Quantile function of the logistic distribution
This functionality does not run in MATLAB.
stats::logisticQuantile(m, s) returns a procedure representing the quantile function (inverse)
of the cumulative distribution function stats::logisticCDF(m, s). For 0 ≤ x ≤ 1, the solution of stats::logisticCDF(m, s)(y) = x is given by
The procedure f := stats::logisticQuantile(m, s) 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, ±infinity, or a symbolic expression:
The call f(x) returns a real floating-point number if x is a floating-point number between 0.0 and 1.0, m can be converted to a real floating-point number, and s can be converted to a positive real floating-point number.
The calls f(0) and f(0.0) produce - infinity; the calls f(1) and f(1.0) produce infinity.
In all other cases, the symbolic expression m + sqrt(3)*s*ln(x/(1-x))/PI is returned.
Numerical values of x are only accepted if 0 ≤ x ≤ 1.
Numerical values of m and s are only accepted if they are real and s is positive.
The function is sensitive to the environment variable DIGITS which determines the numerical working precision.
We evaluate the quantile function with mean m = 0 and standard deviation s = 1 at various points:
f := stats::logisticQuantile(0, 1): f(0), f(1/10), f(0.7), f(0.999999999), f(1)
The value f(x) satisfies stats::logisticCDF(0, 1)(f(x)) = x:
We use symbolic arguments:
f := stats::logisticQuantile(m, s): f(x), f(1/3), f(0.4)
When suitable numerical values are assigned to a and b, the function f starts to produce numerical values:
m := 0: s := 1: f(0.999), f(999/1000)
Numerical values for x are only accepted if 0 ≤ x ≤ 1:
Error: An argument x with 0 <= x <= 1 is expected. [f]
delete f, m, s:
The mean: an arithmetical expression representing a real value
The standard deviation: an arithmetical expression representing a positive real value