dKumIW | R Documentation |
Density, distribution function, quantile function,
random generation and hazard function for the Kumaraswamy Inverse Weibull distribution
with parameters mu
, sigma
and nu
.
dKumIW(x, mu, sigma, nu, log = FALSE) pKumIW(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE) qKumIW(p, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE) rKumIW(n, mu, sigma, nu) hKumIW(x, mu, sigma, nu)
x, q |
vector of quantiles. |
mu |
parameter. |
sigma |
parameter. |
nu |
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 Kumaraswamy Inverse Weibull Distribution with parameters mu
,
sigma
and nu
has density given by
f(x)= μ σ ν x^{-μ - 1} \exp{- σ x^{-μ}} (1 - \exp{- σ x^{-μ}})^{ν - 1},
for x > 0, μ > 0, σ > 0 and ν > 0.
dKumIW
gives the density, pKumIW
gives the distribution
function, qKumIW
gives the quantile function, rKumIW
generates random deviates and hKumIW
gives the hazard function.
Johan David Marin Benjumea, johand.marin@udea.edu.co
almalki2014modificationsRelDists
\insertRefshahbaz2012kumaraswamyRelDists
old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters ## The probability density function par(mfrow = c(1, 1)) curve(dKumIW(x, mu = 1.5, sigma= 1.5, nu = 1), from = 0, to = 8.5, col = "red", las = 1, ylab = "f(x)") ## The cumulative distribution and the Reliability function par(mfrow = c(1, 2)) curve(pKumIW(x, mu = 1.5, sigma= 1.5, nu = 1), from = 0, to = 8.5, ylim = c(0, 1), col = "red", las = 1, ylab = "F(x)") curve(pKumIW(x, mu = 1.5, sigma= 1.5, nu = 1, lower.tail = FALSE), from = 0, to = 6, 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 = qKumIW(p=p, mu = 1.5, sigma= 1.5, nu = 10), y = p, xlab = "Quantile", las = 1, ylab = "Probability") curve(pKumIW(x, mu = 1.5, sigma= 1.5, nu = 10), from = 0, add = TRUE, col = "red") ## The random function hist(rKumIW(1000, mu = 1.5, sigma= 1.5, nu = 5), freq = FALSE, xlab = "x", las = 1, ylim = c(0, 1.5), main = "") curve(dKumIW(x, mu = 1.5, sigma= 1.5, nu = 5), from = 0, to =8, add = TRUE, col = "red") ## The Hazard function par(mfrow=c(1,1)) curve(hKumIW(x, mu = 1.5, sigma= 1.5, nu = 1), from = 0, to = 3, ylim = c(0, 0.7), col = "red", ylab = "Hazard function", las = 1) par(old_par) # restore previous graphical parameters
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