Newdistns (version 1.0)

loggammag1: Log gamma G I distribution

Description

Computes the pdf, cdf, quantile and random numbers of the log gamma G I distribution due to Amini et al. (2013) specified by the pdf $$f (x) = \frac {b^a}{\Gamma (a)} g (x) \left{ -\log \left[ 1 - G (x) \right] \right}^{a - 1} \left[ 1 - G (x) \right]^{b - 1}$$ for $G$ any valid cdf, $g$ the corresponding pdf, $a > 0$, the first shape parameter, $b > 0$, and the second shape parameter.

Usage

dloggammag1(x, spec, a = 1, b = 1, log = FALSE, ...)
ploggammag1(x, spec, a = 1, b = 1, log.p = FALSE, lower.tail = TRUE, ...)
qloggammag1(p, spec, a = 1, b = 1, log.p = FALSE, lower.tail = TRUE, ...)
rloggammag1(n, spec, a = 1, b = 1,  ...)

Arguments

x

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

p

scaler or vector of values 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

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.

References

S. Nadarajah, Newdistns: An R Package for new families of distributions, submitted M. Amini, S. M. T. K. MirMostafaee, J. Ahmadi, Log-gamma-generated families of distributions, Statistics, 2013, doi: 10.1080/02331888.2012.748775

Examples

x=runif(10,min=0,max=1)
dloggammag1(x,"exp",a=1,b=1)
ploggammag1(x,"exp",a=1,b=1)
qloggammag1(x,"exp",a=1,b=1)
rloggammag1(10,"exp",a=1,b=1)