Standard Normal Distribution

A standard normal distribution is a normal distribution with zero mean () and unit variance (), given by the probability density function and distribution function

			(1)
			(2)

over the domain .

It has mean, variance, skewness, and kurtosis excess given by

			(3)
			(4)
			(5)
			(6)

The first quartile of the standard normal distribution occurs when , which is

			(7)
			(8)

(OEIS A092678; Kenney and Keeping 1962, p. 134), where  is the inverse erf function. The absolute value of this is known as the probable error.

REFERENCES:

Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 129 and 134, 1962.

Sloane, N. J. A. Sequence A092678 in "The On-Line Encyclopedia of Integer Sequences."