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]
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)
integer; number of observations
vector of shape parameters, \(k>0\)
vector of scale parameters, \(s>0\)
logical; if TRUE (default),
probabilities are \(P(X \le x)\), and \(P(X > x)\) otherwise
vector of probabilities
vector of quantiles
numeric vector;
dpareto2 gives the density,
ppareto2 gives the cumulative distribution function,
qpareto2 calculates the quantile function,
and rpareto2 generates random deviates.
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 $$f(x)=k s^k/(s+x)^{k+1}.$$
Other distributions: rdpareto2
Other Pareto2: pareto2_estimate_mle,
pareto2_estimate_mmse,
pareto2_test_ad,
pareto2_test_f