rpareto2 {agop} R Documentation

## Pareto Type-II (Lomax) Distribution

### Description

Density, cumulative distribution function, quantile function, and random generation for the Pareto Type-II (Lomax) distribution with shape parameter k>0 and scale parameter s>0.

[TO DO: rewrite in C, add NA handling]

### Usage

rpareto2(n, k = 1, s = 1)

ppareto2(q, k = 1, s = 1, lower.tail = TRUE)

qpareto2(p, k = 1, s = 1, lower.tail = TRUE)

dpareto2(x, k = 1, s = 1)


### Arguments

 n integer; number of observations k vector of shape parameters, k>0 s vector of scale parameters, s>0 lower.tail logical; if TRUE (default), probabilities are P(X \le x), and P(X > x) otherwise p vector of probabilities x, q vector of quantiles

### Details

If X\sim\mathrm{P2}(k,s), then \mathrm{supp}\,X=[0,\infty). The c.d.f. for x\ge 0 is given by

F(x)=1-s^k/(s+x)^k

and the density by

f(x)=k s^k/(s+x)^{k+1}.

### Value

numeric vector; dpareto2 gives the density, ppareto2 gives the cumulative distribution function, qpareto2 calculates the quantile function, and rpareto2 generates random deviates.

Other distributions: rdpareto2()
Other Pareto2: pareto2_estimate_mle(), pareto2_estimate_mmse(), pareto2_test_ad(), pareto2_test_f()