Functions to compute the probability density function, cumulative distribution function, and quantile function for the arcsine distribution.
Usage
arcsine_distribution(x_min = 0, x_max = 1)
arcsine_pdf(x, x_min = 0, x_max = 1)
arcsine_lpdf(x, x_min = 0, x_max = 1)
arcsine_cdf(x, x_min = 0, x_max = 1)
arcsine_lcdf(x, x_min = 0, x_max = 1)
arcsine_quantile(p, x_min = 0, x_max = 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
# Arcsine distribution with default parameters
dist <- arcsine_distribution()
# Apply generic functions
cdf(dist, 0.5)
#> [1] 0.5
logcdf(dist, 0.5)
#> [1] -0.6931472
pdf(dist, 0.5)
#> [1] 0.6366198
logpdf(dist, 0.5)
#> [1] -0.4515827
hazard(dist, 0.5)
#> [1] 1.27324
chf(dist, 0.5)
#> [1] 0.6931472
mean(dist)
#> [1] 0.5
median(dist)
#> [1] 0.5
range(dist)
#> [1] 0 1
quantile(dist, 0.2)
#> [1] 0.0954915
standard_deviation(dist)
#> [1] 0.3535534
support(dist)
#> [1] 0 1
variance(dist)
#> [1] 0.125
skewness(dist)
#> [1] 0
kurtosis(dist)
#> [1] 1.5
kurtosis_excess(dist)
#> [1] -1.5
# Convenience functions
arcsine_pdf(0.5)
#> [1] 0.6366198
arcsine_lpdf(0.5)
#> [1] -0.4515827
arcsine_cdf(0.5)
#> [1] 0.5
arcsine_lcdf(0.5)
#> [1] -0.6931472
arcsine_quantile(0.5)
#> [1] 0.5