dgBetaD: Generalized Beta distribution for discrete variables

In sgr: Sample Generation by Replacement

Generalized Beta distribution for discrete variables

Description

Generalized Beta distribution for discrete variables.

Usage

dgBetaD(x, a = min(x), b = max(x), gam = 1, del = 1, ct = 1)

Arguments

x	Vector of quantilies.
a	Minimum of range of r.v. X.
b	Maximum of range of r.v. X.
gam	Gamma parameter.
del	Delta parameter.
ct	Correction term, default value: 1.

Details

Let X be a discrete r. v. with range

R_X=\{a,a+1,a+2,…, a+t-1,a+t = b \}

and where a \in \mathrm{N} \cup \{0 \} and t \in \mathrm{N}. The Generalized Discrete Beta Distribution for the r.v. X is defined as follows:

DG(x;a,b,γ,δ)= ≤ft\{ \begin{array}{cl} \frac{G^*(x;a,b,γ,δ)}{∑_{x' \in R_X} G^*(x';a,b,γ,δ)} & x \in R_X\\ 0 & x \notin R_X \end{array} \right.

where G^* is a modified version of the generalized beta distribution dgBeta defined as

G^*(x;a,b,γ,δ)=\frac{1}{B(γ,δ)(b-a+2c)^{γ+δ-1}} (x-a+c)^{γ-1}(b-x+c)^{δ-1}

Value

Gives the density.

Author(s)

Massimiliano Pastore & Luigi Lombardi

References

Lombardi, L., Pastore, M. (2014). sgr: A Package for Simulating Conditional Fake Ordinal Data. The R Journal, 6, 164-177.

Pastore, M., Lombardi, L. (2014). The impact of faking on Cronbach's Alpha for dichotomous and ordered rating scores. Quality & Quantity, 48, 1191-1211.

See Also

dgBeta

Examples

x <- 1:7
GA <- c(1,3,1.5,8); DE <- c(1,3,4,2.5)
par(mfrow=c(2,2))
for (j in 1:4) {
  plot(x,dgBetaD(x,gam=GA[j],del=DE[j]),type="h",
       panel.first=points(x,dgBetaD(x,gam=GA[j],del=DE[j]),pch=19),
       main=paste("gamma=",GA[j]," delta=",DE[j],sep=""),ylim=c(0,.6),
       ylab="dgBetaD(x)")  
}

sgr documentation built on April 14, 2022, 5:08 p.m.