Hypergeometric Distribution Functions

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

Usage

hypergeometric_distribution(r, n, N)

hypergeometric_pdf(x, r, n, N)

hypergeometric_lpdf(x, r, n, N)

hypergeometric_cdf(x, r, n, N)

hypergeometric_lcdf(x, r, n, N)

hypergeometric_quantile(p, r, n, N)

Arguments

r

number of successes in the population (r >= 0)

n

number of draws (n >= 0)

N

population size (N >= r)

x

quantile (non-negative integer)

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

# Hypergeometric distribution with r = 5, n = 10, N = 20
dist <- hypergeometric_distribution(5, 10, 20)
# Apply generic functions
cdf(dist, 4)
#> [1] 0.9837461
logcdf(dist, 4)
#> [1] -0.01638741
pdf(dist, 4)
#> [1] 0.1354489
logpdf(dist, 4)
#> [1] -1.999161
hazard(dist, 4)
#> [1] 8.333333
chf(dist, 4)
#> [1] 4.119424
mean(dist)
#> [1] 2.5
median(dist)
#> [1] 3
mode(dist)
#> [1] 3
range(dist)
#> [1] 0 5
quantile(dist, 0.2)
#> [1] 1
standard_deviation(dist)
#> [1] 0.9933993
support(dist)
#> [1] 0 5
variance(dist)
#> [1] 0.9868421
skewness(dist)
#> [1] 0
kurtosis(dist)
#> [1] 5.756863
kurtosis_excess(dist)
#> [1] 2.756863

# Convenience functions
hypergeometric_pdf(3, 5, 10, 20)
#> [1] 0.3482972
hypergeometric_lpdf(3, 5, 10, 20)
#> [1] -1.054699
hypergeometric_cdf(3, 5, 10, 20)
#> [1] 0.8482972
hypergeometric_lcdf(3, 5, 10, 20)
#> [1] -0.1645242
hypergeometric_quantile(0.5, 5, 10, 20)
#> [1] 3