Conditions for belonging of a two-component mixture of distributions to one type
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Abstract
A general case the two-component Gaussian mixture is examined. It is shown that by varying the parameters of components of the mixture a large family of distributions can be obtained. A criterion for the distribution function is found, defining the mixtures’ belonging to one type. The conditions, which the component parameters of uniform mixtures should meet, are determined. Formulas for the transition from a random variable with arbitrary values of the expectation and variance to the standard random variable with zero mean and unit variance were derived.
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References
Величкин А.И. Передача аналоговых сооб- щений по цифровым каналам связи. – М.: Радио и связь, 1983. – 240 с.
Горовецкая Т.А., Красильников А.И., Чан Хыу Дат. Модели и законы распределения флуктуационных сигналов // Электроника и связь. – 2000. – № 9. – С. 5–14.
K.N. Plataniotis and D. Hatzinakos. Gaussian Mixtures and Their Applications to Signal Processing Handbook. Editor Stre– Boca Raton: CRC Press LLC, 2001. – Р. 47.
Лукач. Е. Характеристические функции /Пер. с англ. – М.: Наука, 1979. – 424 с.
Феллер В. Введение в теорию вероятностей и ее приложения. В 2 томах. Т. 1 / Пер. с англ. – М.: Мир, 1984. – 528 с.
Красильников А.И., Пилипенко К.П. Приме- нение двухкомпонентной гауссовской смеси для идентификации одновершинных сим- метричных плотностей вероятностей // Электроника и связь. – 2008. – № 5(46). – С. 20–29.
Красильников А.И., Пилипенко К.П. Одно- вершинная двухкомпонентная гауссовская смесь. Коэффициент эксцесса // Электрони- ка и связь. – 2007. – № 2(37). – С. 32–38.
Тихонов В.И. Статистическая радиотехника. - 2-е изд., перераб и доп.- М.: Радио и связь, 1982. - 624с.
