ABOUT THE ASSESSMENT OF EVEN DEGREES OF SOME INTEGRALS CUTS
Journal: Science and world (Vol.1, No. 17)Publication Date: 2015-01-27
Authors : Pozhidaev A.V.; Pekel'nik N.M.; Khaustova O.I.; Trefilova I.A.;
Page : 29-34
Keywords : power inequality; cumulative distribution curve; gamma-function; Gaussian distribution; optimal estimate.;
Abstract
This research work is devoted to the receiving of spower inequality of the lower cut of integral from density of the standard Gaussian distribution. The necessity of receiving of such estimates arises on the base on the wide circulation of normal distribution in appendices and theoretical researches. The feature of the received results consists in that even degrees 2n of given function are estimated not through the value of subintegral functions in some point, but through the values of the considered function in ax point where a ? any number from the closed interval 1; 2n ?? ??. The difficulty of receiving these estimates is that density of the normal law is a logarithmic concave function that is its logarithm is concave function. In the research work it is shown that both borders for parameter a cannot be improved.
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