In shefalisastry/workout03: R Package: Binomial Variable and Distribution

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(binomial)

Binomial Package

An Introduction to the Binomial Random Variable

This Binomial package calculates probabilities of a Binomial random variable because it allows us to calculate the probabilities to find the number of successes in a fixed number of random trials performed under identical conditions (assuming a constant probability of success on each trial).

What this package contains

This specific package contains 15 functions that the user can use, 10 of which are main functions, and 5 of which are method functions that support these main functions due to their plotting capabilities. Here is a list of what is provided:

• Main Functions

  • bin_choose()
  • bin_probability()
  • bin_distribution(), Method: plot.bindis()
  • bin_cumulative(), Method: plot.bincum()
  • bin_var(), Method: print.binvar()
  • Summary/Auxiliary functions: bin_mean(), bin_variance(), bin_mode(), bin_skewness(), bin_kurtosis()

• Method Functions

  • plot.bindis(),
  • plot.bincum()
  • print.binvar()
  • summary.binvar()
  • print.summary.binvar()

## Check Functions
# These functions will not be called by the user as they are primarily used to check for valid values.
# Function check_prob()
#This function tests whether an input prob is a valid probability value
check_prob <- function(prob) {
  if (prob > 1 | prob < 0) {
    stop('p has to be a number betwen 0 and 1')
  }
  else {
    return(TRUE)
  }
}

# Function check_trials()
# This function tests whether an input trials is a valid value for a number of trials (i.e. n is a non-negative integer)
check_trials <- function(trials){
  if (trials <0) {
    stop('invalid trials value')
  } else {
    return(TRUE)
  }
}

# Function check_success()
# This function tests the success input is a valid value for number of successes
check_success <- function(success, trials){
  if(is.vector(success) == TRUE & sum(success <= trials) == length(success))
    return(TRUE)
  else
    stop('invalid success value')
}

How to Apply These Functions

bin_choose()

This function calculates the number of combinations in which k successes can occur in n trials.

bin_choose(n = 5, k = 2)
bin_choose(5, 0)

bin_probability()

This function calculates the probability of getting k successes in n trials assuming a certain probability of success.

# probability of getting 2 successes in 5 trials
# (assuming prob of success = 0.5)
bin_probability(success = 2, trials = 5, prob = 0.5)

# 55 heads in 100 tosses of a loaded coin with 45% chance of heads
bin_probability(success = 55, trials = 100, prob = 0.45)

bin_distribution()

This function calculates the distribution of the probabilities for each number of successes.

# binomial probability distribution
bin_distribution(trials = 5, prob = 0.5)

bin_cumulative()

This function calculates the distribution of the probability of getting at most k number of successes in n trials.

# binomial cumulative distribution
bin_cumulative(trials = 5, prob = 0.5)

bin_var()

This function calculates a list of the binomial variables by inputting n trials and at a probability level.

bin1 <- bin_variable(trials = 10, p = 0.3)
bin1

aux_mean <- function(trials,prob) {
  multiply_trials_prob <- trials*prob
  return(multiply_trials_prob)
}

bin_mean <- function(trials, prob){
  check_trials(trials)
  check_prob(prob)
  return(aux_mean(trials, prob))
}

aux_variance <- function(trials,prob) {
  variance_trials_prob <- trials*prob*(1-prob)
  return(variance_trials_prob)
}

bin_variance <- function(trials, prob){
  check_trials(trials)
  check_prob(prob)
  return(aux_variance(trials, prob))
}

aux_mode <- function(trials,prob) {
  mode_trials_prob <- floor(trials*prob + prob)
  return(mode_trials_prob)
}

bin_mode <- function(trials, prob){
  check_trials(trials)
  check_prob(prob)
  return(aux_mode(trials, prob))
}

aux_skewness <- function(trials,prob) {
  skewness_trials_prob <- (1-(2*prob))/(sqrt(trials*prob*(1-prob)))
  return(skewness_trials_prob)
}

bin_skewness <- function(trials, prob){
  check_trials(trials)
  check_prob(prob)
  return(aux_skewness(trials, prob))
}

aux_kurtosis <- function(trials,prob) {
  kurtosis_trials_prob <- ((1-6*prob)*(1-prob))/((trials*prob))*(1-prob)
  return(kurtosis_trials_prob)
}

bin_kurtosis <- function(trials, prob){
  check_trials(trials)
  check_prob(prob)
  return(aux_kurtosis(trials, prob))
}

Summary Functions

bin_mean()

This calculates the mean of a binomial distribution.

bin_mean(10, 0.3)

bin_variance()

This calculates the variance of a binomial distribution.

bin_variance(10, 0.3)

bin_mode()

This calculates the variance of a binomial distribution.

bin_mode(10, 0.3)

bin_skewness()

This calculates the skewness, or a measure of the asymmetry of the probability distribution of a random variable of a binomial distribution.

bin_skewness(10, 0.3)

bin_kurtosis()

This calculates the skewness, or a measure of the “tailedness” of the probability distribution of a random variable of a binomial distribution.

bin_kurtosis(10, 0.3)

Method Functions

plot.bindis()

This function creates a barplot the distribution of the probabilities for each number of successes.

plot.bindis <- function(yes){
  barplot(yes$probability, names.arg = yes$success, xlab = "successes", ylab = "probability")
}

# plotting binomial probability distribution
dis1 <- bin_distribution(trials = 5, prob = 0.5)
plot(dis1)

plot.bincum()

This function creates a line plot of the cumulative distribution of the probabilities for each number of successes.

plot.bincum <- function(cum1){
  plot(cum1$success, cum1$cumulative, type = "o")
  lines(cum1$success, cum1$cumulative)
}

dis2 <- bin_cumulative(trials = 5, prob = 0.5)
plot(dis2)

print.binvar()

This function prints the content of a list of the binomial variables by inputting n trials and at a probability level.

print.binvar <- function(x){
  cat('"Binomial Variable"\n\n')
  cat("Parameters\n", append = TRUE)
  cat("-number of trials:", x$trials, append = TRUE)
  cat("\n-probability:", x$prob, append = TRUE)
}
bin1 <- bin_variable(trials = 10, p = 0.3)
bin1

summary.binvar()

This function contains a full summary description of an object "binvar". It includes the elements: trials, mean, variance, mode, skewness, kurtosis.

summary.binvar <- function(x,...){
  object1 <- list(trials = x$trials, prob = x$prob, mean = aux_mean(x$trials, x$prob), variance = aux_variance(x$trials, x$prob), mode = aux_mode(x$trials, x$prob), skewness = aux_skewness(x$trials, x$prob), kurtosis = aux_kurtosis(x$trials, x$prob) )
  class(object1) = "summary.binvar"

  return(object1)
}
bin_summary <- bin_variable(trials = 10, p = 0.3)
bin_summary1 <- summary(bin_summary)
bin_summary1

print.summary.binvar()

This function prints the content and includes a full summary description of "summary.binvar".

print.summary.binvar <- function(x){
  cat('"Summary Binomial"\n\n')
  cat("Parameters\n", append = TRUE)
  cat("-number of trials:", x$trials, append = TRUE)
  cat("\n-prob of success:", x$prob, append = TRUE)
  cat('\n\n"Measures"')
  cat("\n-mean:", aux_mean(x$trials, x$prob), append = TRUE)
  cat("\n-variance:", aux_variance(x$trials, x$prob), append = TRUE)
  cat("\n-mode:", aux_mode(x$trials, x$prob), append = TRUE)
  cat("\n-skewness:", aux_skewness(x$trials, x$prob), append = TRUE)
  cat("\n-kurtosis:", aux_kurtosis(x$trials, x$prob), append = TRUE)
}

bin1 <- bin_variable(trials = 10, p = 0.3)
binsum1 <- summary(bin1)
binsum1

shefalisastry/workout03 documentation built on May 5, 2019, 12:28 a.m.