Representations of the Pearson Type III Distribution

Representations of the Pearson Type III Distribution

Usage

ppearson3(x, location, scale, shape, lower.tail = TRUE)

dpearson3(x, location, scale, shape, log = FALSE)

qpearson3(p, location, scale, shape)

rpearson3(n, location, scale, shape)

Arguments

x

Vector of quantiles.

location

Parameter representing the left-endpoint of the distribution; numeric. Vectors are allowed except for rpearson3().

scale

Scale parameter; positive numeric. Vectors are allowed except for rpearson3().

shape

Shape parameter; positive numeric. Vectors are allowed except for rpearson3().

lower.tail

Logical; if TRUE (default), probabilities are P(X <= x), otherwise, P(X > x).

log

Logical; if TRUE, probabilities are given as log-probabilities.

p

Vector of probabilities.

n

Single positive whole number; number of observations to draw from the distribution.

Value

Vector of evaluated Pearson Type III distribution, with length equal to the recycled lengths of x/p, location, scale, and shape. For rpearson3(), a vector of length n.

Examples

ppearson3(1:10, location = 0, scale = 1, shape = 1)
#>  [1] 0.6321206 0.8646647 0.9502129 0.9816844 0.9932621 0.9975212 0.9990881
#>  [8] 0.9996645 0.9998766 0.9999546
dpearson3(1:10, location = 1:10, scale = 2, shape = 0)
#>  [1] Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
qpearson3(1:9 / 10, location = -2, scale = 10, shape = 2)
#> [1]  3.318116  6.243883  8.973492 11.764213 14.783470 18.223132 22.392165
#> [8] 27.943083 36.897202
set.seed(1)
rpearson3(10, location = 2, scale = 10, shape = 2)
#>  [1] 10.308650 37.707563 36.631704 22.508119 40.854090 27.405402 24.880663
#>  [8] 13.492927  8.810215 10.356237