dSZMW | R Documentation |
Density, distribution function, quantile function,
random generation and hazard function for Sarhan and Zaindins modified weibull distribution
with parameters mu
, sigma
and nu
.
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)
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. |
The Sarhan and Zaindins modified weibull with parameters mu
,
sigma
and nu
has density given by
f(x)=(μ + σ ν x^(ν - 1)) \exp(- μ x - σ x^ν)
for x > 0, μ > 0, σ > 0 and ν > 0.
dSZMW
gives the density, pSZMW
gives the distribution
function, qSZMW
gives the quantile function, rSZMW
generates random deviates and hSZMW
gives the hazard function.
Johan David Marin Benjumea, johand.marin@udea.edu.co
almalki2014modificationsRelDists
\insertRefsarhan2009modifiedRelDists
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
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