FisherF: Create an F distribution

In alexpghayes/distributions: Probability Distributions as S3 Objects

Description

Create an F distribution

Usage

FisherF(df1, df2, lambda = 0)

Arguments

df1	Numerator degrees of freedom. Can be any positive number.
df2	Denominator degrees of freedom. Can be any positive number.
lambda	Non-centrality parameter. Can be any positive number. Defaults to 0.

Details

We recommend reading this documentation on https://alexpghayes.github.io/distributions, where the math will render with additional detail.

In the following, let X be a Gamma random variable with parameters shape = α and rate = β.

Support: x \in (0, ∞)

Mean: \frac{α}{β}

Variance: \frac{α}{β^2}

Probability density function (p.m.f):

f(x) = \frac{β^{α}}{Γ(α)} x^{α - 1} e^{-β x}

Cumulative distribution function (c.d.f):

f(x) = \frac{Γ(α, β x)}{Γ{α}}

Moment generating function (m.g.f):

E(e^(tX)) = \Big(\frac{β}{ β - t}\Big)^{α}, \thinspace t < β

Value

A FisherF object.

Examples

set.seed(27)

X <- FisherF(5, 10, 0.2)
X

random(X, 10)

pdf(X, 2)
log_pdf(X, 2)

cdf(X, 4)
quantile(X, 0.7)

cdf(X, quantile(X, 0.7))
quantile(X, cdf(X, 7))

alexpghayes/distributions documentation built on April 8, 2021, 5:55 a.m.