Quantile function of the uniform distribution

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.


stats::uniformQuantile(a, b)


stats::uniformQuantile(a, b) returns a procedure representing the quantile function (inverse) of the cumulative distribution function stats::uniformCDF(a, b) of the uniform distribution on the interval [a, b]. For 0 ≤ x ≤ 1, the quantile function is given by .

The procedure f := stats::uniformQuantile(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 is a real number between 0 and 1 and a and b can be converted to floating-point numbers, then f(x) returns the value a + x (b - a) as a floating-point number. Otherwise, this value is returned as a symbolic expression.

Numerical values of x are only accepted if 0 ≤ x ≤ 1.

Numerical values for a and b are only accepted if they are real and ab.

Environment Interactions

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


Example 1

We evaluate the quantile function over the interval at various points:

f := stats::uniformQuantile(2, 11/4):
f(0), f(1/10), f(0.5), f(1 - 10^(-5)), f(1)

delete f:

Example 2

We use symbolic arguments:

f := stats::uniformQuantile(a, b): f(x), f(9/10)

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

a := 3: b := 11/2: f(0.999), f(1 - sqrt(2)/10^5)

delete f, a, b:


a, b

arithmetical expressions representing real values; ab is assumed.

Return Values


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