Newdistns (version 2.1)

mbetag: Modified Beta G Distribution

Description

Computes the pdf, cdf, quantile and random numbers of the modified beta G distribution due to Nadarajah et al. (2013) specified by the pdf $$f (x) = \frac {\displaystyle \beta^a}{\displaystyle B(a,b)} \frac {\displaystyle g(x)\left[ G(x) \right]^{a - 1} \left[ 1 - G(x) \right]^{b - 1}}{\displaystyle \left[ 1 - (1 - \beta ) G(x) \right]^{a + b}}$$ for $G$ any valid cdf, $g$ the corresponding pdf, $\beta > 0$, the scale parameter, $a > 0$, 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

dmbetag(x, spec, beta = 1, a = 1, b = 1, log = FALSE, ...)
pmbetag(x, spec, beta = 1, a = 1, b = 1, log.p = FALSE, lower.tail = TRUE, ...)
qmbetag(p, spec, beta = 1, a = 1, b = 1, log.p = FALSE, lower.tail = TRUE, ...)
rmbetag(n, spec, beta = 1, a = 1, b = 1, ...)
mmbetag(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

beta

the value of the scale parameter, must be positive, the default is 1

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 (beta, a, b, r) if g has one parameter or initial values of (beta, 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 S. Nadarajah, M. Teimouri, S. H. Shih, Modified beta distributions, Sankhya, 2013, to appear

Examples

x=runif(10,min=0,max=1)
dmbetag(x,"exp",beta=1,a=1,b=1)
pmbetag(x,"exp",beta=1,a=1,b=1)
qmbetag(x,"exp",beta=1,a=1,b=1)
rmbetag(10,"exp",beta=1,a=1,b=1)
mmbetag("exp",rexp(100),starts=c(1,1,1,1),method="BFGS")