# dUNI: Uniform Distribution bounded between [0,1] In Amalan-ConStat/R-fitODBOD: Modeling Over Dispersed Binomial Outcome Data Using BMD and ABD

## Description

These functions provide the ability for generating probability density values, cumulative probability density values and moments about zero values for the Uniform Distribution bounded between [0,1]

## Usage

 1 dUNI(p) 

## Arguments

 p vector of probabilities

## Details

Setting a=0 and b=1 in the Uniform Distribution a unit bounded Uniform Distribution can be obtained. The probability density function and cumulative density function of a unit bounded Uniform Distribution with random variable P are given by

g_{P}(p) = 1

0 ≤ p ≤ 1

G_{P}(p) = p

0 ≤ p ≤ 1

The mean and the variance are denoted as

E[P]= \frac{1}{a+b}= 0.5

var[P]= \frac{(b-a)^2}{12}= 0.0833

Moments about zero is denoted as

E[P^r]= \frac{e^{rb}-e^{ra}}{r(b-a)}= \frac{e^r-1}{r}

r = 1,2,3,...

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

## Value

The output of dUNI gives a list format consisting

pdf probability density values in vector form

mean mean of unit bounded uniform distribution

var variance of unit bounded uniform distribution

## References

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

Johnson, N. L., Kotz, S. and Balakrishnan, N. (1994) Continuous Univariate Distributions, Vol. 2, Wiley Series in Probability and Mathematical Statistics, Wiley

Uniform
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 #plotting the random variables and probability values plot(seq(0,1,by=0.01),dUNI(seq(0,1,by=0.01))$pdf,type = "l",main="Probability density graph", xlab="Random variable",ylab="Probability density values") dUNI(seq(0,1,by=0.05))$pdf #extract the pdf values dUNI(seq(0,1,by=0.01))$mean #extract the mean dUNI(seq(0,1,by=0.01))$var #extract the variance #plotting the random variables and cumulative probability values plot(seq(0,1,by=0.01),pUNI(seq(0,1,by=0.01)),type = "l",main="Cumulative density graph", xlab="Random variable",ylab="Cumulative density values") pUNI(seq(0,1,by=0.05)) #acquiring the cumulative probability values mazUNI(c(1,2,3)) #acquiring the moment about zero values #only the integer value of moments is taken here because moments cannot be decimal mazUNI(1.9)