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The Student-t distribution
The Student-t, or simply, the t-, distribution has one parameter ν, known as the
degrees of freedom of the distribution. The calculator provides for values of
the upper-tail (cumulative) distribution function for the t-distribution, function
UTPT, given the parameter ν and the value of t, i.e., UTPT(ν,t) = P(T>t) = 1-
P(T<t). For example, UTPT(5,2.5) = 2.7245…E-2.
The Chi-square distribution
The Chi-square (χ
2
) distribution has one parameter ν, known as the degrees of
freedom. The calculator provides for values of the upper-tail (cumulative)
distribution function for the χ
2
-distribution using [UTPC] given the value of x
and the parameter ν. The definition of this function is, therefore, UTPC(ν,x) =
P(X>x) = 1 - P(X<x). For example, UTPC(5, 2.5) = 0.776495…
The F distribution
The F distribution has two parameters νN = numerator degrees of freedom,
and νD = denominator degrees of freedom. The calculator provides for
values of the upper-tail (cumulative) distribution function for the F distribution,
function UTPF, given the parameters νN and νD, and the value of F. The
definition of this function is, therefore, UTPF(νN,νD,F) = P(ℑ >F) = 1 - P(ℑ <F).
For example, to calculate UTPF(10,5, 2.5) = 0.1618347…
Reference
For additional probability distributions and probability applications, refer to
Chapter 17 in the calculator’s user’s guide.