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

over the domain .

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

The probit function gives the quantile function of the standard normal distribution. In particular, the first quartile occurs when , which gives

(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.

See also

Erf, Normal Distribution, Normal Distribution Function, Probability Integral, Probable Error, Tetrachoric Function

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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."

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Standard Normal Distribution

Cite this as:

Weisstein, Eric W. "Standard Normal Distribution." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StandardNormalDistribution.html

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