Description Usage Arguments Value Author(s) References Examples
Computes the pdf, cdf, quantile and random numbers of the generalized beta G distribution due to Alexander et al. (2012) specified by the pdf
f (x) = \frac {c}{B (a, b)} g (x) G^{a c - 1} (x) ≤ft[ 1 - G^c (x) \right]^{b - 1}
for G any valid cdf, g the corresponding pdf, a > 0, the first shape parameter, b > 0, the second shape parameter and c > 0, the third 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
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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 |
c |
the value of the third 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 ( |
data |
a vector of data values for which the distribution is to be fitted |
starts |
initial values of |
method |
the method for optimizing the log likelihood function. It can be one of |
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.
Saralees Nadarajah, Ricardo Rocha
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
C. Alexander, G. M. Cordeiro, E. M. M. Ortega, Generalized beta-generated distributions, Computational Statistics and Data Analysis 56 (2012) 1880-1897
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