Newdistns (version 2.1)

kumg: Kumaraswamy G Distribution

Description

Computes the pdf, cdf, quantile and random numbers of the Kumaraswamy G distribution due to Cordeiro and Castro (2011) specified by the pdf $$f (x) = a b g (x) G^{a - 1} (x) \left[ 1 - G^a (x) \right]^{b - 1}$$ for $G$ any valid cdf, $g$ the corresponding pdf, $a > 0$, the first shape parameter, and $b > 0$, the second shape parameter. Also computes the Cramer-von Misses statistic, Anderson Darling statistic, Kolmogorov Smirnov test statistic and p-value, maximum likelihood estimates, Akaike Information Criterion, Consistent Akaikes Information Criterion, Bayesian Information Criterion, Hannan-Quinn information criterion, standard errors of the maximum likelihood estimates, minimum value of the negative log-likelihood function and convergence status when the distribution is fitted to some data

Usage

dkumg(x, spec, a = 1, b = 1, log = FALSE, ...)
pkumg(x, spec, a = 1, b = 1, log.p = FALSE, lower.tail = TRUE, ...)
qkumg(p, spec, a = 1, b = 1, log.p = FALSE, lower.tail = TRUE, ...)
rkumg(n, spec, a = 1, b = 1, ...)
mkumg(g, data, starts, method = "BFGS")

Arguments

x

scaler or vector of values at which the pdf or cdf needs to be computed

p

scaler or vector of probabilities at which the quantile needs to be computed

n

number of random numbers to be generated

a

the value of the first shape parameter, must be positive, the default is 1

b

the value of the second shape parameter, must be positive, the default is 1

spec

a character string specifying the distribution of G and g (for example, "norm" if G and g correspond to the standard normal).

log

if TRUE then log(pdf) are returned

log.p

if TRUE then log(cdf) are returned and quantiles are computed for exp(p)

lower.tail

if FALSE then 1-cdf are returned and quantiles are computed for 1-p

...

other parameters

g

same as spec but must be one of chisquare ("chisq"), exponential ("exp"), F ("f"), gamma ("gamma"), lognormal ("lognormal"), Weibull ("weibull"), Burr XII ("burrxii"), Chen ("chen"), Frechet ("frechet"), Gompertz ("gompertz"), linear failure rate ("lfr"),

data

a vector of data values for which the distribution is to be fitted

starts

initial values of (a, b, r) if g has one parameter or initial values of (a, b, r, s) if g has two parameters

method

the method for optimizing the log likelihood function. It can be one of "Nelder-Mead", "BFGS", "CG", "L-BFGS-B" or "SANN". The default is "BFGS". The details of these methods

Value

• An object of the same length as x, giving the pdf or cdf values computed at x or an object of the same length as p, giving the quantile values computed at p or an object of the same length as n, giving the random numbers generated or an object giving the values of Cramer-von Misses statistic, Anderson Darling statistic, Kolmogorov Smirnov test statistic and p-value, maximum likelihood estimates, Akaike Information Criterion, Consistent Akaikes Information Criterion, Bayesian Information Criterion, Hannan-Quinn information criterion, standard errors of the maximum likelihood estimates, minimum value of the negative log-likelihood function and convergence status.

References

S. Nadarajah and R. Rocha, Newdistns: An R Package for New Families of Distributions, Journal of Statistical Software, 69(10), 1-32, doi:10.18637/jss.v069.i10 G. M. Cordeiro, M. Castro, A new family of generalized distributions, Journal of Statistical Computation and Simulation 81 (2011) 883-898

Examples

x=runif(10,min=0,max=1)
dkumg(x,"exp",a=1,b=1)
pkumg(x,"exp",a=1,b=1)
qkumg(x,"exp",a=1,b=1)
rkumg(10,"exp",a=1,b=1)
mkumg("exp",rexp(100),starts=c(1,1,1),method="BFGS")