Statistics
CharacteristicFunction
compute the characteristic function
Calling Sequence
Parameters
Description
Computation
Options
Examples
References
CharacteristicFunction(X, t, options)
X
-
algebraic; random variable or distribution
t
algebraic; point
options
(optional) equation of the form numeric=value; specifies options for computing the Characteristic function of a random variable
The CharacteristicFunction function computes the Characteristic function of the specified random variable at the specified point.
The first parameter can be a distribution (see Statistics[Distribution]), a random variable, or an algebraic expression involving random variables (see Statistics[RandomVariable]).
By default, all computations involving random variables are performed symbolically (see option numeric below).
For more information about computation in the Statistics package, see the Statistics[Computation] help page.
The options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[RandomVariables] help page.
numeric=truefalse -- By default, the Characteristic function is computed using exact arithmetic. To compute the Characteristic function numerically, specify the numeric or numeric = true option.
withStatistics:
Compute the Characteristic function of the beta distribution with parameters p and q.
CharacteristicFunctionΒp,q,t
hypergeomp,p+q,It
Define new distribution.
T≔Distribution`=`PDF,t↦piecewiset<0,0,t<1,6⋅t⋅1−t,0:
X≔RandomVariableT:
CDFX,t
0t≤0−2t3+3t2t≤111<t
CharacteristicFunctionX,t
6−2IⅇIt−ⅇItt+2I−tt3
Another distribution
U≔Distribution`=`CDF,t↦Ft,`=`PDF,t↦ft:
Y≔RandomVariableU:
CDFY,t
Ft
CharacteristicFunctionY,t
2π
Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.
See Also
Statistics[Computation]
Statistics[Distributions]
Statistics[RandomVariables]
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