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Probability density function of Fisher's f-distribution (fratio distribution)

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stats::fPDF(a, b)


stats::fPDF(a, b) returns a procedure representing the probability density function

of Fisher's f-distribution with shape parameters a > 0, b > 0.

The procedure f:=stats::fPDF(a, b) can be called in the form f(x) with an arithmetical expression x. The return value of f(x) is either a floating-point number or a symbolic expression:

If x ≤ 0 can be decided, then f(x) returns 0 If x > 0 can be decided, then f(x) returns the value


If x is a floating-point number and both a and b can be converted to positive floating-point numbers, then these values are returned as floating-point numbers. Otherwise, symbolic expressions are returned.

The function f reacts to properties of identifiers set via assume. If x is a symbolic expression with the property x ≤ 0 or x ≥ 0, the corresponding values are returned.

f(- infinity ) and f( infinity ) return 0.

f(x) returns the symbolic call stats::fPDF(a, b)(x) if neither x ≤ 0 nor x > 0 can be decided.

Numerical values for 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. It reacts to properties of identifiers set via assume.


Example 1

We evaluate the probability density function with a = 2 and b = 4 at various points:

f := stats::fPDF(2, 4):
f(-infinity), f(-PI), f(1/2), f(0.5), f(PI), f(infinity)

delete f:

Example 2

If x is a symbolic object without properties, then it cannot be decided whether x ≥ 0 holds. A symbolic function call is returned:

f := stats::fPDF(a, b): f(x)

With suitable properties, it can be decided whether x ≥ 0 holds. An explicit expression is returned:

assume(0 <= x): f(x)

unassume(x): delete f:

Example 3

We use symbolic arguments:

f := stats::fPDF(a, b): f(x)

When numerical values are assigned to a and b, the function f starts to produce numerical values:

a := 2: b := 1: f(3), f(3.0)

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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