“Geometric Distribution”的概念、定义、习题解题方法及翻译-数学辞典

单词

Geometric Distribution

释义

Geometric Distribution

A distribution such that

(1)

where

and for

2, .... The distribution is normalized since

(2)

The Moment-Generating Function is

(3)

Therefore,

and

so the Mean, Variance, Skewness, and Kurtosis are given by

In fact, the moments of the distribution are given analytically in terms of the Polylogarithm function,

(19)

For the case

(corresponding to the distribution of the number of Coin Tosses needed to win in the Saint Petersburg Paradox) this formula immediately gives

so the Mean, Variance, Skewness, and Kurtosis in this case are

The first Cumulant of the geometric distribution is

(28)

and subsequent Cumulants are given by the Recurrence Relation

(29)

See also Saint Petersburg Paradox

References

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 531-532, 1987.

Spiegel, M. R. Theory and Problems of Probability and Statistics. New York: McGraw-Hill, p. 118, 1992.

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。