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 n 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.
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.
