Encyclopedia > Characteristic function

  Article Content

Characteristic function

Some mathematicians use the phrase characteristic function synonymously with "indicator function". The indicator function of a subset A of a set B is the function with domain B, whose value is 1 at each point in A and 0 at each point that is in B but not in A.

In probability theory, the characteristic function of any probability distribution on the real line is given by the following formula, where X is any random variable with the distribution in question:

Here t is a real number and E denotes the expected value.

If X is a vector-valued random variable, one takes the argument t to be a vector and tX to be a dot product.

Related concepts include the moment-generating function and the probability-generating function.

All Wikipedia text is available under the terms of the GNU Free Documentation License

  Search Encyclopedia

Search over one million articles, find something about almost anything!
  Featured Article
Sanskrit language

... was composed in the middle of the second millennium BC. The Vedic form survived until the middle of the first millennium BC. Around this time, as Sanskrit made the ...

This page was created in 70.4 ms