nlogL = gplike (params, x) returns the negative log-likelihood of the data in x corresponding to the generalized Pareto distribution with (1) shape parameter k and (2) scale parameter sigma given in the two-element vector params.

gplike does not accept a location parameter theta and assumes it to be zero. If the location is known to be nonzero, subtract it from x before calling gplike.

[nlogL, acov] = gplike (params, x) returns the inverse of Fisher’s information matrix, acov, a 2-by-2 matrix. If the input parameter values in params are the maximum likelihood estimates, the diagonal elements of acov are their asymptotic variances. acov is based on the observed Fisher’s information, not the expected information.

[…] = gplike (params, x, freq) accepts a frequency vector, freq, of the same size as x. freq typically contains integer frequencies for the corresponding elements in x, but it can contain any non-integer non-negative values. By default, or if left empty, freq = ones (size (x)). This third argument is an Octave extension; MATLAB’s gplike takes two inputs.

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

Source Code: gplike