dIW: The Inverse Weibull distribution

In ousuga/RelDists: Estimation for some Reliability Distributions

The Inverse Weibull distribution

Description

Density, distribution function, quantile function, random generation and hazard function for the inverse weibull distribution with parameters mu and sigma.

Usage

dIW(x, mu, sigma, log = FALSE)

pIW(q, mu, sigma, lower.tail = TRUE, log.p = FALSE)

qIW(p, mu, sigma, lower.tail = TRUE, log.p = FALSE)

rIW(n, mu, sigma)

hIW(x, mu, sigma)

Arguments

x, q	vector of quantiles.
mu	scale parameter.
sigma	shape parameters.
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 inverse weibull distribution with parameters mu and sigma has density given by

f(x) = μ σ x^{-σ-1} \exp(μ x^{-σ})

for x > 0, μ > 0 and σ > 0

Value

dIW gives the density, pIW gives the distribution function, qIW gives the quantile function, rIW generates random deviates and hIW gives the hazard function.

Author(s)

Johan David Marin Benjumea, [e-mail]

References

\insertRef

almalki2014modificationsRelDists

\insertRef

drapella1993complementaryRelDists

Examples

old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters

## The probability density function
curve(dIW(x, mu=5, sigma=2.5), from=0, to=10,
      ylim=c(0, 0.55), col="red", las=1, ylab="f(x)")
#'
## The cumulative distribution and the Reliability function
par(mfrow=c(1, 2))
curve(pIW(x, mu=5, sigma=2.5),
      from=0, to=10,  col="red", las=1, ylab="F(x)")
curve(pIW(x, mu=5, sigma=2.5, lower.tail=FALSE),
      from=0, to=10, col="red", las=1, ylab="R(x)")
            
## The quantile function
p <- seq(from=0, to=0.99999, length.out=100)
plot(x=qIW(p, mu=5, sigma=2.5), y=p, xlab="Quantile",
  las=1, ylab="Probability")
curve(pIW(x, mu=5, sigma=2.5), from=0, add=TRUE, col="red")
  
## The random function
hist(rIW(n=10000, mu=5, sigma=2.5), freq=FALSE, xlim=c(0,60),
  xlab="x", las=1, main="")
curve(dIW(x, mu=5, sigma=2.5), from=0, add=TRUE, col="red")

## The Hazard function
par(mfrow=c(1,1))
curve(hIW(x, mu=5, sigma=2.5), from=0, to=15, ylim=c(0, 0.9),
   col="red", ylab="Hazard function", las=1)

par(old_par) # restore previous graphical parameters

ousuga/RelDists documentation built on Jan. 12, 2023, 10:27 p.m.