Binomial Distribution

The package “binomial” is a method to calculate the various attributes of a binomial distribution given parameters. Below is an example of how to install the package.

devtools::install_github("jacobyeung/Binomial_Package")
library(binomial)

Dependencies: ggplot2

Using the math Choose function

To calculate the number of comibnations in which k successes can occur in n trials, we use the bin_choose() function:

bin_choose(n = 5, k = 2)
#> [1] 10

Creating a Binomial Random Variable

To create a binomial random variable with k trials and probability prob, we use the function bin_variable():

variable = bin_variable(trials = 5, prob = 0.5)

Calculating the Binomial Probability

To calculate the probability of k successes, each independent with probability prob, on n repeated trials, we use the bin_probability() function:

bin_probability(success = 2, trials = 5, prob = 0.5)
#> [1] 0.3125

Calculating the Binomial Distribution

To calculate the binomial distribution of k trials and probability prob, we use the bin_distribution() function:

distribution = bin_distribution(trials = 5, prob = 0.5)
distribution
#>   Success Probability
#> 1       0     0.03125
#> 2       1     0.15625
#> 3       2     0.31250
#> 4       3     0.31250
#> 5       4     0.15625
#> 6       5     0.03125

Displaying the Binomial Distribution

To plot the above calculated binomial distribution, we use the function plot.bindis():

plot.bindis(distribution)

Finding the Cumulative Distribution of a Binomial Random Variable

To find the cumulative distribution of k trials and probability prob, we use the function bin_cumulative():

cumulative_distribution = bin_cumulative(trials = 5, prob = 0.5)
cumulative_distribution
#>   Success Probability cumulative
#> 1       0     0.03125    0.03125
#> 2       1     0.15625    0.18750
#> 3       2     0.31250    0.50000
#> 4       3     0.31250    0.81250
#> 5       4     0.15625    0.96875
#> 6       5     0.03125    1.00000

Displaying the Cumulative Distribution

To plot the above calculated cumulative distribution, we use the function plot.bincum():

plot.bincum(cumulative_distribution)

Creating the Summary of a Binomial Variable

To create the summary of a binomial variable, we use the function summary.binvar():

summary.binvar(variable)
#> "Summary Binomial"
#> 
#> Parameters
#> - number of trials: 5 
#> - prob of success : 0.5 
#> 
#> Measures
#> - mean    : 2.5 
#> - variance: 1.25 
#> - mode    : 3 
#>  - mode    : 2 
#> - skewness: 0 
#> - kurtosis: -0.4

Displaing the Summary of a Binomial Variable

To display the summary of a binomial variable, we use the function print.summary.binvar():

print.summary.binvar(variable)
#> "Summary Binomial"
#> 
#> Parameters
#> - number of trials: 5 
#> - prob of success : 0.5 
#> 
#> Measures
#> - mean    :  
#> - variance:  
#> - mode    :  
#> - skewness:  
#> - kurtosis: