Cumulative distribution function of the exponential distribution
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stats::exponentialCDF(a
, b
)
stats::exponentialCDF(a, b)
returns a procedure
representing the cumulative distribution function
of the exponential distribution with real location parameter a and scale parameter b > 0.
The procedure f := stats::exponentialCDF(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 ≤ a can
be decided, then f(x)
returns 0.
If x > a can
be decided, then f(x)
returns the value
.
If x is a floatingpoint number and both a and b can be converted to floatingpoint numbers, 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 ≤ a or x ≤ a,
the corresponding values are returned.
f(x)
returns the symbolic call stats::exponentialCDF(a,
b)(x)
if neither x ≤ a nor x > a can
be decided.
Numerical values for a and b are only accepted if they are real and b is positive.
The function is sensitive to the environment variable DIGITS
which
determines the numerical working precision.
We evaluate the cumulative distribution function with a = 0 and b = 1 at various points:
f := stats::exponentialCDF(0, 1): f(infinity), f(PI), f(1/2), f(0.5), f(PI), f(infinity)
delete f:
If a
or x
are symbolic
objects without properties, then it cannot be decided whether x ≥ a holds.
A symbolic function call is returned:
f := stats::exponentialCDF(a, b): f(x)
With suitable properties, it can be decided whether x ≥ a holds. An explicit expression is returned:
assume(a <= x): f(x)
Note that assume(a <= x)
attached properties
both to a
and x
. When cleaning
up, the properties have to be removed separately for a
and x
via unassume
:
unassume(a): unassume(x): delete f:
We use symbolic arguments:
f := stats::exponentialCDF(a, b): f(x)
When numerical values are assigned to a and b,
the function f
starts to produce numerical values:
a := 0: b := 2: f(3), f(3.0)
delete f, a, b:

The location parameter: an arithmetical expression representing a real value 

The scale parameter: an arithmetical expression representing a positive real value 