# Probability integral

From AMS Glossary

## probability integral

The classical form (still widely used in engineering work) of the definite integral of the special normal distribution for which the mean μ = 0 and standard deviation σ = .

Geometrically, the probability integral equals the area under this density curve between - Modern statistical usage favors the unit normal variate

*z*and*z*, where*z*is an arbitrary positive number. Often denoted by the symbol erf*z*(read "error function of*z*") the probability integral is defined thus:*u*, which is such that μ = 0 and σ = 1. The relation between the probability integral erf*z*and the distribution function*F*(*u*) of the unit normal variate*u*is as follows:*See*unit normal distribution.