The binomial distribution model deals with finding the probability of success of an event which has only two possible outcomes in a series of experiments. For example, tossing of a coin always gives a head or a tail. The probability of finding exactly 3 heads in tossing a coin repeatedly for 10 times is estimated during the binomial distribution.

R has four in-built functions to generate binomial distribution. They are described below.

dbinom(x, size, prob)

pbinom(x, size, prob)

qbinom(p, size, prob)

rbinom(n, size, prob)

Following is the description of the parameters used −

x is a vector of numbers.
p is a vector of probabilities.
n is number of observations.
size is the number of trials.
prob is the probability of success of each trial.

dbinom()

This function gives the probability density distribution at each point.

# Create a sample of 50 numbers which are incremented by 1.
x <- seq(0,50,by = 1)
# Create the binomial distribution.
y <- dbinom(x,50,0.5)
# Give the chart file a name.
png(file = "dbinom.png")

# Plot the graph for this sample.
plot(x,y)
# Save the file.
dev.off()

When we execute the above code, it produces the following result −

r 1

pbinom()

This function gives the cumulative probability of an event. It is a single value representing the probability.

# Probability of getting 26 or less heads from a 51 tosses of a coin.
x <- pbinom(26,51,0.5)
print(x)

When we execute the above code, it produces the following result −

[1] 0.610116

qbinom()

This function takes the probability value and gives a number whose cumulative value matches the probability value.

# How many heads will have a probability of 0.25 will come out when a coin
# is tossed 51 times.
x <- qbinom(0.25,51,1/2)
print(x)

When we execute the above code, it produces the following result −

[1] 23

rbinom()

This function generates required number of random values of given probability from a given sample.

# Find 8 random values from a sample of 150 with probability of 0.4.
x <- rbinom(8,150,.4)
print(x)

When we execute the above code, it produces the following result −

[1] 58 61 59 66 55 60 61 67

R – Poisson Regression

Poisson Regression involves regression models in which the response variable is in the form of counts and not fractional numbers. For example, the count of number of births or number of wins in a football match series. Also the values of the response variables follow a Poisson distribution.

The general mathematical equation for Poisson regression is −

log(y) = a + b1x1 + b2x2 + bnxn.....

Following is the description of the parameters used −

y is the response variable.
a and b are the numeric coefficients.
x is the predictor variable.

The function used to create the Poisson regression model is the glm() function.

Syntax

The basic syntax for glm() function in Poisson regression is −

glm(formula,data,family)

Following is the description of the parameters used in above functions −

formula is the symbol presenting the relationship between the variables.
data is the data set giving the values of these variables.
family is R object to specify the details of the model. It’s value is ‘Poisson’ for Logistic Regression.

Example

We have the in-built data set “warpbreaks” which describes the effect of wool type (A or B) and tension (low, medium or high) on the number of warp breaks per loom. Let’s consider “breaks” as the response variable which is a count of number of breaks. The wool “type” and “tension” are taken as predictor variables.

Input Data

input <- warpbreaks

print(head(input))

When we execute the above code, it produces the following result −

      breaks   wool  tension

1     26       A     L

2     30       A     L

3     54       A     L

4     25       A     L

5     70       A     L

6     52       A     L

Create Regression Model

output <-glm(formula = breaks ~ wool+tension, data = warpbreaks,
   family = poisson)
print(summary(output))
When we execute the above code, it produces the following result −
Call:
glm(formula = breaks ~ wool + tension, family = poisson, data = warpbreaks)


Deviance Residuals:
    Min       1Q     Median       3Q      Max 

  -3.6871  -1.6503  -0.4269     1.1902   4.2616 

Coefficients:

            Estimate Std. Error z value Pr(>|z|)   

(Intercept)  3.69196    0.04541  81.302  < 2e-16 ***

woolB       -0.20599    0.05157  -3.994 6.49e-05 ***

tensionM    -0.32132    0.06027  -5.332 9.73e-08 ***

tensionH    -0.51849    0.06396  -8.107 5.21e-16 ***

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 297.37  on 53  degrees of freedom

Residual deviance: 210.39  on 50  degrees of freedom

AIC: 493.06

Number of Fisher Scoring iterations: 4

In the summary we look for the p-value in the last column to be less than 0.05 to consider an impact of the predictor variable on the response variable. As seen the wool type B having tension type M and H have impact on the count of breaks.

So, this brings us to the end of blog. This Tecklearn ‘Binomial Distribution and Poisson Regression in R’ blog helps you with commonly asked questions if you are looking out for a job in Data Science. If you wish to learn R Language and build a career in Data Science domain, then check out our interactive, Data Science using R Language Training, that comes with 24*7 support to guide you throughout your learning period. Please find the link for course details:

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Introduction to R

Introduction to R
Data Exploration
Operators in R
Inbuilt Functions in R
Flow Control Statements & User Defined Functions
Data Structures in R

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Need for Data Manipulation
Introduction to dplyr package
Select (), filter(), mutate(), sample_n(), sample_frac() & count() functions
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Machine Learning Use-Cases
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Machine Learning Categories
Supervised Learning algorithm: Linear Regression and Logistic Regression

Logistic Regression

Intro to Logistic Regression
Simple Logistic Regression in R
Multiple Logistic Regression in R
Confusion Matrix
ROC Curve

Classification Techniques

What are classification and its use cases?
What is Decision Tree?
Algorithm for Decision Tree Induction
Creating a Perfect Decision Tree
Confusion Matrix
What is Random Forest?
What is Naive Bayes?
Support Vector Machine: Classification

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Decision Tree in R
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Gini Index
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Types of Recommendations
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Difference: User-Based and Item-Based Recommendation
Recommendation use cases

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What is Time Series data?
Time Series variables
Different components of Time Series data
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