pUNI: Uniform Distribution Bounded Between [0,1]

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

pUNI(p)

Value

The output of pUNI gives the cumulative density values in vector form.

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

$$g_{P}(p) = 1$$ $0 \le p \le 1$ $$G_{P}(p) = p$$ $0 \le p \le 1$

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.

References

horsnell1957economicalfitODBOD johnson1995continuousfitODBOD

Examples

Run this code

#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)

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