April 2016
Intermediate to advanced
384 pages
11h 9m
English
book
Transportation Statistics and Microsimulation
by Clifford Spiegelman, Eun Sug Park, Laurence R. Rilett
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Common Probability Distributions ◾ 85
95th percentile for an F-distribution with 2 and 5 degrees of freedom can
be obtained as 5.786.
5.3.8 Beta Distribution
e parent of the F-distribution is the beta distribution. Besides parenting
the F-distribution the beta distribution is a very exible distribution for
modeling random variables that are restricted to the interval of 0 to 1. Its
pdf is
fx xx(;,)
()
()()
().αβ
αβ
αβ
αβ
=
+
−
−−
Γ
ΓΓ
11
1
(5.28)
It can be seen that when both α and β are equal to 1, the uniform dis-
tribution is a special case of the beta distribution. In Chapter 14 we will
discuss Bayesian estimation. e beta distribution wil