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GenPareto

The Generalized Pareto Distribution


Description

Density function, distribution function, quantile function and random generation for the generalized Pareto distribution (GenPareto) with location, scale and shape parameters.

Usage

dGenPareto(x, loc=0, scale=1, shape=0, log = FALSE)
pGenPareto(q, loc=0, scale=1, shape=0, lower.tail = TRUE)
qGenPareto(p, loc=0, scale=1, shape=0, lower.tail = TRUE)
rGenPareto(n, loc=0, scale=1, shape=0)

Arguments

x, q

Vector of quantiles.

p

Vector of probabilities.

n

Number of observations.

loc, scale, shape

Location, scale and shape parameters; the shape argument cannot be a vector (must have length one).

log

Logical; if TRUE, the log density is returned.

lower.tail

Logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]

Details

The generalized Pareto distribution function (Pickands, 1975) with parameters loc = a, scale = b and shape = s is

G(z) = 1 - {1+s(z-a)/b}^(-1/s)

for 1+s(z-a)/b > 0 and z > a, where b > 0. If s = 0 the distribution is defined by continuity.

Value

dGenPareto gives the density function, pGenPareto gives the distribution function, qGenPareto gives the quantile function, and rGenPareto generates random deviates.

Author(s)

Alec Stephenson <alec_stephenson@hotmail.com>

References

Pickands, J. (1975) Statistical inference using Extreme Order statistics. Annals of Statistics, 3, 119–131.

See Also

Examples

dGenPareto(2:4, 1, 0.5, 0.8)
pGenPareto(2:4, 1, 0.5, 0.8)
qGenPareto(seq(0.9, 0.6, -0.1), 2, 0.5, 0.8)
rGenPareto(6, 1, 0.5, 0.8)
p <- (1:9)/10
pGenPareto(qGenPareto(p, 1, 2, 0.8), 1, 2, 0.8)
## [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

DescTools

Tools for Descriptive Statistics

v0.99.41
GPL (>= 2)
Authors
Andri Signorell [aut, cre], Ken Aho [ctb], Andreas Alfons [ctb], Nanina Anderegg [ctb], Tomas Aragon [ctb], Chandima Arachchige [ctb], Antti Arppe [ctb], Adrian Baddeley [ctb], Kamil Barton [ctb], Ben Bolker [ctb], Hans W. Borchers [ctb], Frederico Caeiro [ctb], Stephane Champely [ctb], Daniel Chessel [ctb], Leanne Chhay [ctb], Nicholas Cooper [ctb], Clint Cummins [ctb], Michael Dewey [ctb], Harold C. Doran [ctb], Stephane Dray [ctb], Charles Dupont [ctb], Dirk Eddelbuettel [ctb], Claus Ekstrom [ctb], Martin Elff [ctb], Jeff Enos [ctb], Richard W. Farebrother [ctb], John Fox [ctb], Romain Francois [ctb], Michael Friendly [ctb], Tal Galili [ctb], Matthias Gamer [ctb], Joseph L. Gastwirth [ctb], Vilmantas Gegzna [ctb], Yulia R. Gel [ctb], Sereina Graber [ctb], Juergen Gross [ctb], Gabor Grothendieck [ctb], Frank E. Harrell Jr [ctb], Richard Heiberger [ctb], Michael Hoehle [ctb], Christian W. Hoffmann [ctb], Soeren Hojsgaard [ctb], Torsten Hothorn [ctb], Markus Huerzeler [ctb], Wallace W. Hui [ctb], Pete Hurd [ctb], Rob J. Hyndman [ctb], Christopher Jackson [ctb], Matthias Kohl [ctb], Mikko Korpela [ctb], Max Kuhn [ctb], Detlew Labes [ctb], Friederich Leisch [ctb], Jim Lemon [ctb], Dong Li [ctb], Martin Maechler [ctb], Arni Magnusson [ctb], Ben Mainwaring [ctb], Daniel Malter [ctb], George Marsaglia [ctb], John Marsaglia [ctb], Alina Matei [ctb], David Meyer [ctb], Weiwen Miao [ctb], Giovanni Millo [ctb], Yongyi Min [ctb], David Mitchell [ctb], Franziska Mueller [ctb], Markus Naepflin [ctb], Daniel Navarro [ctb], Henric Nilsson [ctb], Klaus Nordhausen [ctb], Derek Ogle [ctb], Hong Ooi [ctb], Nick Parsons [ctb], Sandrine Pavoine [ctb], Tony Plate [ctb], Luke Prendergast [ctb], Roland Rapold [ctb], William Revelle [ctb], Tyler Rinker [ctb], Brian D. Ripley [ctb], Caroline Rodriguez [ctb], Nathan Russell [ctb], Nick Sabbe [ctb], Ralph Scherer [ctb], Venkatraman E. Seshan [ctb], Michael Smithson [ctb], Greg Snow [ctb], Karline Soetaert [ctb], Werner A. Stahel [ctb], Alec Stephenson [ctb], Mark Stevenson [ctb], Ralf Stubner [ctb], Matthias Templ [ctb], Duncan Temple Lang [ctb], Terry Therneau [ctb], Yves Tille [ctb], Luis Torgo [ctb], Adrian Trapletti [ctb], Joshua Ulrich [ctb], Kevin Ushey [ctb], Jeremy VanDerWal [ctb], Bill Venables [ctb], John Verzani [ctb], Pablo J. Villacorta Iglesias [ctb], Gregory R. Warnes [ctb], Stefan Wellek [ctb], Hadley Wickham [ctb], Rand R. Wilcox [ctb], Peter Wolf [ctb], Daniel Wollschlaeger [ctb], Joseph Wood [ctb], Ying Wu [ctb], Thomas Yee [ctb], Achim Zeileis [ctb]
Initial release
2021-04-09

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