# expg: Exponentiated G Distribution In Newdistns: Computes Pdf, Cdf, Quantile and Random Numbers, Measures of Inference for 19 General Families of Distributions

## Description

Computes the pdf, cdf, quantile and random numbers of the exponentiated G distribution due to Gupta et al. (1998) specified by the pdf

f (x) = a g (x) G^{a - 1} (x)

for G any valid cdf, g the corresponding pdf and a > 0, the shape parameter. Also computes the Cramer-von Misses statistic, Anderson Darling statistic, Kolmogorov Smirnov test statistic and p-value, maximum likelihood estimates, Akaike Information Crite rion, 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

 ```1 2 3 4 5``` ```dexpg(x, spec, a = 1, log = FALSE, ...) pexpg(x, spec, a = 1, log.p = FALSE, lower.tail = TRUE, ...) qexpg(p, spec, a = 1, log.p = FALSE, lower.tail = TRUE, ...) rexpg(n, spec, a = 1, ...) mexpg(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 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"), log-logistic ("log-logistic"), Lomax ("lomax") and Rayleigh ("rayleigh"). Each of these distributions has one parameter (`r`) or two parameters (`r`, `s`), for details including the density function and parameter specifications see Nadarajah and Rocha (2014) `data` a vector of data values for which the distribution is to be fitted `starts` initial values of `(a, r)` if `g` has one parameter or initial values of `(a, 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 can be found in the manual pages for `optim`

## 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

R. C. Gupta, P. L. Gupta, R. D. Gupta, Modeling failure time data by Lehman alternatives, Communications in Statisticsâ€”Theory and Methods 27 (1998) 887-904

## Examples

 ```1 2 3 4 5 6``` ```x=runif(10,min=0,max=1) dexpg(x,"exp",a=1) pexpg(x,"exp",a=1) qexpg(x,"exp",a=1) rexpg(10,"exp",a=1) mexpg("exp",rexp(100),starts=c(1,1),method="BFGS") ```

Newdistns documentation built on May 1, 2019, 10:32 p.m.