KumBXII: Kumaraswamy BURR XII 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 KumBXII distribution with parameters lambda, phi, c, k and s.

dkumBXII(x, s, c, k, lambda, phi, log = FALSE)

pkumBXII(q, s, c, k, lambda, phi, lower.tail = TRUE, log.p = FALSE)

qkumBXII(p, s, c, k, lambda, phi, lower.tail = TRUE, log.p = FALSE)

rkumBXII(n, s, c, k, lambda, phi, cens.prop = 0)

`x, q`	numeric vector of quantiles.
`s`	scale parameter s > 0.
`c`	shape parameter c > 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 KumBXII distribution was described by Parna<c3><ad>ba et al (2013) and has density

f(x) = λφcks^(-c)x^(c-1)(1+(x/s)^c)^(-k-1)(1-(1+(x/s)^c)^(-k))^(λ-1)* (1-(1-(1+(x/s)^c)^(-k))^λ)^(φ-1)

with scale parameter s, shape parameters λ, φ, k and c. The parameters λ and phi, come from the Kumaraswamy Generalized family introduced by Cordeiro and Castro (2011).

With lambda = phi = 1 KumBXII becomes the BXII distribution introduced by Zimmer et al (1998). For phi = 1 KumBXII equals the Exponentiated BXII distribution.

When s = 1/m and k = 1 KumBXII becomes the Kumaraswamy Log-Logistic (KumLL) dsitribution. Additionally, with lambda = phi = 1 it reduces to the Log-Logistic distribution to the Exponentiated Weibull distribution.

For lambda = c = 1 and lambda = phi = c = 1, it reduces to the Kumaraswamy Pareto type II and Pareto type II distributions, respectively.

If k tends to infinite, it is identical to the Kumaraswamy Weibull (KwW) distribution. In addition, if lambda = phi = 1, it gives the Weibull distribution.

The KwBXII distribution is not only convenient for modelling comfortable unimodal-shaped failure rates, but it is also suitable for testing goodness-of-fit of some special models such as the KwLL, KwW and Weibull distributions

dkumBXII gives the density, pkumBXII gives the distribution function, qkumBXII gives the quantile function, and rkumBXII generates random values.

The length of the result is determined by n for rkumBXII, 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 <a.neisse@gmail.com>

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

PARANA<c3><8d>BA, P. F.; Ortega, E. M.; Cordeiro, G. M.; Pascoa, M. A. D. The Kumaraswamy Burr XII distribution: theory and practice. Journal of Statistical Computation and Simulation, 2013, 83.11: 2117-2143.

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

ZIMMER, W. J.; KEATS, J. B.; WANG, F. K. The Burr XII distribution in reliability analysis. Journal of quality technology, 1998, 30.4: 386-394.

LINK TO OTHER PACKAGE DISTRIBUTIONS

# Generating values and comparing with the function
x <- rkumBXII(10000, s = 0.5, c = 10, k = 1.5, lambda = 2, phi = 0.2)
hist(x, probability = T, breaks = 100)
curve(dkumBXII(x, s = 0.5, c = 10, k = 1.5, lambda = 2, phi = 0.2),
     from = 0, to = 6, add = T)