Probability Integral

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Probability Integral

 

the name of several mutually related special functions. The integral

is called the Gaussian probability integral. For a random quantity X having a normal distribution with an expected value 0 and variance σ2, the probability of the inequality ǀXǀ ≤ x is equal to Φ(x/≤. In addition to this, the name “probability integral” is used for the integrals

The latter function is usually designated erf (x) (from “error function”).

REFERENCE

Bol’shev, L. N., and N.V. Smirnov. Tablitsy matematicheskoi statistiki. Moscow, 1965.
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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