# Binomial Distribution in R [With Practical Examples]

Filed Under: R Programming

Hello, readers! In this article, we will be focusing on Binomial Distribution in R – dbinom(), qbinom(), rbinom() and pbinom() functions, in detail.

So, let us begin!!

## First, what is Binomial Distribution in R?

The domain of statistics deals with various kinds of distribution to give us an insight of the variation in the data points. By data distribution, we mean the emergence and state of the data in statistical terms such as mean, median, variance, etc.

Now, having an idea about the data distribution helps us analyze the data for further processing.

There are different types of data distributions:

So today, we will be focusing on Binomial Distribution of data in R.

In Binomial Distribution, we tend to estimate the probability of the event where there are only two (2) possible levels of outcomes in the events or series of outcomes. That is, the chances of the outcome groups are just two.

So, we can get the probability that estimates the likelihood of a value accepting one of the two available independent value from the range of parameters.

In R programming, we would be dealing with the below variations of Binomial Probability Distribution–

• dbinom() function
• qbinom() function
• rbinom() function
• pbinom() function

Let us have a look at them one by one!

### 1. R dbinom() function

R provides us with `dbinom()` function that enables us to calculate the probability density values at every point for the data where we expect only two possible outcomes for the event.

So, we tend to understand the binomial data in terms of the probability density values.

Syntax:

```dbinom(x,y,prob)
```
• x: value or vector
• y: number of trails
• prob: probability of success for every trail conducted.

Example:

```info <- seq(0,25,by = 1)

data <- dbinom(info,25,0.5)

plot(info,data)
```

Output:

### 2. R pbinom() function

R `pbinom()` function works upon the cumulative frequency of the data values effectively.

It results as a single probability value that represents the probability of getting a particular value which is less than or equal to ‘x’ from a set of ‘y’ trails or events.

Example:

```data <- pbinom(25,50,0.5)
print(data)
```

Output:

``` 0.5561376
```

### 3. R qbinom() function

R `qbinom()` function offers us the quantile probability for the data values. That is, qbinom() function provides us with the single data value whose cumulative probability matches the probability value.

And, it represents a value which will have a probability ‘a’ for a number of trails ‘x’.

Example:

```data <- qbinom(0.55,50,0.5)
print(data)
```

Output:

```25
```

### 4. R rbinom() function

As the name suggests, the R rbinom() function generates random numbers that follow the binomial distribution of data.

And hence, it would give us ‘x’ numbers that would follow a probability of ‘prob’ within the ‘y’ trail of events successfully.

Example:

```data <- rbinom(10,50,0.8)
print(data)
```

As a result, the function has generated 10 numbers whose probability is 0.8 within 50 trail of events.

Output:

```38 40 44 37 38 42 36 40 45 42
```

## Conclusion

By this, we have come to the end this topic. Feel free to comment below in case you come across any question.

Try implementing the concept of Binomial Distribution using various data values, with the functions mentioned above and do let us know about your understanding in the comment section.

For more such posts related to R programming, Stay tuned and till then, Happy Learning!! ðŸ™‚

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