Abstract
Abstract 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.
Keywords
Variance (accounting)MathematicsStatisticsEconometricsMathematical economicsApplied mathematicsEconomics
Affiliated Institutions
Related Publications
Explicit local exchange-correlation potentials
The possibilities of the Hohenberg-Kohn-Sham local density theory are explored in view of recent advances in the theory of the interacting electron gas. The authors discuss and ...
Stable signal recovery from incomplete and inaccurate measurements
Abstract Suppose we wish to recover a vector x 0 β β π (e.g., a digital signal or image) from incomplete and contaminated observations y = A x 0 + e ; A is an π Γ π matrix wi...
Balanced Repeated Replications for Standard Errors
Abstract Balanced repeated replications (BRR) is a general method for computing standard errors. It is useful when mathematical distribution theory is impractical or lacking, an...
Compressed sensing and best π-term approximation
Compressed sensing is a new concept in signal processing where one seeks to minimize the number of measurements to be taken from signals while still retaining the information ne...
Upsilon production cross section in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi><mml:mi>p</mml:mi></mml:math>collisions at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>=</mml:mo><mml:mn>7</mml:mn><mml:mtext>β</mml:mtext><mml:mtext>β</mml:mtext><mml:mi>TeV</mml:mi></mml:math>
The Y(1S), Y(2S), and Y(3S) production cross sections in proton-proton collisions at root s = 7 TeV are measured using a data sample collected with the CMS detector at the LHC, ...
Publication Info
- Year
- 1960
- Type
- article
- Volume
- 55
- Issue
- 292
- Pages
- 708-708
- Citations
- 258
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
258
OpenAlex
Cite This
Leo A. Goodman
(1960).
On the Exact Variance of Products.
Journal of the American Statistical Association
, 55
(292)
, 708-708.
https://doi.org/10.2307/2281592
Identifiers
- DOI
- 10.2307/2281592