In Dyang11/binomial: Binomial Functions and analysis

knitr::opts_chunk$set(collapse = T, comment = "#>")
library(Binomial)

Introduction:

This document is an introduction to the Binomial package. The binomial package is a implementation of basical statistical functions; the methods are designed to calculate and visualize binomial distributions.

Binomial Basics

Let's consider a case with 10 trials, with each trial having a 0.7 chance of succeededing.

Basic Statistical Measures

Included in the package are 5 base summary functions:

• Mean
• Variance
• Mode
• Skewness
• Kurtosis

Let's review each one more carefully.

Bin_Mean

The binomial mean is the average number of successes in n trials given p probability of success. To get the mean, call bin_mean(trials, probability)

bin_mean(10,0.7)

Bin_Variance

The binomial variance is the square of the standard deviation of a binomial distribution. To get the variance, call bin_variance(trials, probability)

bin_variance(10,0.7)

Bin_Mode

The binomial mode is the most likely number of succeses. To obtain the mode, call bin_mode(trials,probability)

bin_mode(10,0.7)

Bin_Skewness

The binomial skewness is a measure of the asymmetry of the binomial distribution. To obtain the skewness, call bin_skewness(trials,probability)

bin_skewness(10,0.7)

Bin_Kurtosis

The binomial kurtosis is a measure of the sharpness of a peak in a frequency-distirbution curve. To obtain the kurtosis, call bin_kurtosis(trials,probability)

bin_kurtosis(10,0.7)

Summarize all variables with bin_variable

bin_variable(trials,probability) provides a basic return

bin_variable(10,0.7)

To easily obtain a summary of all the above binomial variables, use summary(bin_variable(trials,probability))

summary(bin_variable(10,0.7))

Binomial Distribution Calculations

The following main functions are to calculate binomial distributions. Two methods are used to calculate some more basic statistics:

• bin_choose
• bin_probability

These functions can be used to model coin flips, for example.

Bin_choose

bin_choose(trials, successes) provides the number of permutations to obtain the specific number of successes in the given amount of trials.

bin_choose(10,6)
#This means there are 210 different ways to obtain 6 successes in 10 trials

Bin_probability

bin_probability(successes,trials,probability) provides the percent chance of obtaining k successes in n trials with a p probability of succeeding on each trial. This function can be used to determine how likely it is to get 1, 2, or 3 heads for 5 total coin flips.

bin_probability(6,10,0.6)
#This means there is a around a 25% chance of obtaining 6 successes in 10 trials where each trial has a 60% chance of succeeding.

bin_probability(1:3,5,0.5)
#Calling bin_probability with multiple success values gives us the seperate probability of obtaining each success value. There is about a 15% chance of obtaining 1 success and about the same 31% chance of obtaining 2 or 3 successes out of 5. 

Binomial Distribution Visualization

Finally, the two following functions provide a visualization method for binomial distributions.

• bin_distribution
• bin_cumulative

Visualize likelihood distributions with bin_distribution and bin_cumulative

bin_distirbution(trials,probability) returns a data frame with how likely it is to obtiain each possible success number in n trials.

#This function call provides the likelihood of seeing 0, 1, 2, 3, or 4 heads in 4 coin tosses.
bin_distribution(4,0.5)

An easier way to see this data is with a frequency histogram, which can be obtaining by calling plot(bin_distribution(trials,probability))

plot(bin_distribution(4,0.5))
#Here, we see that flipping 2 heads is the most likely option in 4 coin tosses.

bin_cumulative(trials,probability) provides additional information about the cumulative probability

#This function call provides the likelihood of seeing 0, 1, 2, 3, or 4 heads in 4 coin tosses, along with the cumulative probability.
bin_cumulative(4,0.5)

Finally, the cumulative probability can be visualized by plot(bin_cumulative(trials,probability))

plot(bin_cumulative(10,0.5))
#We see that most iterations of 10 coin flips will have less than 8 "heads"; the cumulative probability that we get less than 8 heads is above 90%

Dyang11/binomial documentation built on June 1, 2019, 4:56 a.m.