egap {NovelDistns}

Exponentiated Gull Alpha Power Family of distribution

Description

Computes the pdf, cdf, quantile, and random numbers and estimates the parameters of the exponentiated gull alpha power family of distribution specified by the cdf.

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

where \theta is the baseline family parameter vector. Also, 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

regap(n, dist, param)
qegap(p, dist, param, log.p = FALSE, lower.tail = TRUE)
pegap(data, dist, param, log.p = FALSE, lower.tail = TRUE)
degap(data, dist, param, log = FALSE)
mlegap(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=(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, 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

Examples

x=runif(10,min=0,max=1)
regap(10,"exp",c(0.3,0.5,0.7))
qegap(0.6,"exp",c(0.3,0.5,0.7))
pegap(x,"exp",c(0.3,0.5,0.7))
degap(x,"exp",c(0.3,0.5,0.7))
mlegap(x,"exp",c(0.3,0.5,0.7))