Cumulative distribution function¶
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fdtr(df1, df2, x)¶ Returns the area from zero to x under the F density function (also known as Snedcor’s density or the variance ratio density).
Parameters:
Description¶
This is the density of x = (u1/df1)/(u2/df2), where u1 and u2 are random variables having Chi square distributions with df1 and df2 degrees of freedom, respectively.
The incomplete beta integral is used according to the formula:
P(x) = incbet(df1/2, df2/2, (df1 * x/(df2 + df1*x))
The arguments a and b are greater than zero, and x is nonnegative.
Accuracy¶
Tested at random points (a, b, x).
| x | a, b | relative error | |||
|---|---|---|---|---|---|
| arithmetic | domain | domain | # trials | peak | rms |
| IEEE | 0, 1 | 0, 100 | 100000 | 9.8e-15 | 1.7e-15 |
| IEEE | 1, 5 | 0, 100 | 100000 | 6.5e-15 | 3.5e-16 |
| IEEE | 0, 1 | 1, 10000 | 100000 | 2.2e-11 | 3.3e-12 |
| IEEE | 1, 5 | 1, 10000 | 100000 | 1.1e-11 | 1.7e-13 |
See also incbet().
Error messages¶
| message | condition | value returned |
|---|---|---|
| fdtr domain | a<0, b<0, x<0 | 0 |