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Quantile function of Fisher's f-distribution (fratio distribution)

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stats::fQuantile(a, b)


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.

Environment Interactions

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.


Example 1

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:

stats::fCDF(PI, 11)(f(0.987654321))

delete f:

Example 2

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: Argument x must be between 0 and 1. [f]
delete f, a, b:


a, b

The shape parameters: arithmetical expressions representing positive real values

Return Values


See Also

MuPAD Functions

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