t-Student Density Function

A t-Student Density Function is a Probability Density Function that ...

• AKA: t-Student Distribution.
  • …
• Counter-Example(s):
  • a Gaussian Density Function.
• See: Probability Function.

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References

2006

• (Dubnicka, 2006h) ⇒ Suzanne R. Dubnicka. (2006). “The Normal Distribution and Related Distributions - Handout 8. Kansas State University, Introduction to Probability and Statistics I, STAT 510 - Fall 2006.
  • TERMINOLOGY : Suppose that Z N(0, 1) and V 2( ) are independent random variables. Let T = .... Then T is said to have a t distribution with degrees of freedom, denoted T t().
  • PROBABILITY DENSITY FUNCTION: If T t( ), then the pdf of T is given by ...
    • FACTS ABOUT THE t DISTRIBUTION:
    • 1. The pdf is symmetric about 0.
    • 2. The shape of the pdf is similar to that of the standard normal pdf except it is a bit flatter so that its tails are a bit thicker.
    • 3. As  ! 1, the pdf of the t distribution tends to the pdf of the standard normal distribution.
    • 4. If T t( ), then E(T) = 0 provided > 1 and Var(X) = ...

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