pCOMPBin {fitODBOD}

COM Poisson Binomial Distribution

Description

These functions provide the ability for generating probability function values and cumulative probability function values for the COM Poisson Binomial Distribution.

Usage

pCOMPBin(x,n,p,v)

Arguments

x

vector of binomial random variables.

n

single value for no of binomial trials.

p

single value for probability of success.

v

single value for v.

Details

The probability function and cumulative function can be constructed and are denoted below

The cumulative probability function is the summation of probability function values.

P_{COMPBin}(x) = \frac{{n \choose x}^v p^x (1-p)^{n-x}}{\sum_{j=0}^{n} {n \choose j}^v p^j (1-p)^{(n-j)}}

x = 0,1,2,3,...n

n = 1,2,3,...

0 < p < 1

-\infty < v < +\infty

NOTE : If input parameters are not in given domain conditions necessary error messages will be provided to go further.

Value

The output of pCOMPBin gives cumulative probability values in vector form.

References

Borges P, Rodrigues J, Balakrishnan N, Bazan J (2014). “A COM–Poisson type generalization of the binomial distribution and its properties and applications.” Statistics and Probability Letters, 87, 158–166.

Examples

#plotting the random variables and probability values
col <- rainbow(5)
a <- c(0.58,0.59,0.6,0.61,0.62)
b <- c(0.022,0.023,0.024,0.025,0.026)
plot(0,0,main="COM Poisson 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,dCOMPBin(0:10,10,a[i],b[i])$pdf,col = col[i],lwd=2.85)
points(0:10,dCOMPBin(0:10,10,a[i],b[i])$pdf,col = col[i],pch=16)
}

dCOMPBin(0:10,10,0.58,0.022)$pdf      #extracting the pdf values
dCOMPBin(0:10,10,0.58,0.022)$mean     #extracting the mean
dCOMPBin(0:10,10,0.58,0.022)$var      #extracting the variance

#plotting the random variables and cumulative probability values
col <- rainbow(5)
a <- c(0.58,0.59,0.6,0.61,0.62)
b <- c(0.022,0.023,0.024,0.025,0.026)
plot(0,0,main="COM Poisson Binomial probability function graph",xlab="Binomial random variable",
ylab="Probability function values",xlim = c(0,10),ylim = c(0,1))
for (i in 1:5)
{
lines(0:10,pCOMPBin(0:10,10,a[i],b[i]),col = col[i],lwd=2.85)
points(0:10,pCOMPBin(0:10,10,a[i],b[i]),col = col[i],pch=16)
}

pCOMPBin(0:10,10,0.58,0.022)      #acquiring the cumulative probability values