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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 | 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`.