Description Usage Arguments Details Value References Examples

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

1 | ```
dAddBin(x,n,p,alpha)
``` |

`x` |
vector of binomial random variables |

`n` |
single value for no of binomial trials |

`p` |
single value for probability of success |

`alpha` |
single value for alpha parameter |

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_{AddBin}(x)= {n \choose x} p^x (1-p)^{n-x}(\frac{alpha}{2}(\frac{x(x-1)}{p}+\frac{(n-x)(n-x-1)}{(1-p)}-\frac{alpha(n-1)n}{2})+1)*

The alpha is in between

*\frac{-2}{n(n-1)}min(\frac{p}{1-p},\frac{1-p}{p}) ≤ alpha ≤ (\frac{n+(2p-1)^2}{4p(1-p)})^{-1}*

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

*n = 1,2,3,...*

*0 < p < 1*

*-1 < alpha < 1*

The mean and the variance are denoted as

*E_{Addbin}[x]=np*

*Var_{Addbin}[x]=np(1-p)(1+(n-1)alpha)*

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

The output of `dAddBin`

gives a list format consisting

`pdf`

probability function values in vector form

`mean`

mean of Additive Binomial Distribution

`var`

variance of Additive Binomial Distribution

Johnson, N. L., Kemp, A. W., & Kotz, S. (2005). Univariate discrete distributions (Vol. 444). Hoboken, NJ: Wiley-Interscience.

L. L. Kupper, J.K.H., 1978. The Use of a Correlated Binomial Model for the Analysis of Certain Toxicological Experiments. Biometrics, 34(1), pp.69-76.

Paul, S.R., 1985. A three-parameter generalization of the binomial distribution. Communications in Statistics - Theory and Methods, 14(6), pp.1497-1506.

Available at: http://www.tandfonline.com/doi/abs/10.1080/03610928508828990 .

Jorge G. Morel and Nagaraj K. Neerchal. Overdispersion Models in SAS. SAS Institute, 2012.

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="Additive 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,dAddBin(0:10,10,a[i],b[i])$pdf,col = col[i],lwd=2.85)
points(0:10,dAddBin(0:10,10,a[i],b[i])$pdf,col = col[i],pch=16)
}
dAddBin(0:10,10,0.58,0.022)$pdf #extracting the probability values
dAddBin(0:10,10,0.58,0.022)$mean #extracting the mean
dAddBin(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="Additive 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,pAddBin(0:10,10,a[i],b[i]),col = col[i],lwd=2.85)
points(0:10,pAddBin(0:10,10,a[i],b[i]),col = col[i],pch=16)
}
pAddBin(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.

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