degp3 function

Density, cumulative density, quantiles and random number generation for the extended generalized Pareto distribution 3

Density, cumulative density, quantiles and random number generation for the EGP3 distribution of Papastathopoulos and Tawn

degp3(x, kappa = 1, sigma, xi, u = 0, log.d = FALSE)

pegp3(q, kappa = 1, sigma, xi, u = 0, lower.tail = TRUE, log.p = FALSE)

qegp3(p, kappa = 1, sigma, xi, u = 0, lower.tail = TRUE, log.p = FALSE)

regp3(n, kappa = 1, sigma, xi, u = 0)

Arguments

• x, q, p: Value, quantile or probability respectively.
• kappa: The power parameter (Papastathopoulos and Tawn call it the shape parameter and call what we call the shape parameter the tail index.)
• sigma: Scale parameter.
• xi: Shape parameter.
• u: Threshold
• log.d, log.p: Whether or not to work on the log scale.
• lower.tail: Whether to return the lower tail.
• n: Number of random numbers to simulate.

Examples

x <- regp3(1000, kappa=2, sigma=1, xi=.5)
  hist(x)
  x <- regp3(1000, kappa=2, sigma=exp(rnorm(1000, 1, .25)), xi=rnorm(1000, .5, .2))
  hist(x)
  plot(pegp3(x, kappa=2, sigma=1, xi=.5))

References

I. Papastathopoulos and J. A. Tawn, Extended generalized Pareto modles for tail estimation, Journal of Statistical Planning and Inference, 143, 131 -- 143, 2013

Author(s)

Harry Southworth