CoSMoS (version 2.2.0)

ParetoII: Pareto Type II distribution

Description

Provides density, distribution function, quantile function, random value generation, and raw moments of order r for the Pareto type II distribution.

Usage

dparetoII(x, scale, shape, log = FALSE)
pparetoII(q, scale, shape, lower.tail = TRUE, log.p = FALSE)
qparetoII(p, scale, shape, lower.tail = TRUE, log.p = FALSE)
rparetoII(n, scale, shape)
mparetoII(r, scale, shape)

Value

dparetoII returns a numeric vector of density values. pparetoII returns a numeric vector of cumulative probabilities. qparetoII returns a numeric vector of quantiles. rparetoII returns a numeric vector of random deviates. mparetoII returns the raw moment of order r.

Arguments

x, q

vector of quantiles.

scale, shape

scale and shape parameters; the shape argument cannot be a vector (must have length one).

log, log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

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

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

r

raw moment order.

See Also

fitDist, moments

Examples

## plot the density

ggplot(data.frame(x = c(0, 20)),
       aes(x)) +
  stat_function(fun = dparetoII,
                args = list(scale = 1,
                            shape = .3),
                colour = "royalblue4") +
  labs(x = "",
       y = "Density") +
  theme_classic()