Description Usage Arguments Details Value References Examples

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

1 | ```
pCOMPBin(x,n,p,v)
``` |

`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 |

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

The output of `pCOMPBin`

gives cumulative probability values in vector form.

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.

Available at: http://conteudo.icmc.usp.br/CMS/Arquivos/arquivos_enviados/BIBLIOTECA_113_NSE_90.pdf

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
``` |

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