mazUNI() R function from [fitODBOD]

Uniform Distribution Bounded Between [0,1]

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].


mazUNI(r)

Arguments

r: vector of moments

Returns

The output of mazUNI gives the moments about zero in vector form.

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.

Examples


#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)

References

\insertRef horsnell1957economicalfitODBOD

\insertRef johnson1995continuousfitODBOD

mazUNI function