In YushengXia/Workout_03: Binomial Functions

knitr::opts_chunk$set(echo = TRUE)
library(binomial)

Binomial Package

The package '"Binomial"' is a package that contains many functions that relate to the famous binomial probability distribution. The package contains five main functions:

• bin_choose(n, k) to calculate the number of combinations in which k successes can occur in n trials.
• bin_probability(k, n, p) to calculate the probability of getting k successes in n trials with a p success probability.
• bin_distribution(n, p) to return a dataframe of class '"bindis"' that has number of successes (up to n) in first column and probability of success number in second.
• bin_cumulative(n, p) to return a dataframe of class '"bincum"' that is the same as bin_distribution() but also contains a column of cumulative probability.
• bin_var(n, p) to return a named list of class '"binvar"' that contains the number of trials n and probability of success p.

In addition, the package also contains various methods that allow for easy plotting and summary functions to be displayed to users.

bin_choose()

The bin_choose(n, k) function allows a user to see the total number of possible combinations of getting k successes in n trials.

#Possible combinations in 4 trials with 3 successes.
bin_choose(4, 3)

In order for bin_choose(n, k) to be successfully run, n must be a positive integer number while k must be a positive integer less than or equal to n.

bin_probability()

The bin_probability(k, n, p) function allows a user to calculate the probability of getting k successes given n trials and probability p of a single success.

#Proability of getting 4 successes in 5 trials with a probability 0.2 of success
bin_probability(4, 5, 0.2)

Bin_probability(k, n, p) has the same limitations on inputs n and p as on bin_choose(n, p), and the input k must be a integer greater than or equal to 0 that is also less than or equal to n.

bin_distribution()

The bin_distribution(n, p) function returns a dataframe that contains two columns, one column that shows all possible successes leading to n, and another that has the probability of each possible success number with the probability of one success given by p.

#Dataframe of possible successes in 5 trials and 0.3 success per trial.
bin_distribution(5, 0.3)

After creating the dataframe, users can call the method plot to plot a bargraph of the dataframe given that the dataframe is of class '"bindis"'.

#Bar graph of possible successes and probability of possible successes in 5 trials with 0.3 success per trial.
dis1 <- bin_distribution(5, 0.3)
plot.bindis(dis1)

Just like the functions above it, bin_distribution(n, p) can only take an input n that is an integer greater than or equal to 0 and a probability p that is between 0 and 1.

bin_cumulative()

The bin_cumulative(n, p) function returns a dataframe similar to that of bin_distribution, but has an additional column that shows the cumulative distribution given each additional success. Given the nature of probabilities, the cumulative probability leading up to n successes is 1. The dataframe output is of class '"bincum"'.

#Dataframe with cumulative probability added.
bin_cumulative(5, 0.3)

After creating the dataframe, users can call on the method plot to plot a cumulative line graph of the dataframe given that the dataframe is of class '"bincum"'.

#Cumulative line graph of possible successes and cumulative probability of successes in 5 trials with 0.3 success per trial.
dis2 <- bin_cumulative(5, 0.5)
plot.bincum(dis2)

Just like the functions above it, bin_cumulative(n, p) can only take an input n that is an integer greater than or equal to 0 and a probability p that is between 0 and 1.

bin_variable()

The bin_variable(n, p) function that returns a named list that is of class '"binvar"' and has the number of trials and probability of success printed out to see.

#Using bin_variable()
bin1 <- bin_variable(10, 0.3)
bin1

After using bin_variable to create the named list, users are able to call upon the method summary to show the key summary statistics regarding the binomial distribution for that particular number of trials and probability.

#Summary statistics for n = 10 and p = 0.3
bin1 <- bin_variable(10, 0.3)
summary(bin1)

Just like the functions above it, bin_variablen, p) can only take an input n that is an integer greater than or equal to 0 and a probability p that is between 0 and 1.

YushengXia/Workout_03 documentation built on May 5, 2019, 12:26 a.m.