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].

dUNI(p)

Arguments

p	vector of probabilities.

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.

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

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.

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))$pdf     #extract the pdf values
#>  [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
dUNI(seq(0,1,by=0.01))$mean    #extract the mean
#> [1] 0.5
dUNI(seq(0,1,by=0.01))$var     #extract the variance
#> [1] 0.08333333

#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
#>  [1] 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70
#> [16] 0.75 0.80 0.85 0.90 0.95 1.00

mazUNI(c(1,2,3))    #acquiring the moment about zero values
#> [1] 0.5000000 0.3333333 0.2500000

#only the integer value of moments is taken here because moments cannot be decimal
mazUNI(1.9)
#> [1] 0.5