# pCOMPBin: COM Poisson Binomial Distribution In Amalan-ConStat/R-fitODBOD: Modeling Over Dispersed Binomial Outcome Data Using BMD and ABD

## Description

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

## Usage

 1 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}}{∑_{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

-∞ < v < +∞

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

Extracted from

Borges, P., Rodrigues, J., Balakrishnan, N. and Bazan, J., 2014. A COM-Poisson type generalization of the binomial distribution and its properties and applications. Statistics & Probability Letters, 87, pp.158-166.

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 #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 

Amalan-ConStat/R-fitODBOD documentation built on Oct. 1, 2018, 7:13 p.m.