Fisher F Distribution Functions

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

Usage

fisher_f_distribution(df1, df2)

fisher_f_pdf(x, df1, df2)

fisher_f_lpdf(x, df1, df2)

fisher_f_cdf(x, df1, df2)

fisher_f_lcdf(x, df1, df2)

fisher_f_quantile(p, df1, df2)

Arguments

df1

degrees of freedom for the numerator (df1 > 0)

df2

degrees of freedom for the denominator (df2 > 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

# Fisher F distribution with df1 = 5, df2 = 10
dist <- fisher_f_distribution(5, 10)
# Apply generic functions
cdf(dist, 0.5)
#> [1] 0.2299751
logcdf(dist, 0.5)
#> [1] -1.469784
pdf(dist, 0.5)
#> [1] 0.687607
logpdf(dist, 0.5)
#> [1] -0.3745378
hazard(dist, 0.5)
#> [1] 0.8929673
chf(dist, 0.5)
#> [1] 0.2613325
mean(dist)
#> [1] 1.25
median(dist)
#> [1] 0.9319332
mode(dist)
#> [1] 0.5
range(dist)
#> [1]  0.000000e+00 1.797693e+308
quantile(dist, 0.2)
#> [1] 0.4563364
standard_deviation(dist)
#> [1] 1.163687
support(dist)
#> [1]  0.000000e+00 1.797693e+308
variance(dist)
#> [1] 1.354167
skewness(dist)
#> [1] 3.86702
kurtosis(dist)
#> [1] 53.86154
kurtosis_excess(dist)
#> [1] 50.86154

# Convenience functions
fisher_f_pdf(1, 5, 10)
#> [1] 0.4954798
fisher_f_lpdf(1, 5, 10)
#> [1] -0.7022287
fisher_f_cdf(1, 5, 10)
#> [1] 0.5348806
fisher_f_lcdf(1, 5, 10)
#> [1] -0.6257118
fisher_f_quantile(0.5, 5, 10)
#> [1] 0.9319332