Student's t-distribution

Student's t-distribution is a continuous one-dimensional distribution having one parameter - number of degrees of freedom. The form of Student's distribution looks like a form of normal distribution (the more degrees of freedom it has, the less difference from the normal distribution we can see). The difference is that the Student's distribution tails are slower tending to zero than the tails of normal distribution.

Usually Student's distribution is used to estimate the mean of normal random variables. Let X₁, ..., X_n - independent normal random variables having mean μ and variance σ². Then, we can get the following estimates for μ and σ²:

At that, the mean estimate does not equal μ, it fluctuates around this value. The difference between the true mean and its estimate divided by the scaling coefficient

has the distribution which is called Student's distribution with N degrees of freedom. There are some other divisions of statistics where we can find random variables having Student's distribution. For example, Student's distribution is used to estimate the significance of the Pearson's correlation coefficient.

Algorithms

StudentTDistribution subroutine is used to calculate the probability density function of Student's distribution. Inverse cumulative distribution function is calculated by using the InvStudentTDistribution subroutine.

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