KumPar: Kumarasuammy Pareto Distribution

In aneisse/survdistr: Survival Analysis Distributions

Description

Density, distribution function, quantile function and random generation for the KumPar distribution with parameters lambda, phi, beta and k.

Usage

dkumpar(x, beta, k, lambda, phi, log = FALSE)

pkumpar(q, beta, k, lambda, phi, lower.tail = TRUE, log.p = FALSE)

qkumpar(p, beta, k, lambda, phi, lower.tail = TRUE, log.p = FALSE)

hkumpar(q, beta, k, lambda, phi)

rkumpar(n, beta, k, lambda, phi, cens.prop = 0)

Arguments

x, q	numeric vector of quantiles x > β.
beta	scale parameter β > 0.
k	shape parameter \k > 0.
lambda	shape parameter λ > 0.
phi	shape parameter φ ≥ 0.
log, log.p	logical; if TRUE, probabilities/densities p are given as log(p).
lower.tail	logical; if TRUE, probabilities are P[X ≤ x], otherwise, P[X ≥ x]
n	desired size of the random number sample.
cens.prop	proportion of censored data to be simulated. If greater than 0, a matrix will be returned instead of a vector. The matrix will contain the random values and a censorship indicator variable.

Details

The KumLL distribution was described by Pereira et al (2012) and has density

f(x) = (λφkβ^k)/(x^(k+1))(1-(β/x)^k)^(λ-1) (1-(1-(β/x)^k)^λ)^(φ-1)

for x > β and with scale parameter β, shape parameters λ, φ and k.

The parameters λ and phi, come from the Kumaraswamy Generalized family introduced by Cordeiro and Castro (2011).

With phi = 1 KumPar becomes the Exponentiated Pareto distribution. In addition, when lambda = 1 it becomes the Pareto distribution.

Value

dkumpar gives the density, pkumpar gives the distribution function, qkumpar gives the quantile function, and rkumpar generates random values.

The length of the result is determined by n for rkumpar, for the other fucntions the length is the same as the vector passed to the first argument.

Only the first element of the logical arguments are used.

Author(s)

Anderson Neisse <[e-mail]>

Source

The source code of all distributions in this package can also be found on the survdistr Github repository.

References

PEREIRA, M. B.; SILVA, R. B.; ZEA, L. M.; CORDEIRO, G. M. The kumaraswamy Pareto distribution. arXiv preprint arXiv:1204.1389, 2012.

CORDEIRO, G. M.; DE CASTRO, M. A new family of generalized distributions. Journal of statistical computation and simulation, 2011, 81.7: 883-898.

See Also

LINK TO OTHER PACKAGE DISTRIBUTIONS

Examples

# Generating values and comparing with the function
x <- rkumpar(10000, beta = 2, k = 0.5, lambda = 3, phi = 10)
hist(x, probability = T, breaks = 100)
curve(dkumpar(x, beta = 2, k = 0.5, lambda = 3, phi = 10),
      from = 2, to = 80, add = T)

aneisse/survdistr documentation built on May 22, 2019, 2:16 p.m.