The F cumulative distribution function is given by the integral
The inverse distribution function
FInv(p;n, m) gives the value of
x for which the integral
FDist(x;n, m) has the value p. These
function names automatically turn gray when they are entered in mathematics
mode. The relationship between these two functions is illustrated in the
following examples.
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= | 4.3419×10-2 | |
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= | .1 | |
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= | .9 | |
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= | 3.7797 |
Standard F distribution tables list some of the values of the inverse F
distribution function. Thus, for example, the 4.4th percentile for the F
distribution having degrees of freedom
3, 5
is
FInv(.044;3, 5) = .1, and the 90th percentile for the F distribution having
degrees of freedom
2, 5
is
FInv(.90;2, 5) = 3.7797.
The following plots show distribution functions
FDist(x;n, m) and
density functions
FDen(x;n, m) for
n, m
=
1, 1
,
2, 5
,
3, 15
, and
0≤x≤5.