### 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`

`pdf =` 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.

`cdf =` 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.

`q =` 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.

`pdf =` 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.

`cdf =` 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.

`q =` 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.