Statistics.Distributions.T

Student’s t distribution.

This distribution is always centered around 0.0 and allows a degrees of freedom parameter.

Summary

cdf(x, df)

The cumulative density function

pdf(x, df)

The probability density function

ppf(x, df)

The percentile-point function

rand(df)

Draw a random number from a t distribution with specified degrees of freedom

Functions

cdf(x, df)

The cumulative density function

NOTE: this currently uses the very slow Simpson’s Rule to execute a numerical integration of the pdf function to approximate the CDF. This leads to a trade-off between precision and speed.

A robust implementation of the 2F1 hypergeometric function is required to properly calculate the CDF of the t distribution.

Examples

iex> Statistics.Distributions.T.cdf(0, 3)
0.4909182507070275
pdf(x, df)

The probability density function

Examples

iex> Statistics.Distributions.T.pdf(0, 3)
0.3675525969478612
iex> Statistics.Distributions.T.pdf(3.2, 1)
0.028319384891796327
ppf(x, df)

The percentile-point function

NOTE: this is very slow due to the current implementation of the CDF

rand(df)

Draw a random number from a t distribution with specified degrees of freedom