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Nonnormality and Product Moment Correlation

The Journal of Experimental Education, 1961
ALTHOUGH THE Pearson product moment correlation coefficient has been used as an index of r e 1 at ionship between two variables for more than 50 years, there continues to be considerable controversy concerning the circumstances under which its use is appropriate.
Raymond C. Norris, Howard F. Hjelm
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On the Convergence of Product Moments

Canadian Mathematical Bulletin, 1967
Let Ⓗ be an abstract space and for every positive integer n let Fn, θ(x, y), θ ∈ Ⓗ, be a family of distribution n, 0 function s of random variables (Xn, Yn)θ, θ ∈ Ⓗ. For every θ ∈ Ⓗ, Eθg (Xn, Yn) will denote the expected value of the function g of (Xn, Yn
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Lmoment diagrams should replace product moment diagrams

Water Resources Research, 1993
It is well known that product moment ratio estimators of the coefficient of variationCν, skewness γ, and kurtosis κ exhibit substantial bias and variance for the small (n≤ 100) samples normally encountered in hydrologic applications. Consequently,Lmoment ratio estimators, termedLcoefficient of variation τ2,Lskewness τ3, andLkurtosis τ4are now advocated
Richard M. Vogel, Neil M. Fennessey
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Product Moments of Multivariate Random Vectors

Communications in Statistics - Theory and Methods, 2003
Abstract We derive a formula for the product moment in terms of the joint survival function when (X 1,…,X p) is a non-negative random vector. In the course of the derivation, we present an independent approach for deriving the formula for (which is already known in the literature).
Saralees Nadarajah, Kosto Mitov
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Products vs. Money Moments

2018
An overview of retail banking products and why banks need to stop trying to sell products and realize they are purveyors of emotionally charged services. Outlining the concept of money moments and describing the origins and fundamentals of invisible banking.
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On interpreting the product moment correlation coefficient*

Statistica Neerlandica, 1980
Abstract  In interpreting the product moment correlation coefficient we can take advantage of the fact that functions of it exist which admit interpretation as probabilities of error in certain situations.
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The Product Moment Correlation

2012
It seems most living creatures observe relationships, perhaps as a survival instinct. We observe signs that the weather is changing and prepare ourselves for the winter season. We observe that when seat belts are worn in cars that the number of fatalities in car accidents decrease.
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Range Restrictions for Product-Moment Correlation Matrices

Psychometrika, 1981
It is well-known that for a trivariate distribution if two correlations are fixed the remaining one is constrained. Indeed, if one correlation is fixed, then the remaining two are constrained. Both results are extended to the case of a multivariate distribution. The results are applied to some special patterned matrices.
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Pearson Product Moment Coefficient of Correlation

1978
In the first seven chapters of this text, we have dealt with situations in which each one of the N people in our study had a score, X, on some test or other measurement. It is now time for us to expand our view and consider the perfectly realistic situation in which each individual may have scores on two (or more) different variables.
Albert K. Kurtz, Samuel T. Mayo
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The Product-Moment Coefficient of Correlation

1984
The values of one variable are often found to vary in accordance with the values of another. Yields of crops, for instance, vary with rainfall. The numbers of shops in different towns vary according to the population sizes of the towns. The amounts spent on education in developing countries vary with the amounts spent on medical services.
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