Probability-weighted moments estimation of generalised Pareto parameters

Uses the methodology of Hosking and Wallis (1987) to estimate the parameters of the generalised Pareto (GP) distribution.

Usage

gp_pwm(gp_data, u = 0)

Arguments

gp_data

A numeric vector of raw data, assumed to be a random sample from a probability distribution.

u

A numeric scalar. A threshold. The GP distribution is fitted to the excesses of u.

Value

A list with components

• est: A numeric vector. PWM estimates of GP parameters \(\sigma\) (scale) and \(\xi\) (shape).

• se: A numeric vector. Estimated standard errors of \(\sigma\) and \(\xi\).

• cov: A numeric matrix. Estimate covariance matrix of the the PWM estimators of \(\sigma\) and \(\xi\).

References

Hosking, J. R. M. and Wallis, J. R. (1987) Parameter and Quantile Estimation for the Generalized Pareto Distribution. Technometrics, 29(3), 339-349. doi:10.2307/1269343 .

See also

gp for details of the parameterisation of the GP distribution.

Examples

u <- quantile(gom, probs = 0.65)
gp_pwm(gom, u)
#> $est
#>      sigma         xi 
#> 1.77767265 0.08739445 
#> 
#> $se
#>     sigma        xi 
#> 0.2605594 0.1099028 
#> 
#> $cov
#>             sigma          xi
#> sigma  0.06789120 -0.02025464
#> xi    -0.02025464  0.01207863
#>