Newdistns (version 2.1)

betag: Beta G Distribution

Description

Computes the pdf, cdf, quantile and random numbers of the beta G distribution due to Eugene et al. (2002) specified by the pdf $$f (x) = \frac {\displaystyle 1}{\displaystyle B(a,b)} g(x)\left[ G(x) \right]^{a - 1} \left[ 1 - G(x) \right]^{b - 1}$$ 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

dbetag(x, spec, a = 1, b = 1, log = FALSE, ...)
pbetag(x, spec, a = 1, b = 1, log.p = FALSE, lower.tail = TRUE, ...)
qbetag(p, spec, a = 1, b = 1, log.p = FALSE, lower.tail = TRUE, ...)
rbetag(n, spec, a = 1, b = 1, ...)
mbetag(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 N. Eugene, C. Lee, F. Famoye, Beta-normal distribution and its applications, Communications in Statistics---Theory and Methods, 31 (2002) 497-512

Examples

x=runif(10,min=0,max=1)
dbetag(x,"exp",a=1,b=1)
pbetag(x,"exp",a=1,b=1)
qbetag(x,"exp",a=1,b=1)
rbetag(10,"exp",a=1,b=1)
mbetag("exp",rexp(100),starts=c(1,1,1),method="BFGS")