha, theta, lambda, a, b)

hKMW(x, alpha, theta, lambda, a, b, log = FALSE)

Arguments

x,q

vector of quantiles.

alpha

parameter one.

lambda

parameter three.

a

parameter four.

b

parameter five.

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.

beta

parameter two.

Details

The kumaraswamy modified weibull with parameters alpha, theta, lambda, a and b has density given by

f(x)=a*b*alpha*x^(theta-1)*(theta+lambda*x)*exp(lambda*x-alpha*x^(theta)*exp(lambda*x))* (1-exp(-alpha*x^theta*exp(lambda*x)))^(a-1)* (1-(1-exp(-aplha*x^theta*exp(lambda*x)))^a)^(b-1)

for x>0.

Value

dKMW gives the density, pKMW gives the distribution function, qKMW gives the quantile function, rKMW generates random deviates and hKMW gives the hazard function.

Examples

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## The probability density function
curve(dKMW(x, alpha = 1, theta = 0.6, lambda = 2, a = 2, b = 1.2), from = 0, to = 3, 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(pKMW(x, alpha = 1, theta = 0.6, lambda = 2, a = 2, b = 1.2), from = 0, to = 3, col = "red", las = 1, ylab = "The cumulative distribution function")
curve(pKMW(x, alpha = 1, theta = 0.6, lambda = 2, a = 2, b = 1.2, lower.tail=FALSE), from = 0, to = 3, col = "red", las = 1, ylab = "The Reliability function")

## The quantile function
p <- seq(from = 0, to = 0.99999, length.out = 100)
plot(x = qKMW(p, alpha = 1, theta = 0.6, lambda = 2, a = 2, b = 1.2), y = p, xlab = "Quantile", las = 1, ylab = "Probability")
curve(pKMW(x, alpha = 1, theta = 0.6, lambda = 2, a = 2, b = 1.2), from = 0, add = TRUE, col = "red")

## The random function
hist(rKMW(n = 1000,alpha = 1, theta = 0.6, lambda = 2, a = 2, b = 1.2), freq = FALSE, ylim = c(0, 2), xlab = "x", las = 1, main = "")
curve(dKMW(x, alpha = 1, theta = 0.6, lambda = 2, a = 2, b = 1.2),  from = 0, to = 3, add = TRUE, col = "red")

## The Hazard function
curve(hKMW(x, alpha = 1, theta = 0.6, lambda = 2, a = 2, b = 1.2), from = 0, to = 1, ylim = c(0, 10), col = "red", ylab = "The Hazard function", las = 1)

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