R - Binomial Distribution
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.
Live Demo# 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 −
pbinom()
This function gives the cumulative probability of an event. It is a single value representing the probability.
Live Demo# 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.
Live Demo# 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.
Live Demo# 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