agop (version 0.1-3)

rpareto2: 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 $s>0$.

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

x,q

vector of quantiles

p

vector of probabilities

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

Value

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

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

See Also

Other Pareto2: pareto2_estimate_mle, pareto2_estimate_mmse, pareto2_test_f