Lindley distribution

Density, distribution function, quantile function, random generation and hazard function for the Lindley distribution with parameter mu.

Usage

dLIN(x, mu, log = FALSE)

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

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

rLIN(n, mu)

hLIN(x, mu, log = FALSE)

Arguments

x, q

vector of quantiles.

mu

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

dLIN gives the density, pLIN gives the distribution function, qLIN gives the quantile function, rLIN generates random deviates and hLIN gives the hazard function.

Details

Lindley Distribution with parameter mu has density given by

\(f(x) = \frac{\mu^2}{\mu+1} (1+x) \exp(-\mu x),\)

for x > 0 and \(\mu > 0\). These function were taken form LindleyR package.

References

Lindley DV (1958). “Fiducial distributions and Bayes' theorem.” Journal of the Royal Statistical Society. Series B (Methodological), 102–107.

Lindley DV (1965). Introduction to probability and statistics: from a Bayesian viewpoint. 2. Inference. CUP Archive.

Author

Freddy Hernandez, fhernanb@unal.edu.co

Examples

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

## The probability density function
curve(dLIN(x, mu=1.5), from=0.0001, to=10,
      col="red", las=1, ylab="f(x)")


## The cumulative distribution and the Reliability function
par(mfrow=c(1, 2))
curve(pLIN(x, mu=2), from=0.0001, to=10, col="red", las=1, ylab="F(x)")
curve(pLIN(x, mu=2, lower.tail=FALSE), from=0.0001, 
      to=10, col="red", las=1, ylab="R(x)")


## The quantile function
p <- seq(from=0, to=0.99999, length.out=100)
plot(x=qLIN(p, mu=2), y=p, xlab="Quantile", las=1, ylab="Probability")
curve(pLIN(x, mu=2), from=0, add=TRUE, col="red")

## The random function
hist(rLIN(n=10000, mu=2), freq=FALSE, xlab="x", las=1, main="")
curve(dLIN(x, mu=2), from=0.09, to=5, add=TRUE, col="red")


## The Hazard function
curve(hLIN(x, mu=2), from=0.001, to=10, col="red", ylab="Hazard function", las=1)

par(old_par) # restore previous graphical parameters