dBetaBin {fitODBOD} | R Documentation |
Beta-Binomial Distribution
Description
These functions provide the ability for generating probability function values and cumulative probability function values for the Beta-Binomial Distribution.
Usage
dBetaBin(x,n,a,b)
Arguments
x |
vector of binomial random variables. |
n |
single value for no of binomial trials. |
a |
single value for shape parameter alpha representing as a. |
b |
single value for shape parameter beta representing as b. |
Details
Mixing Beta distribution with Binomial distribution will create the Beta-Binomial distribution. The probability function and cumulative probability function can be constructed and are denoted below.
The cumulative probability function is the summation of probability function values.
The mean, variance and over dispersion are denoted as
Defined as B(a,b)
is the beta function.
Value
The output of dBetaBin
gives a list format consisting
pdf
probability function values in vector form.
mean
mean of the Beta-Binomial Distribution.
var
variance of the Beta-Binomial Distribution.
over.dis.para
over dispersion value of the Beta-Binomial Distribution.
References
Young-Xu Y, Chan KA (2008). “Pooling overdispersed binomial data to estimate event rate.” BMC medical research methodology, 8, 1–12. Trenkler G (1996). “Continuous univariate distributions.” Computational Statistics and Data Analysis, 21(1), 119–119. HUGHES G, MADDEN L (1993). “Using the beta-binomial distribution to describe aggegated patterns of disease incidence.” Phytopathology, 83(7), 759–763.
Examples
#plotting the random variables and probability values
col <- rainbow(5)
a <- c(1,2,5,10,0.2)
plot(0,0,main="Beta-binomial probability function graph",xlab="Binomial random variable",
ylab="Probability function values",xlim = c(0,10),ylim = c(0,0.5))
for (i in 1:5)
{
lines(0:10,dBetaBin(0:10,10,a[i],a[i])$pdf,col = col[i],lwd=2.85)
points(0:10,dBetaBin(0:10,10,a[i],a[i])$pdf,col = col[i],pch=16)
}
dBetaBin(0:10,10,4,.2)$pdf #extracting the pdf values
dBetaBin(0:10,10,4,.2)$mean #extracting the mean
dBetaBin(0:10,10,4,.2)$var #extracting the variance
dBetaBin(0:10,10,4,.2)$over.dis.para #extracting the over dispersion value
#plotting the random variables and cumulative probability values
col <- rainbow(4)
a <- c(1,2,5,10)
plot(0,0,main="Cumulative probability function graph",xlab="Binomial random variable",
ylab="Cumulative probability function values",xlim = c(0,10),ylim = c(0,1))
for (i in 1:4)
{
lines(0:10,pBetaBin(0:10,10,a[i],a[i]),col = col[i])
points(0:10,pBetaBin(0:10,10,a[i],a[i]),col = col[i])
}
pBetaBin(0:10,10,4,.2) #acquiring the cumulative probability values