A note on the exact variance of product

淡江大學機構典藏 > 理學院 > 數學學系暨研究所 > 期刊論文 > Item 987654321/41549

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題名:	A note on the exact variance of product
作者:	Chen, Tien-wen;Horn, Der-kie
貢獻者:	淡江大學數學學系
日期:	1973
上傳時間:	2010-01-28 07:48:26 (UTC+8)
出版者:	淡江大學數學學系
摘要:	A simple exact formula for the variance of the product of two random variables, say, x and y, is given as a function of the means and central product-moments of x and y. The usual approximate variance formula for xy is compared with this exact formula; e.g., we note, in the special case where x and y are independent, that the “variance” computed by the approximate formula is less than the exact variance, and that the accuracy of the approximation depends on the sum of the reciprocals of the squared coefficients of variation of x and y. The case where x and y need not be independent is also studied, and exact variance formulas are presented for several different “product estimates.” (The usefulness of exact formulas becomes apparent when the variances of these estimates are compared.) When x and y are independent, simple unbiased estimates of these exact variances are suggested; in the more general case, consistent estimates are presented.
關聯:	Tamkang Journal of Mathematics = 淡江數學 4(2), pp.41-44
顯示於類別:	[數學學系暨研究所] 期刊論文

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