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Quantile function of the logistic distribution

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stats::logisticQuantile(m, s)


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.

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 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:

stats::logisticCDF(0, 1)(f(0.987654321))

delete f:

Example 2

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: Argument x must be between 0 and 1. [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

Return Values


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