Pareto 2 (Lomax) and Bernoulli-Pareto 2 distributions

Description

Functions implementing the Pareto 2 (Lomax) and Bernoulli-Pareto 2 distributions. In the latter case, zero values occur with probability 1-prob and non-zero values follow the Pareto 2 distribution with scale and shape parameters. dpareto2 and dbpareto2 give the probability density functions (pdf); ppareto2 and pbpareto2 give the cumulative distribution functions (cdf); qpareto2 and qbpareto2 give the quantile functions (inverse cdfs), and rpareto2 and rbpareto2 are used for generating random variates.

Usage

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dpareto2(x, scale, shape)
ppareto2(q, scale, shape)
qpareto2(p, scale, shape)
rpareto2(n, scale, shape)
dbpareto2(x, prob, scale, shape)
pbpareto2(q, prob, scale, shape)
qbpareto2(p, prob, scale, shape)
rbpareto2(n, prob, scale, shape)

Arguments

x, q

vector of quantiles.

p

vector of cumulative probabilities.

n

number of random samples.

prob

probability of a non-zero value.

scale

scale parameter of the pareto2 distribution.

shape

shape parameter of the pareto2 distribution.

Value

dpareto2 and dbpareto2 gives the pdfs; ppareto2 and pbpareto2 gives the cdfs; qpareto2 and qbpareto2 gives the inverse cdfs (or quantile functions); and rpareto2 and rbpareto2 generate random variates.

References

Arnold, B.C., 1983. The Pareto Distributions, International Co-operative Publishing House, Fairland, MD.

Lomax, K.S., 1954. Business failures: another example of the analysis of failure data. Journal of the American Statistical Association, 49(268): 847-852.

See Also

bgamma, bweibull, blnorm

Examples

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  plot(rbpareto2(365, prob = 0.2, scale = 1, shape = 1), type = "h")