fitODBOD (version 1.5.3)

pUniBin: Uniform Binomial Distribution

Description

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

Usage

pUniBin(x,n)

Value

The output of pUniBin gives cumulative probability function values in vector form.

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.

References

horsnell1957economicalfitODBOD okagbue2014usingfitODBOD

Examples

#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