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R Statistic

Binomial distribution in R

We have one experiment with two possible results (success and fail) where the probability of success is Π. In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments.

If we repeat independent trials in the same conditions the variable…

x = number of success in n trails

follow a binomial distribution of n parameters and Π, and we write X ∈ Bin (n, Π). We can calculate mean and standard deviation too. The function dbinom in R calculate the odds of one variable follow binomial distribution. We can use..

dbinom(x, size, prob, log = FALSE)
pbinom(q, size, prob, lower.tail = TRUE, log.p = FALSE)
qbinom(p, size, prob, lower.tail = TRUE, log.p = FALSE)
rbinom(n, size, prob)

We show this with an example in R. 

n=8
prob=0.15
x=0:n
p=dbinom(x, size=n, prob=prob)
# p1=round(p,4)
names(p)=x
r=barplot(p,col=’grey85′,ylim=c(0,0.45),
          main=paste(“Bin(n=8,p=”,prob,”)”,sep=””))
text(r,p,round(p,2),pos=3,cex=0.7)

Showing binomial datas in R

We get the Fig. 1 for one probability of 0.15, Fig. 2 for 0.25, Fig 3. for 0.50, Fig 4. for 0.75.

binomial
Figure 1. Binomial distribution, prob 0.15
binomial
Figure 2. prob 0.25
binomial
Figure 3. prob 0.50
Figure 4. prob 0.75

The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution, not a binomial one. However, for N much larger than n, the binomial distribution remains a good approximation, and is widely used. We can work in R and see what is the behaviour of our data follow this distribution. Make sure your data are following this distribution to fit them. Now is your time to move.

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