# Student's t Distribution

Student's t distribution is commonly used to test if the difference between the means of two samples is statistically significant. It is a variation of the normal distribution that takes into account that the mean of a sample is only an estimate for the mean of the population.

The Student t distribution has one shape parameter: the degrees of freedom, commonly denoted by the Greek letter ν. The probability density function is:

The Student t distribution is implemented by the StudentTDistribution class. It has one constructor with the degrees of freedom as its only argument.

The following constructs the Student t distribution with 8 degrees of freedom:

`var studentT = new StudentTDistribution(8);`

The StudentTDistribution class has one specific properties, DegreesOfFreedom, which returns the degrees of freedom of the distribution.

StudentTDistribution has one static (*Shared* in Visual Basic) method, Sample, which generates a
random sample using a user-supplied uniform random number generator. The second and third parameters are the
location and scale parameters of the distribution.

```
var random = new MersenneTwister();
double sample = StudentTDistribution.Sample(random, 8);
```

The above example uses the MersenneTwister class to generate uniform random numbers.

For details of the properties and methods common to all continuous distribution classes, see the topic on continuous distributions..