README

Overview

"binomial" is an R package that provides functions to check whether the inputs are valid, calculate the probability based on given parameters, graph the distribution and display a summary of expected value, variance, etc.

• bin_choose() calculates the number of combinations given number of trials and success
• bin_probability() calculates the probaility of getting k success out of n trials, given probability per trial
• bin_distribution() generates a table with all the possible success and corresponding overall probability, given the number of trials and probability of success per trial
• bin_cum() calculates cumulative probability based on the table with success and probability derived
• plot() gives graphs of data frames derived
• bin_variable() creates a binomial variable
• bin_summary() generates a summary of the binomial variable
• bin_mean() calculates the mean of the binomial distribution
• bin_variance() calculates the variance of the binomial distribution
• bin_mode() calculates the mode of the binomial distribution
• bin_skewness() calculates the skewness the given binomial distribution
• bin_kurtosis() calculates the kurtosis the given binomial distribution

Motivation

This package has been developed to illustrate the mechanism and usage of binomial distribution

Installation

Install the development version from GitHub via the package "devtools":

# development version from GitHub:
# install.packages("devtools") 

# install "cointoss" (without vignettes)
devtools::install_github("stat133-sp19/hw-stat133-HonglingLei/workout3/binomial")

# install "cointoss" (with vignettes)
devtools::install_github("stat133-sp19/hw-stat133-HonglingLei/workout3/binomial", build_vignettes = TRUE)

Usage

library(binomial)

# calculate number of combinations given number of trials and success
bin_choose(n=5,k=2)
#> [1] 10

# calculate the possibility of getting k success out of n trials, given the prob of success per trial
bin_probability(success = 2, trials = 5, prob = 0.5)
#> [1] 0.3125

# generate a table with all the possible success and corresponding overall probability
dis1 <- bin_distribution(trials = 5, prob = 0.5)
dis1
#>   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

# Calculate cumulative probability by adding up the previous probability based on the table with success and probability we get
bin_cum<- bin_cumulative(trials = 5, prob = 0.5)
bin_cum
#>   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

# Calculate summary measures
bin_mean(10,0.5)
#> [1] 5
bin_variance(10,0.5)
#> [1] 2.5
bin_mode(10,0.5)
#> [1] 5
bin_skewness(10,0.5)
#> [1] 0
bin_kurtosis(10,0.5)
#> [1] -0.2

# Create a binomial variable
bin_var <- bin_variable(trials=5, prob=0.5)
bin_var
#> [1] "Binomial variable"
#> [1] " "
#> [1] "Paramaters"
#> [1] "- number of trials: 5"
#> [1] "- prob of success : 0.5"

# Obtain a summary of the binomial variable
bin_sum <- summary(bin_var)
bin_sum
#> [1] "Summary Binomial"
#> [1] ""
#> [1] "Paramaters"
#> [1] "- number of trials: 5"
#> [1] "- prob of success : 0.5"
#> [1] ""
#> [1] "Measures"
#> [1] "- mean    : 2.5"
#> [1] "- variance: 1.25"
#> [1] "- mode    : 3" "- mode    : 2"
#> [1] "- skewness: 0"
#> [1] "- kurtosis: -0.4"

# If you want to plot graphs of the distribution, you can see more details in vignettes/Introduction.Rmd