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

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Description

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

Usage

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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)

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.

Author(s)

Harry Southworth

References

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

Examples

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  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))

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