Cumulative distribution function

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).

  • df1 (int) – degrees of freedom
  • df2 (int) – degrees of freedom
  • x (float) – positive F variable


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.


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