GenPareto: The Generalized Pareto Distribution
In ebalderama/hurdlr: Zero-Inflated and Hurdle Modelling Using Bayesian Inference

Description Usage Arguments Details Value Author(s) Examples

Density, distribution function, quantile function and random generation for the Generalized Pareto distribution with parameters mu, sigma, and xi.

dgpd(x, mu = 0, sigma = 1, xi = 1, log = F)

mgpd(x, mu = 0, sigma = 1, xi = 1, log = F)

pgpd(q, mu = 0, sigma = 1, xi = 1, lower.tail = T)

qgpd(p, mu = 0, sigma = 1, xi = 1, lower.tail = T)

rgpd(n, mu = 0, sigma = 1, xi = 1)

`x, q`	vector of quantiles.
`mu`	location parameter.
`sigma`	(non-negative) scale parameter.
`xi`	shape parameter.
`log`	logical; if `TRUE`, probabilities p are given as log(p).
`lower.tail`	logical; if `TRUE`, probabilities are P[X ≤ x], otherwise, P[X > x].
`p`	numeric predictor matrix.
`n`	number of random values to return.

The generalized pareto distribution has density

f(x) = sigma^(1/xi) / (sigma + xi*(x-mu))^(1/xi + 1)

dgpd gives the continuous density, pgpd gives the distribution function, qgpd gives the quantile function, and rgpd generates random deviates.

mgpd gives a probability mass function for a discretized version of GPD.

Taylor Trippe <ttrippe@luc.edu>
Earvin Balderama <ebalderama@luc.edu>

dexp(1,rate=.5) #Exp(rate) equivalent to gpd with mu=0 AND xi=0, and sigma=1/rate.
dgpd(1,mu=0,sigma=2,xi=0) #cannot take xi=0.
dgpd(1,mu=0,sigma=2,xi=0.0000001) #but can get close.

##"mass" function of GPD
mgpd(8) == pgpd(8.5) - pgpd(7.5)