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 floatingpoint number, ±infinity
, or a symbolic
expression:
The call f(x)
returns a real floatingpoint
number if x
is a floatingpoint number between 0.0
and 1.0
, m
can
be converted to a real floatingpoint number, and s
can
be converted to a positive real floatingpoint 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/(1x))/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
:
stats::logisticCDF(0, 1)(f(0.987654321))
delete f:
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:
f(0.5)
f(2)
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 