HP 48gII The F distribution, The Student-tdistribution, The Chi-squaredistribution

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 (χ2) 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 χ2-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.

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