Quantile function of the uniform distribution
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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 floatingpoint number or a symbolic expression:
If x
is a real number between 0
and 1
and a
and b
can
be converted to floatingpoint numbers, then f(x)
returns
the value a + x (b  a) as
a floatingpoint 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)
delete f:
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. 