sgr (version 1.3.1)

dgBetaD: 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.

Value

Gives the density.

Details

Let \(X\) be a discrete r. v. with range $$R_X=\{a,a+1,a+2,\ldots, a+t-1,a+t = b \} $$ 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: $$DG(x;a,b,\gamma,\delta)= \left\{ \begin{array}{cl} \frac{G^*(x;a,b,\gamma,\delta)}{\sum_{x' \in R_X} G^*(x';a,b,\gamma,\delta)} & x \in R_X\\ 0 & x \notin R_X \end{array} \right. $$ where \(G^*\) is a modified version of the generalized beta distribution dgBeta defined as $$ G^*(x;a,b,\gamma,\delta)=\frac{1}{B(\gamma,\delta)(b-a+2c)^{\gamma+\delta-1}} (x-a+c)^{\gamma-1}(b-x+c)^{\delta-1} $$

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

# NOT RUN {
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)")  
}
# }