Description Usage Arguments Details Value Author(s) References Examples
Computes the pdf, cdf, quantile, and random numbers, draws the q-q plot, and estimates the parameters of the beta exponential G
distribution. The General form for the probability density function (pdf) of the beta exponential G
distribution due to Alzaatreh et al. (2013) is given by
f(x,{Θ}) = \frac{{d\,g(x-μ,θ ){{≤ft[ {1 - {{≤ft( {1 - G(x-μ,θ )} \right)}^d}} \right]}^{b - 1}}{{≤ft( {1 - G(x-μ,θ )} \right)}^{ad - 1}}}}{{B(a,b)}},
where θ is the baseline family parameter vector. Also, a>0, b>0, d>0, and μ are the extra parameters induced to the baseline cumulative distribution function (cdf) G
whose pdf is g
. The general form for the cumulative distribution function (cdf) of the beta exponential G
distribution is given by
F(x,{Θ}) = 1 - \frac{{\int_0^{{{≤ft( {1 - G(x-μ,θ )} \right)}^d}} {{y^{a - 1}}{{≤ft( {1 - y} \right)}^{b - 1}}} dy}}{{B(a,b)}}.
Here, the baseline G
refers to the cdf of famous families such as: Birnbaum-Saunders, Burr type XII, Exponential, Chen, Chisquare, F, Frechet, Gamma, Gompertz, Linear failure rate (lfr), Log-normal, Log-logistic, Lomax, Rayleigh, and Weibull. The parameter vector is Θ=(a,b,d,θ,μ) where θ is the baseline G
family's parameter space. If θ consists of the shape and scale parameters, the last component of θ is the scale parameter (here, a, b, and d are the first, second, and the third shape parameters). Always, the location parameter μ is placed in the last component of Θ.
1 2 3 4 5 6 | dbetaexpg(mydata, g, param, location = TRUE, log=FALSE)
pbetaexpg(mydata, g, param, location = TRUE, log.p = FALSE, lower.tail = TRUE)
qbetaexpg(p, g, param, location = TRUE, log.p = FALSE, lower.tail = TRUE)
rbetaexpg(n, g, param, location = TRUE)
qqbetaexpg(mydata, g, location ="TRUE", method)
mpsbetaexpg(mydata, g, location = TRUE, method, sig.level)
|
g |
The name of family's pdf including: " |
p |
a vector of value(s) between 0 and 1 at which the quantile needs to be computed. |
n |
number of realizations to be generated. |
mydata |
Vector of observations. |
param |
parameter vector Θ=(a,b,d,θ,μ) |
location |
If |
log |
If |
log.p |
If |
lower.tail |
If |
method |
The used method for maximizing the sum of log-spacing function. It will be " |
sig.level |
Significance level for the Chi-square goodness-of-fit test. |
It can be shown that the Moran's statistic follows a normal distribution. Also, a chi-square approximation exists for small samples whose mean and variance approximately are m(log
(m)+0.57722)-0.5-1/(12m) and m(π^2/6-1)-0.5-1/(6m), respectively, with m=n+1
, see Cheng and Stephens (1989). So, a hypothesis tesing can be constructed based on a sample of n
independent realizations at the given significance level, indicated in above as sig.level
.
A vector of the same length as mydata
, giving the pdf values computed at mydata
.
A vector of the same length as mydata
, giving the cdf values computed at mydata
.
A vector of the same length as p
, giving the quantile values computed at p
.
A vector of the same length as n
, giving the random numbers realizations.
A sequence of goodness-of-fit statistics such as: Akaike Information Criterion (AIC
), Consistent Akaike Information Criterion (CAIC
), Bayesian Information Criterion (BIC
), Hannan-Quinn information criterion (HQIC
), Cramer-von Misses statistic (CM
), Anderson Darling statistic (AD
), log-likelihood statistic (log
), and Moran's statistic (M
). The Kolmogorov-Smirnov (KS
) test statistic and corresponding p-value
. The Chi-square test statistic, critical upper tail Chi-square distribution, related p-value
, and the convergence status.
Mahdi Teimouri
Cheng, R. C. H. and Stephens, M. A. (1989). A goodness-of-fit test using Moran's statistic with estimated parameters, Biometrika, 76 (2), 385-392.
Alzaatreh, A., Lee, C., and Famoye, F. (2013). A new method for generating families of continuous distributions, Metron, 71, 63-79.
1 2 3 4 5 6 7 | mydata<-rweibull(100,shape=2,scale=2)+3
dbetaexpg(mydata, "weibull", c(1,1,1,2,2,3))
pbetaexpg(mydata, "weibull", c(1,1,1,2,2,3))
qbetaexpg(runif(100), "weibull", c(1,1,1,2,2,3))
rbetaexpg(100, "weibull", c(1,1,1,2,2,3))
qqbetaexpg(mydata, "weibull", TRUE, "Nelder-Mead")
mpsbetaexpg(mydata, "weibull", TRUE, "Nelder-Mead", 0.05)
|
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