dgBeta | R Documentation |
The generalized beta distribution extends the classical beta distribution beyond the [0,1] range (Whitby, 1971).
dgBeta(x, a = min(x), b = max(x), gam = 1, del = 1)
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. |
The Generalized Beta Distribution is defined as follows:
G(x;a,b,γ,δ) = \frac{1}{B(γ,δ)(b-a)^{γ+δ-1}} (x-a)^{γ-1}(b-x)^{δ-1}
where B(γ,δ) is the beta function. The parameters a \in R and b \in R (with a < b) are the left and right end points, respectively. The parameters γ > 0 and δ > 0 are the governing shape parameters for a and b respectively. For all the values of the r.v. X that fall outside the interval [a, b], G simply takes value 0. The generalized beta distribution reduces to the beta distribution when a = 0 and b = 1.
Gives the density.
Massimiliano Pastore & Luigi Lombardi
Whitby, O. (1971). Estimation of parameters in the generalized beta distribution (Technical Report NO. 29). Department of Statistics: Standford University.
dgBetaD
curve(dgBeta(x)) curve(dgBeta(x,gam=3,del=3)) curve(dgBeta(x,gam=1.5,del=2.5)) 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,dgBeta(x,gam=GA[j],del=DE[j]),type="h", panel.first=points(x,dgBeta(x,gam=GA[j],del=DE[j]),pch=19), main=paste("gamma=",GA[j]," delta=",DE[j],sep=""),ylim=c(0,.6), ylab="dgBeta(x)") }
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