# dUniBin: Uniform 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 Uniform Binomial Distribution.

## Usage

 1 dUniBin(x,n) 

## Arguments

 x vector of binomial random variables n single value for no of binomial trials

## Details

Mixing unit bounded uniform distribution with binomial distribution will create the Uniform 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

P_{UniBin}(x)= \frac{1}{n+1}

n = 1,2,...

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

The mean, variance and over dispersion are denoted as

E_{UniBin}[X]= \frac{n}{2}

Var_{UniBin}[X]= \frac{n(n+2)}{12}

over dispersion= \frac{1}{3}

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

## Value

The output of dUniBin gives a list format consisting

pdf probability function values in vector form

mean mean of the Uniform Binomial Distribution

var variance of the Uniform Binomial Distribution

ove.dis.para over dispersion value of Uniform Binomial Distribution

## References

Horsnell, G. (1957). Economic acceptance sampling schemes. Journal of the Royal Statistical Society, Series A, 120:148-191.

Okagbue, H. et al., 2014. Using the Average of the Extreme Values of a Triangular Distribution for a Transformation, and Its Approximant via the Continuous Uniform Distribution. British Journal of Mathematics & Computer Science, 4(24), pp.3497-3507.

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 #plotting the binomial random variables and probability values plot(0:10,dUniBin(0:10,10)$pdf,type="l",main="Uniform binomial probability function graph", xlab=" Binomial random variable",ylab="Probability function values") points(0:10,dUniBin(0:10,10)$pdf) dUniBin(0:300,300)$pdf #extracting the pdf values dUniBin(0:10,10)$mean #extracting the mean dUniBin(0:10,10)$var #extracting the variance dUniBin(0:10,10)$over.dis.para #extracting the over dispersion #plotting the binomial random variables and cumulative probability values plot(0:10,pUniBin(0:10,10),type="l",main="Cumulative probability function graph", xlab=" Binomial random variable",ylab="Cumulative probability function values") points(0:10,pUniBin(0:10,10)) pUniBin(0:15,15) #acquiring the cumulative probability values 

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