Fractional Binomial Distributions

Generating fractional binomial random variables and computing density, cumulative distribution, and quantiles of fractional binomial distributions. (Lee, J. (2023) .)

frbinom

The goal of frbinom is to generate random variables of fractional binomial distribution and compute its density, cumulative distribution, and quantiles.

Installation

You can install the development version of frbinom from GitHub with:

# install.packages("devtools")
devtools::install_github("leejeo25/frbinom")

Example

10 random variables of a fractional binomial distribution.

library(frbinom)
rfrbinom(n=10, size=50, prob=.6, h=.7, c=.2)
#>  [1] 34 33 40 34 39 32 34 25 34 37

The probability density of the fractional binomial distribution.

dfrbinom(x=seq(0,50,1), size=50, prob=.6, h=.7, c=.2)
#>  [1] 3.309256e-02 1.431863e-03 1.557437e-03 1.698900e-03 1.858815e-03
#>  [6] 2.040225e-03 2.246763e-03 2.482766e-03 2.753423e-03 3.064954e-03
#> [11] 3.424806e-03 3.841903e-03 4.326913e-03 4.892553e-03 5.553920e-03
#> [16] 6.328817e-03 7.238051e-03 8.305650e-03 9.558921e-03 1.102823e-02
#> [21] 1.274636e-02 1.474727e-02 1.706397e-02 1.972538e-02 2.275181e-02
#> [26] 2.614900e-02 2.990078e-02 3.396057e-02 3.824255e-02 4.261379e-02
#> [31] 4.688921e-02 5.083182e-02 5.416082e-02 5.657003e-02 5.775753e-02
#> [36] 5.746564e-02 5.552719e-02 5.191025e-02 4.675122e-02 4.036456e-02
#> [41] 3.322041e-02 2.588705e-02 1.894504e-02 1.289015e-02 8.049503e-03
#> [46] 4.535348e-03 2.251572e-03 9.509789e-04 3.228462e-04 7.917274e-05
#> [51] 1.070436e-05

The histogram of fractional binomial random variables overlaid with its density.

x<-rfrbinom(10000, 50, .6, .7, .2)
den.<-dfrbinom(seq(0,50,1), 50, .6, .7, .2)
hist(x, breaks=51, probability = TRUE, main="Histogram of fractional binomial random variables and its density")
lines(seq(0,50,1), den., type="l")