Quantile function of Fisher's f-distribution (fratio distribution)
This functionality does not run in MATLAB.
stats::fQuantile(a, b) returns a procedure representing the quantile function (inverse) of the cumulative distribution function stats::fCDF(a, b). For 0 ≤ x ≤ 1, the solution of stats::fCDF(a, b)(y) = x is given by y = stats::fQuantile(a, b)(x).
The procedure f:=stats::fQuantile(a, b) can be called in the form f(x) with arithmetical expressions x. The return value of f(x) is either a floating-point number, infinity, or a symbolic expression:
If x is a real number between 0 and 1 and a and b can be converted to positive floating-point numbers, then f(x) returns a positive floating-point number approximating the solution y of stats::fCDF(a, b)(y) = x.
The calls f(0) and f(0.0) produce 0.0 for all values of a and b.
The calls f(1) and f(1.0) produce infinity for all values of a and b.
In all other cases, f(x) returns the symbolic call stats::fQuantile(a, b)(x).
Numerical values of x are only accepted if 0 ≤ x ≤ 1.
Numerical values of a and b are only accepted if they are real and positive.
The function is sensitive to the environment variable DIGITS which determines the numerical working precision. The procedure generated by stats::fQuantile is sensitive to properties of identifiers, which can be set via assume.
We evaluate the quantile function with a = π and b = 11 at various points:
f := stats::fQuantile(PI, 11): f(0), f(1/10), f(0.5), f(1 - 10^(-10)), f(1)
The value f(x) satisfies stats::fCDF(π, 11)(f(x)) = x:
We use symbolic arguments:
f := stats::fQuantile(a, b): f(x), f(9/10)
When positive real values are assigned to a and b, the function f starts to produce floating-point values:
a := 17: b := 6: f(0.999), f(1 - sqrt(2)/10^5)
Numerical values for x are only accepted if 0 ≤ x ≤ 1:
Error: An argument x with 0 <= x <= 1 is expected. [f]
delete f, a, b:
The shape parameters: arithmetical expressions representing positive real values