Lecture 6 Gamma distribution, -distribution, Student t-distribution


What is the gamma distribution?

    The gamma distribution is a continuous distribution depending on two parameters, and . It gives rise to three special cases 1The exponential distribution( =1;f= 1 2The r-Erlang distribution( =r;f= 1 3The chi-squared distribution( =  2

What is Student's t distribution?

    Student’s t Distribution De?nition. For independent r.v.’s Z and U where Z ? N(0, 1) U ? ? 2 r the distribution of T = Z / U/r is the t distribution with r degrees of freedom.

Do you use induction or induction in the gamma distribution?

    In general you use induction. We will need (half integers) e.g. 5 2 Theorem 1 2 ! = p ? Lecture 14 : The Gamma Distribution and its Relatives 18/ 18 I won’t prove this. Try it. 3 2 1 2

What is the gamma distribution of the Erlang distribution?

    Z1 1 f(x)dx=1 The key point of the gamma distribution is that it is of the form (constant) (power of x) ecx;c>0: The r-Erlang distribution from Lecture 13 is almost the most general gamma distribution.
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