Functions to compute the probability density function, cumulative distribution function, and quantile function for the Holtsmark distribution.
Usage
holtsmark_distribution(location = 0, scale = 1)
holtsmark_pdf(x, location = 0, scale = 1)
holtsmark_lpdf(x, location = 0, scale = 1)
holtsmark_cdf(x, location = 0, scale = 1)
holtsmark_lcdf(x, location = 0, scale = 1)
holtsmark_quantile(p, location = 0, scale = 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
# Holtsmark distribution with location 0 and scale 1
dist <- holtsmark_distribution(0, 1)
# Apply generic functions
cdf(dist, 0.5)
#> [1] 0.6394042
logcdf(dist, 0.5)
#> [1] -0.4472184
pdf(dist, 0.5)
#> [1] 0.2622968
logpdf(dist, 0.5)
#> [1] -1.338278
hazard(dist, 0.5)
#> [1] 0.7273985
chf(dist, 0.5)
#> [1] 1.019998
mean(dist)
#> [1] 0
median(dist)
#> [1] 0
mode(dist)
#> [1] 0
range(dist)
#> [1] -Inf Inf
quantile(dist, 0.2)
#> [1] -1.234616
standard_deviation(dist)
#> [1] Inf
support(dist)
#> [1] -Inf Inf
variance(dist)
#> [1] Inf
# Convenience functions
holtsmark_pdf(3)
#> [1] 0.03150942
holtsmark_lpdf(3)
#> [1] -3.457469
holtsmark_cdf(3)
#> [1] 0.9484022
holtsmark_lcdf(3)
#> [1] -0.05297661
holtsmark_quantile(0.5)
#> [1] 0