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.