KumPar: Kumarasuammy Pareto Distribution
In aneisse/survdistr: Survival Analysis Distributions

Description Usage Arguments Details Value Author(s) Source References See Also Examples

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

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)

`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.

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.

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.

Anderson Neisse <[email protected]>

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

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.

LINK TO OTHER PACKAGE DISTRIBUTIONS

# 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)