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By Ilya Polyak

Medical descriptions of the weather have usually been in line with the research of common meteorological values taken from assorted positions world wide. lately but it has turn into obvious that those averages may be thought of with different records that finally signify spatial and temporal variability. This ebook is designed to fulfill that want. it's in response to a direction in computational records taught via the writer that arose from numerous tasks at the layout and improvement of software program for the learn of weather swap, utilizing records and strategies of random services.

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72), it is possible to determine the correlation function of the point estimates: 28 1 Digital Filters The moving average procedure changes not only the statistical but also the harmonic structure of the observations. 67). 68), the point estimate (ft is that is, each harmonic with the frequency u is multiplied by the factor which does not depend on time /. 68). 67). The basis for constructing different classes of filters is presented by the character of the random and deterministic variations of the observations (or by different statistical and physical assumptions).

64) shows that, for a fixed number of observations k, an increase in the degree of v leads to an increase in the variance of the point estimates. If A; becomes equal to the number of parameters, this variance equals the observed variance value. 5 Examples Now let us consider several examples of the graphs of the normalized variances of the point estimates. 1. 4 presents normalized variances of the point estimates for the polynomial approximation of the unequally spaced observations. The number of points is 31, and the polynomial degree rn varies from zero to six.

2: Normalized variances of the point estimates, when the number of observations is fixed (A; = 30) and the polynomial degree m varies. many types and shapes. 48) can be called the menorah equation. 3 illustrates the dependence of CQQ on the number of points k for different degrees m. As this illustration clearly shows, increasing the number of observations to more than 30 does not greatly decrease the point estimate variance (when m < 5). 3 to determine the sample size, which is necessary to obtain estimate (]0 with the required accuracy.

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