Two common probabilities you will calculate in statistics is P(X = x) and P(X ≤ x). R provides your some simple ways to calculate these probabilities. In this article, we will learn how to calculate probabilities for Discrete Distributions in R.
To calculate P(X = x), we can use the density functions. R has
many functions for this all prefixed with
d. For example, we can use
dbinom to calculate the binomial distribution.
dbinom(7, size = 100, prob = 0.5)
##  1.262774e-20
The above shows us the P(X = 7) when X is from a Bin(100, .5) distribution.
To calculate the probability that an item is less than x or
P(X ≤ x), we can use the probability mass function, or the CDF. R
has many methods all prefixed with
p. For example, we can use
for the binomial distribution.
pbinom(7, size = 10, prob = 0.5)
##  0.9453125
The above shows us the P(X ≤ 7) when X is from a Bin(10, .5) distribution.
Next, we can take a look at getting the quantile from a distribution.
This is also known as the inverse CDF. To do this, we can use the
distribution functions prefixed with a
q. In our case, we will use
qbinom(0.9453125, size = 10, prob = 0.5)
##  7
In the above example, we put in the P(X ≤ 7) which we got from our previous example. We can see the value returned is 7 which is the value of X we used in our pdf.
We can also generate random samples from any of the distributions.
Again, we follow the same pattern of having a short name for the
binom, preceded by a prefix,
r. To generate
random samples, we can use
rbinom(10, size = 10, prob = .5)
##  2 3 8 6 9 6 4 6 4 7
The example above will generate a random sample, which is multiple values of X from a Bin(10, .5) distribution. In our case, we supplied 10 as the first argument, thus our sample size will be 10.
R provides many other continuous distributions with the same structure as above. Here is a list of many distributions and their respective functions.
|Wilcoxon Rank Sum Statistic||pwilcox||qwilcox||dwilcox||rwilcox|
|Wilcoxon Signed Rank Statistic||psignrank||qsignrank||dsignrank||rsignrank|