dpareto {vsgoftest}

The Pareto distribution

Description

Density, cumulative distribution function, quantile function and random generation for the Pareto distribution.

Usage

dpareto(x, mu, c, log = FALSE)
ppareto(q, mu, c, lower.tail = TRUE, log.p = FALSE)
qpareto(p, mu, c, lower.tail = TRUE, log.p = FALSE)
rpareto(n, mu, c)

Arguments

x, q

(numeric, vector) a vector of quantiles.

p

(numeric, vector) a vector of probablities.

n

(numeric, vector) sample size to be generated.

mu

(numeric, single value) the shape parameter.

c

(numeric, single value) the scale parameter.

log, log.p

(logical, single value) if TRUE, probabilities are given as \log(p). Default is FALSE.

lower.tail

(logical, single value) if TRUE (default), probabilities are P(X\le x); otherwise P(X>x).

Details

The pareto distribution with shape parameter \mu>0 and scale parameter c>0 has density

f(x) = \mu c^\mu x^{-1-\mu},

for x \ge 0.

Value

dpareto gives the density, ppareto gives the distribution function, qpareto gives the quantile function, and rpareto generates random deviates.

The length of the result is determined by n for rnorm, and is the maximum of the lengths of the numerical arguments for the other functions.

Author(s)

J. Lequesne [e-mail]

References

Arnold, B.C. Pareto distribution, International Cooperative Publishing House, Fairland (1983).

Philbrick, S.W. A practical guide to the single parameter Pareto distribution. Proceedings of the Casualty Actuarial Society LXXII, 44, 44-85 (1985).

Examples

n<- 100
rpareto(n,mu=2,c=1)