Understanding Student's t-distribution

Student's t-distribution is also known as t-distribution. It is applied to estimate the mean of the population from a normal distribution. Moreover, it is the basis of conducting Student's t-test. In the following recipe, we will introduce how to use R to perform Student's t-distribution.

Getting ready

In this recipe, you need to prepare your environment with R installed.

How to do it…

Please perform the following steps to generate samples from t-distribution:

1. First, we can use rt to generate three samples with the degree of freedom equal to 10:

   > set.seed(123)
   > rt(3, df = 10)
   [1] -0.6246844 -1.3782806 -0.1181245
   

2. Then, we use dt to obtain the density at x=3 with a degree of freedom equal to 10:

   > dt(3,df=10)
   [1] 0.01140055
   

3. Furthermore, we can visualize the Student's t-distribution's degree of freedom equals 1:

   > plot(seq(-5,5,0.1), dt(seq(-5,5,0.1), df = 1), type='l', main="Student's t-distribution of df = 1")
   

   

   Figure 18: Student's t-distribution...