Internal

PSIS.GeneralizedPareto — Type

GeneralizedPareto{T<:Real}

The generalized Pareto distribution.

Constructor

GeneralizedPareto(μ, σ, k)

Construct the generalized Pareto distribution (GPD) with location parameter $μ$, scale parameter $σ$ and shape parameter $k$.

Note

The shape parameter $k$ is equivalent to the commonly used shape parameter $ξ$. This is the same parameterization used by Vehtari et al. [1] and is related to that used by Zhang and Stephens [2] as $k \mapsto -k$.

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PSIS.fit_gpd — Method

fit_gpd(x; μ=0, kwargs...)

Fit a GeneralizedPareto with location μ to the data x.

The fit is performed using the Empirical Bayes method of Zhang and Stephens [2].

Keywords

prior_adjusted::Bool=true, If true, a weakly informative Normal prior centered on $\frac{1}{2}$ is used for the shape $k$.
sorted::Bool=issorted(x): If true, x is assumed to be sorted. If false, a sorted copy of x is made.
min_points::Int=30: The minimum number of quadrature points to use when estimating the posterior mean of $\theta = \frac{\xi}{\sigma}$.

References

[2] Zhang & Stephens, Technometrics 51:3 (2009)

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