Quantile function of the uniform distribution
This functionality does not run in MATLAB.
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 a ≤ b.
The function is sensitive to the environment variable DIGITS which determines the numerical working precision.
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)
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:
arithmetical expressions representing real values; a ≤ b is assumed.