Uniform Binomial Distribution

Source: R/Uniform.R

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

dUniBin(x,n)

Arguments

x

vector of binomial random variables.
n

single value for no of binomial trials.

Value

The output of dUniBin gives a list format consisting

pdf probability function values in vector form.

mean mean of the Uniform Binomial Distribution.

var variance of the Uniform Binomial Distribution.

ove.dis.para over dispersion value of Uniform Binomial Distribution.

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

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

Okagbue, H. et al., 2014. Using the Average of the Extreme Values of a Triangular Distribution for a Transformation, and Its Approximant via the Continuous Uniform Distribution. British Journal of Mathematics & Computer Science, 4(24), pp.3497-3507.

Available at: http://www.sciencedomain.org/abstract.php?iid=699&id=6&aid=6427 .

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
#>   [1] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#>   [7] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#>  [13] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#>  [19] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#>  [25] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#>  [31] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#>  [37] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#>  [43] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#>  [49] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#>  [55] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#>  [61] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#>  [67] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#>  [73] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#>  [79] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#>  [85] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#>  [91] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#>  [97] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [103] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [109] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [115] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [121] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [127] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [133] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [139] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [145] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [151] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [157] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [163] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [169] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [175] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [181] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [187] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [193] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [199] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [205] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [211] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [217] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [223] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [229] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [235] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [241] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [247] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [253] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [259] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [265] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [271] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [277] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [283] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [289] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [295] 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259 0.003322259
#> [301] 0.003322259
dUniBin(0:10,10)$mean   #extracting the mean
#> [1] 5
dUniBin(0:10,10)$var    #extracting the variance
#> [1] 10
dUniBin(0:10,10)$over.dis.para  #extracting the over dispersion
#> [1] 0.3333333

#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
#>  [1] 0.0625 0.1250 0.1875 0.2500 0.3125 0.3750 0.4375 0.5000 0.5625 0.6250
#> [11] 0.6875 0.7500 0.8125 0.8750 0.9375 1.0000