### 26.5 Distributions

Octave has functions for computing the Probability Density Function (PDF), the Cumulative Distribution function (CDF), and the quantile (the inverse of the CDF) for arbitrary user-defined distributions (discrete) and for experimental data (empirical).

The following table summarizes the supported distributions (in alphabetical order).

Distribution | PDF | CDF | Quantile
--- | --- | --- | ---
Univariate Discrete Distribution | `discrete_pdf` | `discrete_cdf` | `discrete_inv`
Empirical Distribution | `empirical_pdf` | `empirical_cdf` | `empirical_inv`

discrete_pdf (x, v, p)

  For each element of x, compute the probability density function (PDF) at x of a univariate discrete distribution which assumes the values in v with probabilities p.

discrete_cdf (x, v, p)

  For each element of x, compute the cumulative distribution function (CDF) at x of a univariate discrete distribution which assumes the values in v with probabilities p.

discrete_inv (x, v, p)

  For each element of x, compute the quantile (the inverse of the CDF) at x of the univariate distribution which assumes the values in v with probabilities p.

empirical_pdf (x, data)

  For each element of x, compute the probability density function (PDF) at x of the empirical distribution obtained from the univariate sample data.

empirical_cdf (x, data)

  For each element of x, compute the cumulative distribution function (CDF) at x of the empirical distribution obtained from the univariate sample data.

empirical_inv (x, data)

  For each element of x, compute the quantile (the inverse of the CDF) at x of the empirical distribution obtained from the univariate sample data.