### Function Reference: `gpstat`

statistics: [m, v] = gpstat (k, sigma, theta)

Compute statistics of the generalized Pareto distribution.

`[m, v] = gpstat (k, sigma, theta)` returns the mean and variance of the generalized Pareto distribution with shape parameter k, scale parameter sigma, and location parameter theta.

The size of m (mean) and v (variance) is the common size of the input arguments. A scalar input functions as a constant matrix of the same size as the other inputs.

When k = 0 and theta = 0, the generalized Pareto distribution is equivalent to the exponential distribution. When `k > 0` and `theta = sigma / k`, the generalized Pareto distribution is equivalent to the Pareto distribution. The mean of the generalized Pareto distribution is not finite when `k >= 1`, and the variance is not finite when `k >= 1/2`. When `k >= 0`, the generalized Pareto distribution has positive density for `x > theta`, or, when `k < 0`, for `0 <= (x - theta) / sigma <= -1 / k`.

Further information about the generalized Pareto distribution can be found at https://en.wikipedia.org/wiki/Generalized_Pareto_distribution

See also: gpcdf, gpinv, gppdf, gprnd, gpfit, gplike

Source Code: gpstat