The binomial distribution is also known as a discrete probability distribution, which is used to find the probability of success of an event. The event has only two possible outcomes in a series of experiments. The tossing of the coin is the best example of the binomial distribution. When a coin is tossed, it gives either a head or a tail. The probability of finding exactly three heads in repeatedly tossing the coin ten times is approximate during the binomial distribution.
R allows us to create binomial distribution by providing the following function:
These functions can have the following parameters:
| S.No | Parameter | Description |
|---|---|---|
| 1. | x | It is a vector of numbers. |
| 2. | p | It is a vector of probabilities. |
| 3. | n | It is a vector of observations. |
| 4. | size | It is the number of trials. |
| 5. | prob | It is the probability of the success of each trial. |
Let’s start understanding how these functions are used with the help of the examples
dbinom(): Direct Look-Up, Points
The dbinom() function of R calculates the probability density distribution at each point. In simple words, it calculates the density function of the particular binomial distribution.
Example
# Creating a sample of 100 numbers which are incremented by 1.5. x <- seq(0,100,by = 1) # Creating the binomial distribution. y <- dbinom(x,50,0.5) # Giving a name to the chart file. png(file = "dbinom.png") # Plotting the graph. plot(x,y) # Saving the file. dev.off()
Output:
pbinom():Direct Look-Up, Intervals
The dbinom() function of R calculates the cumulative probability(a single value representing the probability) of an event. In simple words, it calculates the cumulative distribution function of the particular binomial distribution.
Example
# Probability of getting 20 or fewer heads from 48 tosses of a coin. x <- pbinom(20,48,0.5) #Showing output print(x)
Output:
qbinom(): Inverse Look-Up
The quinoa() function of R takes the probability value and generates a number whose cumulative value matches the probability value. In simple words, it calculates the inverse cumulative distribution function of the binomial distribution.
Let’s find the number of heads that have a probability of 0.45 when a coin is tossed 51 times.
Example
# Finding number of heads with the help of qbinom() function x <- qbinom(0.45,48,0.5) #Showing output print(x)
Output:
rbinom()
The rbinom() function of R is used to generate a required number of random values for a given probability from a given sample.
Let’s see an example in which we find nine random values from a sample of 160 with a probability of 0.5.
Example
# Finding random values x <- rbinom(9,160,0.5) #Showing output print(x)
Output:
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