stats
::chisquareCDF
Cumulative distribution function of the chisquare distribution
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stats::chisquareCDF(m
)
stats::chisquareCDF(m)
returns a procedure
representing the cumulative distribution function
of the chisquare distribution with mean m > 0.
The procedure f := stats::chisquareCDF(m)
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 ≤ 0 can
be decided, then f(x)
returns 0.
If x > 0 can
be decided, then f(x)
returns the value .
If x is a floatingpoint number and m can be converted to a positive floatingpoint number, then these values are returned as floatingpoint numbers. Otherwise, symbolic expressions are returned.
The function f
reacts to properties of identifiers
set via assume
.
If x is
a symbolic expression with the property x ≤
0 or x ≥
0, the corresponding values are returned.
f(x)
returns the symbolic call stats::chisquareCDF(m)(x)
if
neither x ≤ 0 nor x >
0 can be decided.
Numerical values for m
are only accepted
if they are real and positive.
Note that, for large m
, exact results may
be costly to compute. If floatingpoint values are desired, it is
recommended to pass floatingpoint arguments x
to f
rather
than to compute exact results f(x)
and convert
them via float
.
Cf. Example 4.
The function is sensitive to the environment variable DIGITS
which
determines the numerical working precision.
We evaluate the cumulative distribution function with mean m = 2 at various points:
f := stats::chisquareCDF(2): f(infinity), f(3), f(1/2), f(0.5), f(PI), f(infinity)
delete f:
If x
is a symbolic object without properties,
then it cannot be decided whether x ≥
0 holds. A symbolic function call is returned:
f := stats::chisquareCDF(m): f(x)
With suitable properties, it can be decided whether x ≥ 0 holds. An explicit expression is returned:
assume(0 <= x): f(x)
For integer values of m
, the special function igamma
can be expressed
in terms of more elementary functions:
m := 6: f(x)
m := 5: f(x)
unassume(x): delete f, m:
We use a symbolic mean m
:
f := stats::chisquareCDF(m): f(3), f(3.0)
When a numerical value is assigned to m
,
the function f
starts to produce numerical values:
m := PI: f(3), f(3.0)
delete f, m:
We consider a chisquare distribution with large mean m
= 1000:
f := stats::chisquareCDF(1000):
For floatingpoint approximations, one should not compute an
exact result and convert it via float
. For large mean m,
it is faster to pass a floatingpoint argument to f
.
The following call takes some time, because an exact computation of
the huge integer gamma(m/2) = gamma(500) = 499!
is
involved:
float(f(1023))
The following call is much faster:
f(float(1023))
delete f:

The mean: an arithmetical expression representing a positive real value 