dKumIW {RelDists} | R Documentation |
The Kumaraswamy Inverse Weibull distribution
Description
Density, distribution function, quantile function,
random generation and hazard function for the Kumaraswamy Inverse Weibull distribution
with parameters mu
, sigma
and nu
.
Usage
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)
Arguments
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. |
Details
The Kumaraswamy Inverse Weibull Distribution with parameters mu
,
sigma
and nu
has density given by
f(x)= \mu \sigma \nu x^{-\mu - 1} \exp{- \sigma x^{-\mu}} (1 - \exp{- \sigma x^{-\mu}})^{\nu - 1},
for x > 0
, \mu > 0
, \sigma > 0
and \nu > 0
.
Value
dKumIW
gives the density, pKumIW
gives the distribution
function, qKumIW
gives the quantile function, rKumIW
generates random deviates and hKumIW
gives the hazard function.
Author(s)
Johan David Marin Benjumea, johand.marin@udea.edu.co
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.
Shahbaz MQ, Shahbaz S, Butt NS (2012). “The Kumaraswamy-Inverse Weibull Distribution.” Shahbaz, MQ, Shahbaz, S., & Butt, NS (2012). The Kumaraswamy–Inverse Weibull Distribution. Pakistan journal of statistics and operation research, 8(3), 479–489.
Examples
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