Description Usage Arguments Details Value Author(s) Source References See Also Examples
Density, distribution function, quantile function and random generation
for the KumW distribution with parameters lambda
, phi
,
c
, k
and s
.
1 2 3 4 5 6 7 8 9 10 11 |
x, q |
numeric vector of quantiles. |
beta |
scale parameter β > 0. |
c |
shape parameter c > 0. |
lambda |
shape parameter λ > 0. |
phi |
shape parameter φ ≥ 0. |
log, log.p |
logical; if |
lower.tail |
logical; if |
n |
desired size of the random number sample. |
cens.prop |
proportion of censored data to be simulated. If greater than |
The KumW distribution was described by Cordeiro et al (2010) and has density
f(x) = λφcβ^cx^(x-1)e^(-(βx)^c)(1-e^(-(βx)^c))^(λ-1) (1-(1-e^(-(βx)^c))^λ)^(φ-1)
with scale parameter β, shape parameters λ, φ and c. The parameters λ and phi, come from the Kumaraswamy Generalized family introduced by Cordeiro and Castro (2011).
The KumW is a special case of KumBII introduced by Parna<c3><ad>ba et al (2013).
With phi = 1
KumW becomes the Exponentiated Weibull distribution.
In addition, when lambda = 1
it becomes the Weibull distribution.
When phi = c = 1
then the KumW distribution becomes the exponentiated exponential
distribution .
The above are arguably the most important sub-models to KumW. More su-models are decribed by Cordeiro et al (2010) as well as some expasions for the KumW pdf.
dkumw
gives the density, pkumw
gives the distribution
function, qkumw
gives the quantile function, and rkumw
generates random values.
The length of the result is determined by n
for rkumw
, 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.
CORDEIRO, G. M.; ORTEGA, E. M. M; NADARAJAH, S.. The Kumaraswamy Weibull distribution with application to failure data. Journal of the Franklin Institute, 2010, 347.8: 1399-1429.
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.
LINK TO OTHER PACKAGE DISTRIBUTIONS
1 2 3 4 5 6 7 8 9 | # Equivalency with the Weibull
all.equal(dkumw(5, beta = 0.5, c = 2, lambda = 1, phi = 1),
dweibull(5, shape = 2, scale = 1/0.5))
# Generating values and comparing with the function
x <- rkumw(10000, beta = 1.5, c = 0.5, lambda = 3, phi = 10)
hist(x, probability = T, breaks = 100)
curve(dkumw(x, beta = 1.5, c = 0.5, lambda = 3, phi = 10),
from = 0, to = 2, add = T)
|
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