Kolmogorov-Smirnov Distribution Functions

Functions to compute the probability density function, cumulative distribution function, and quantile function for the Kolmogorov-Smirnov distribution.

Usage

kolmogorov_smirnov_distribution(n)

kolmogorov_smirnov_pdf(x, n)

kolmogorov_smirnov_lpdf(x, n)

kolmogorov_smirnov_cdf(x, n)

kolmogorov_smirnov_lcdf(x, n)

kolmogorov_smirnov_quantile(p, n)

Arguments

n

sample size (n > 0)

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

# Kolmogorov-Smirnov distribution with sample size n = 10
dist <- kolmogorov_smirnov_distribution(10)
# Apply generic functions
cdf(dist, 2)
#> [1] 1
logcdf(dist, 2)
#> [1] 0
pdf(dist, 2)
#> [1] 2.887762e-33
logpdf(dist, 2)
#> [1] -74.92483
hazard(dist, 2)
#> [1] 80
chf(dist, 2)
#> [1] 79.30685
mean(dist)
#> [1] 0.2747169
median(dist)
#> [1] 0.2617017
mode(dist)
#> [1] 0.2325754
range(dist)
#> [1]  0.000000e+00 1.797693e+308
quantile(dist, 0.2)
#> [1] 0.2039076
standard_deviation(dist)
#> [1] 0.08232448
support(dist)
#> [1]  0.000000e+00 1.797693e+308
variance(dist)
#> [1] 0.00677732
skewness(dist)
#> [1] 0.8604261
kurtosis(dist)
#> [1] 3.881619
kurtosis_excess(dist)
#> [1] 0.881619

# Convenience functions
kolmogorov_smirnov_pdf(0.5, 10)
#> [1] 0.2695176
kolmogorov_smirnov_lpdf(0.5, 10)
#> [1] -1.311122
kolmogorov_smirnov_cdf(0.5, 10)
#> [1] 0.9865241
kolmogorov_smirnov_lcdf(0.5, 10)
#> [1] -0.01356751
kolmogorov_smirnov_quantile(0.5, 10)
#> [1] 0.2617017