Standard Normal Distribution
المؤلف:
Kenney, J. F. and Keeping, E. S
المصدر:
Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand
الجزء والصفحة:
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14-4-2021
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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
over the domain 
.
It has mean, variance, skewness, and kurtosis excess given by
The first quartile of the standard normal distribution occurs when 
, which is
(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."
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