Density, distribution function, quantile function,
random generation and hazard function for Sarhan and Zaindins modified weibull distribution
with parameters mu, sigma and nu.
Usage
dSZMW(x, mu, sigma, nu, log = FALSE)
pSZMW(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)
qSZMW(p, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)
rSZMW(n, mu, sigma, nu)
hSZMW(x, mu, sigma, nu)Arguments
- x, q
vector of quantiles.
- mu
scale parameter.
- sigma
shape parameter.
- nu
shape 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.
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.
Details
The Sarhan and Zaindins modified weibull with parameters mu,
sigma and nu has density given by
\(f(x)=(\mu + \sigma \nu x^(\nu - 1)) \exp(- \mu x - \sigma x^\nu)\)
for \(x > 0\), \(\mu > 0\), \(\sigma > 0\) and \(\nu > 0\).
References
Almalki SJ, Nadarajah S (2014). “Modifications of the Weibull distribution: A review.” Reliability Engineering & System Safety, 124, 32--55. doi:10.1016/j.ress.2013.11.010 .
Sarhan AM, Zaindin M (2009). “Modified Weibull distribution.” APPS. Applied Sciences, 11, 123--136.
Author
Johan David Marin Benjumea, johand.marin@udea.edu.co
Examples
old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters
## The probability density function
curve(dSZMW(x, mu = 2, sigma = 1.5, nu = 0.2), from = 0, to = 2,
ylim = c(0, 1.7), col = "red", las = 1, ylab = "f(x)")
## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pSZMW(x, mu = 2, sigma = 1.5, nu = 0.2), from = 0, to = 2, ylim = c(0, 1),
col = "red", las = 1, ylab = "F(x)")
curve(pSZMW(x, mu = 2, sigma = 1.5, nu = 0.2, lower.tail = FALSE), from = 0,
to = 2, 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 = qSZMW(p = p, mu = 2, sigma = 1.5, nu = 0.2), y = p, xlab = "Quantile",
las = 1, ylab = "Probability")
curve(pSZMW(x, mu = 2, sigma = 1.5, nu = 0.2), from = 0, add = TRUE, col = "red")
## The random function
hist(rSZMW(n = 1000, mu = 2, sigma = 1.5, nu = 0.2), freq = FALSE, xlab = "x",
las = 1, main = "")
curve(dSZMW(x, mu = 2, sigma = 1.5, nu = 0.2), from = 0, add = TRUE, col = "red")
## The Hazard function
par(mfrow=c(1,1))
curve(hSZMW(x, mu = 2, sigma = 1.5, nu = 0.2), from = 0, to = 3, ylim = c(0, 8),
col = "red", ylab = "Hazard function", las = 1)
par(old_par) # restore previous graphical parameters