eggap {NovelDistns}

Exponentiated Generalized Gull Alpha Power Family of distribution

Description

Computes the pdf, cdf, quantile, and random numbers and estimates the parameters of the exponentiated G gull alpha power family of distribution due to Kilai et al. (2022) specified by the cdf.

F(x,{\Theta}) = \left[1-\left(1-\frac{\alpha G(x)}{\alpha^{G(x)}}\right)^{a}\right]^{b}

where \theta is the baseline family parameter vector. Also, a>0, b>0 are the extra parameters induced to the baseline cumulative distribution function (cdf) G whose pdf is g. Here, the baseline G refers to the cdf of: exponential, rayleigh and weibull.

Usage

reggap(n, dist, param)
qeggap(p, dist, param, log.p = FALSE, lower.tail = TRUE)
peggap(data, dist, param, log.p = FALSE, lower.tail = TRUE)
deggap(data, dist, param, log = FALSE)
mleggap(data, dist,starts, method="SANN")

Arguments

n

number of realizations to be generated.

p

quantile value between 0 and 1.

data

Vector of observations.

param

parameter vector \Theta=(a,b,\theta,\alpha)

log

If TRUE, then log(pdf) is returned.

log.p

If TRUE, then log(cdf) is returned and quantile is computed for exp(-p).

lower.tail

If FALSE, then 1-cdf is returned and quantile is computed for 1-p.

dist

The name of family's pdf including: "exponential", "rayleigh", "weibull", "lomax"

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

starts

initial values of (theta, a, b, alpha)

Value

1. A vector of the same length as data, giving the pdf values computed at data.

2. A vector of the same length as data, giving the cdf values computed at data.

3. A vector of the same length as p, giving the quantile values computed at p.

4. A vector of the same length as n, giving the random numbers realizations.

5. 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). The Kolmogorov-Smirnov (KS) test statistic and corresponding p-value and the convergence status.

Author(s)

Mutua Kilai, Gichuhi A. Waititu, Wanjoya A. Kibira

References

Mutua Kilai et al (2022) A new generalization of Gull Alpha Power Family of distributions with application to modeling COVID-19 mortality rates, https://doi.org/10.1016/j.rinp.2022.105339.

Examples

x=runif(10,min=0,max=1)
reggap(10,"exp",c(0.3,0.5,0.7,0.8))
qeggap(0.6,"exp",c(0.3,0.5,0.7,0.8))
peggap(x,"exp",c(0.3,0.5,0.7,0.8))
deggap(x,"exp",c(0.3,0.5,0.7,0.8))
mleggap(x,"exp",c(0.3,0.5,0.7,0.8))