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The Point Evaluation Method for Approximating Function Means, Variances and Covariances

✍ Scribed by B. F. J. Manly

Publisher
John Wiley and Sons
Year
1986
Tongue
English
Weight
360 KB
Volume
28
Category
Article
ISSN
0323-3847

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✦ Synopsis

A perennial problem in etatiatice is the determination of bieeee, variences and coverianow for funotiom of random variable8 Xi. X,, ..., X, which themselves have 4 known distribution. A oommon approaoh in h u g h equatione baeed upon Taylor d e a approximatione but a "point evaluation" method may sometime8 be a useful alternative. Thia involveu approximating the mdtivariate distribution of the X variablea by the 2n pointa given by Xi =pi fa,. X2=p,faz. ..., X,, = =pnfa,,, wherepc in the mean and a1 the standard deviation of Xb with appropriate point weighta. An advantage over the Taylor neriea approach that funotion derivatives do not have to be explioitely oalculated. The point eV81~8t'iOn method is partionlarly ueeful in O~BBB where the X VMablee are nnoomlated. Then the evaluation of the 2" point6 0813 be replaced by the evaluation of 2% pointa The point eV81118ti0~1 method b illnetmtd with powers of a normally distributed variable, and with estimation of gene frequenCiee from ABO blood group frequencies.

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