Want to share your content on R-bloggers? click here if you have a blog, or here if you don't. Binomial Distribution in R, Binomial distribution was invented by  James Bernoulli which was posthumously published in 1713.

Let n ( finite) Bernoulli trials be conducted with probability “p” of success and “q” of a failure.

The probability of x success out of n Bernoulli trials is given by

f(x)=(ncx)pxqn-x

where x=0, 1 , 2, …..,n. 0<=p<=1 and p+q=1

## Important Features

1) If n=1, the binomial distribution reduces to Bernoulli distribution.

2) Binomial distribution has two parameters n and p.

3) The mean of the binomial distribution is np.

4) The variance of a binomial distribution is npq.

5) The moment generating function of a binomial distribution is (q+pet)n.

6) The characteristic function of b (n, p) is (q+peit)n

Naive Bayes Classification in R » Prediction Model »

## Binomial Distribution in R

Let’s see how to plot binomial distribution in R.

First need to create a probability mass function while using dbinom(x, size, prob)

plot(x, y, type = ‘h’) to plot the probability mass function.

As discussed earlier we need to mention the number of trials and probability of success on a given trial in the dbinom() function.

Let’s take an example, binomial distribution with size = 50 and prob = 0.45,

success <- 0:50
plot(success, dbinom(success, size=50, prob=.45),type='h') The x-axis indicates the number of successes and the y-axis displays the probability of obtaining that number of successes in 50 trials.

Principal component analysis (PCA) in R »

Let’s change the title and axis labels for better visualization.

success <- 0:50
plot(success,dbinom(success,size=50,prob=.45),
type='h',
main='Binomial Distribution (n=50, p=0.45)',
ylab='Probability',
xlab ='Successes',
lwd=3) For actual probabilities, you can make use of the below code.

options(scipen=999)
success <- 0:50
dbinom(success, size=50, prob=.45)
 0.000000000000104264022198 0.000000000004265346362643 0.000000000085500806632979 0.000000001119283286831728
 0.000000010760382507495824 0.000000080996333783695804 0.000000497022957309043696 0.000002556118066160793185
 0.000011241110131866213424 0.000042920602321670976069 0.000143979111424515039339 0.000428367604238223827727
 0.001139068402178920400014 0.002724205549267060596369 0.005890652259129421607076 0.011567098981563259108007
 0.020702478290865976989776 0.033876782657780636631717 0.050815173986670875150296 0.070022823484025109586071
 0.088801671600195419831181 0.103794161610618038138476 0.111943290001534315192266 0.111500826404690306370426
 0.102631442486135343594711 0.087330027424566109006676 0.068703692903941820935287 0.049966322111957714446895
 0.033581261938880557771370 0.020843541893098262163253 0.011937664902410870595983 0.006301406693354699890819
 0.003061194728874021189075 0.001366153019497504247579 0.000558880780703519723998 0.000209035928367031056995
 0.000071262248306942535775 0.000022061531416891290479 0.000006175117645397758965 0.000001554575071568665523
 0.000000349779391102952633 0.000000069800765408571026 0.000000012237796532671604 0.000000001862835835840054
 0.000000000242476565408934 0.000000000026451988953702 0.000000000002352449610507 0.000000000000163806936128
 0.000000000000008376491052 0.000000000000000279734395 0.000000000000000004577472

Adding text labels to ggplot2 Bar Chart »

The post Binomial Distribution in R-Quick Guide appeared first on finnstats.