Extreme Value Distribution Functions

Functions to compute the probability density function, cumulative distribution function, and quantile function for the Extreme Value distribution.

Usage

extreme_value_distribution(location = 0, scale = 1)

extreme_value_pdf(x, location = 0, scale = 1)

extreme_value_lpdf(x, location = 0, scale = 1)

extreme_value_cdf(x, location = 0, scale = 1)

extreme_value_lcdf(x, location = 0, scale = 1)

extreme_value_quantile(p, location = 0, scale = 1)

Arguments

location

location parameter (default is 0)

scale

scale parameter (default is 1)

x

quantile

p

probability (0 <= p <= 1)

Value

A single numeric value with the computed probability density, log-probability density, cumulative distribution, log-cumulative distribution, or quantile depending on the function called.

See also

Boost Documentation for more details on the mathematical background.

Examples

# Extreme Value distribution with location = 0, scale = 1
dist <- extreme_value_distribution(0, 1)
# Apply generic functions
cdf(dist, 0.5)
#> [1] 0.5452392
logcdf(dist, 0.5)
#> [1] -0.6065307
pdf(dist, 0.5)
#> [1] 0.3307043
logpdf(dist, 0.5)
#> [1] -1.106531
hazard(dist, 0.5)
#> [1] 0.727205
chf(dist, 0.5)
#> [1] 0.7879837
mean(dist)
#> [1] 0.5772157
median(dist)
#> [1] 0.3665129
mode(dist)
#> [1] 0
range(dist)
#> [1] -Inf  Inf
quantile(dist, 0.2)
#> [1] -0.475885
standard_deviation(dist)
#> [1] 1.28255
support(dist)
#> [1] -1.797693e+308  1.797693e+308
variance(dist)
#> [1] 1.644934
skewness(dist)
#> [1] 1.139547
kurtosis(dist)
#> [1] 5.4
kurtosis_excess(dist)
#> [1] 2.4

# Convenience functions
extreme_value_pdf(0)
#> [1] 0.3678794
extreme_value_lpdf(0)
#> [1] -1
extreme_value_cdf(0)
#> [1] 0.3678794
extreme_value_lcdf(0)
#> [1] -1
extreme_value_quantile(0.5)
#> [1] 0.3665129