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Analysis of variance on function spaces
Series Statistics, 1984In this paper, we introduce the notion of analysis of variance on spaces of real functions defined on a product set and the ordinary analysis of variance in two way arrays appear as a special case. In order to obtain the results the theory of gaussian measures on Banach spaces is employed and a decomposition into orthogonal subspaces of a direct ...
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Psychometric functions for the discrimination of spectral variance
The Journal of the Acoustical Society of America, 1996An experiment was conducted to measure the shape of the psychometric function for the discrimination of spectral variance. The stimuli were simultaneous tone complexes comprised of the six octave frequencies from 250 to 8000 Hz. On each presentation the levels of components in dB were drawn independently and at random from one of two normal ...
Eunmi Oh +2 more
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On the variance of additive functions
1983Let f be a real-valued additive arithmetical function. The quantity $$D^2 (f,t) = x^{ - 1} \sum\limits_{n \leqq x} {(f(n) - t)^2 }$$ (1.1) assumes its minimum at $$t = M(f)\mathop = \limits^{def} x^{ - 1} \sum\limits_{n \leqq x} {\left[ {\frac{x} {{p^k }}} \right](f(p^k ) - f(p^{k - 1} ))}$$ (1.2) we call its value $$D^2 (f) = D^
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Analysis of variance for functional data. [PDF]
, 1994 In this dissertation we present an extension to the well known theory of multivariate analysis of variance. In various situations data are continuous stochastic functions of time or space. The speed of pollutants diffusing through a river, the real amplitude of a signal received from a broadcasting satellite, or the hydraulic conductivity rates at a ...
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The variance function of the Erlang process
Annals of the Institute of Statistical Mathematics, 1970A relatively simple exact expression of closed form is obtained for the varianceσ 2(t) of the asynchronous counting distribution for a counting period of lengtht,t>0, in an Erlang process. Useful bounds are placed upon the error of the linear approximation toσ 2(t). Implications of these results are examined.
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The Approximate Variance of a Function of Random Variables
Biometrical Journal, 1999In this communication we approximate the variance of a function of random variables by using a second degree Taylor series expansion, and demonstrate the increased accuracy this second degree approximation gives over the usual Delta method by using some examples from genetics.
Robert C. Elston, Hemant K. Tiwari
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On the variance of the sum of digits function
1990Delange and Trollope proved that the average value of the sum of digits in base 2 representation of the integers 0, 1, ..., N − 1 is given by ½log2N + δ(log2N), where δ(x) is a continuous periodic function of period 1.
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Average function and variance function for diagnostic purposes
Measurement, 1990Abstract According to our experience, the variance function as the standard deviation of the average function is well suited as a diagnostic tool to monitor mechanical movements. Nonlinear effects during the movement can be detected using touch-induced or rub-induced vibrations to obtain direct information about loads to be expected.
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On the Variance of Measurable Extremal Functions
1992We consider problems of the form $$ P(\eta ,\xi )\quad \rho (\eta ,\xi ): = {\inf _{x}}\;f(\eta ,\xi ,x) $$ (1) with (η,ξ) representing a random vector of R K+L with respect to the Borel algebra B K+L and a given probability measure P with compact support Ω; f is supposed to be a proper convex normal integrand ensuring measurability of the ...
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