NMW: The Almaki and Yuan's modified Weibull distribution
In ousuga/reldist: Reliability and survival distributions

Description Usage Arguments Details Value Examples

Density, distribution function, quantile function, random generation and hazard function for the Almaki and Yuan's modified weibull distribution with parameters alpha, beta, theta, gamma and lambda.

dNMW(x, alpha, beta, theta, gamma, lambda, log = FALSE)

pNMW(q, alpha, beta, theta, gamma, lambda, lower.tail = TRUE, log.p = FALSE)

qNMW(p, alpha, beta, theta, gamma, lambda, lower.tail = TRUE, log.p = FALSE)

rNMW(n, alpha, beta, theta, gamma, lambda)

hNMW(x, alpha, beta, theta, gamma, lambda, log = FALSE)

`x,q`	vector of quantiles.
`alpha`	parameter one.
`beta`	parameter two.
`theta`	parameter three.
`gamma`	parameter four.
`lambda`	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.

The Almaki and Yuans modified weibull with parameters alpha, beta, theta, gamma and lambda has density given by

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

for x>0.

dNMW gives the density, pNMW gives the distribution function, qNMW gives the quantile function, rNMW generates random deviates and hNMW gives the hazard function.

## The probability density function
curve(dNMW(x, alpha = 1.15, beta = 0.15, theta = 0.75, gamma = 5, lambda = 2), from = 0, to = 1.4, ylim = c(0, 3), col = "red", las = 1, ylab = "The probability density function")

## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pNMW(x, alpha = 1.15, beta = 0.15, theta = 0.75, gamma = 5, lambda = 2), from = 0, to = 1.4, col = "red", las = 1, ylab = "The cumulative distribution function")
curve(pNMW(x, alpha = 1.15, beta = 0.15, theta = 0.75, gamma = 5, lambda = 2, lower.tail = FALSE), from = 0, to = 1.4, col = "red", las = 1, ylab = "The Reliability function")

## The quantile function
p <- seq(from = 0, to = 0.998, length.out = 100)
plot(x=qNMW(p, alpha = 1.15, beta = 0.15, theta = 0.75, gamma = 5, lambda = 2), y = p, xlab = "Quantile", las = 1, ylab = "Probability")
curve(pNMW(x, alpha = 1.15, beta = 0.15, theta = 0.75, gamma = 5, lambda = 2), from = 0, add = TRUE, col = "red")

## The random function
hist(rNMW(n = 1000, alpha = 1.15, beta = 0.15, theta = 0.75, gamma = 5, lambda = 2), freq = FALSE, ylim = c(0, 3), xlab = "x", las = 1, main = "")
curve(dNMW(x, alpha = 1.15, beta = 0.15, theta = 0.75, gamma = 5, lambda = 2),  from = 0, ylim = c(0, 3), add = T, col = "red")

## The Hazard function
curve(hNMW(x, alpha = 1.15, beta = 0.15, theta = 0.75, gamma = 5, lambda = 2), from = 0, to = 1.5, ylim = c(0, 8), col = "red", ylab = "The hazard function", las = 1)