Statistical Science

Closed Form Summation for Classical Distributions: Variations on a Theme of De Moivre

Persi Diaconis and Sandy Zabell

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Abstract

De Moivre gave a simple closed form expression for the mean absolute deviation of the binomial distribution. Later authors showed that similar closed form expressions hold for many of the other classical families. We review the history of these identities and extend them to obtain summation formulas for the expectations of all polynomials orthogonal to the constants.

Article information

Source
Statist. Sci., Volume 6, Number 3 (1991), 284-302.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.ss/1177011699

Digital Object Identifier
doi:10.1214/ss/1177011699

Mathematical Reviews number (MathSciNet)
MR1144242

Zentralblatt MATH identifier
0955.60500

JSTOR
links.jstor.org

Keywords
Binomial distribution Stirling's formula history of probability Pearson curves Stein's identity mean absolute deviation

Citation

Diaconis, Persi; Zabell, Sandy. Closed Form Summation for Classical Distributions: Variations on a Theme of De Moivre. Statist. Sci. 6 (1991), no. 3, 284--302. doi:10.1214/ss/1177011699. https://projecteuclid.org/euclid.ss/1177011699


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