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Quantile function of the beta distribution

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stats::betaQuantile(a, b)


stats::betaQuantile(a, b) returns a procedure representing the quantile function (inverse) of the cumulative distribution function stats::betaCDF(a, b). For 0 ≤ x ≤ 1, the solution of stats::betaCDF(a, b)(y) = x is given by y = stats::betaQuantile(a, b)(x).

The procedure f := stats::betaQuantile(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 a and b can be converted to positive floating-point numbers and x is a real number between 0 and 1, then the return value f(x) is a floating-point number between 0.0 and 1.0 approximating the real solution y of stats::betaCDF(a, b)(y) = x.

  • f(0), f(0.0), f(1), and f(1.0) produce 0, 0.0, 1, and 1.0, respectively, for all values of a and b.

  • In all other cases, f(x) returns the symbolic call stats::betaQuantile(a, b)(x).

Numerical values of a and b are only accepted if they are positive.

Environment Interactions

The function is sensitive to the environment variable DIGITS which determines the numerical working precision.


Example 1

We evaluate the quantile function with a = π and b = 11 at the point :

f := stats::betaQuantile(PI, 11): f(9/10)

The value f(x) satisfies stats::betaCDF(PI, 11)(f(x)) = x:

stats::betaCDF(PI, 11)(f(0.98765))

delete f:

Example 2

For symbolic arguments, symbolic calls are returned:

f := stats::betaQuantile(a, b): f(x), f(0.9)

If a, b evaluate to real numbers and x to a real number between 0 and 1, then the call f(x) produces a float:

a := 17: b := 6: f(0.9)

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 of the beta distribution: arithmetical expressions representing positive real values.

Return Values


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