| Автор | Dickey, James M. |
| Дата выпуска | 1985 |
| dc.description | ABSTRACTThe Hardy, Littlewood, Polya class of power means (w<sub>i</sub>z<sup>a</sup> <sub>1</sub> + …+w<sub>n</sub> z<sup>a</sup> <sub>n</sub>)<sup>1/a</sup>, including the usual harmonic, geometric, and arithmetic mean values, has been generalized by Bruno deFinetti and B. C. Carlson. These two generalizations are here simultaneously extended to a comprehensive generalized mean value involving an arbitrary continuous strictly monotonic function and a linear form in the data values with Dirichlet-distributed coefficients. Properties are given which relate the new mean naturally to its deFinetti and Carlson subclasses. Statistical interpretations and possible further extensions arc discussed. |
| Формат | application.pdf |
| Издатель | Taylor & Francis Group |
| Копирайт | Copyright Taylor and Francis Group, LLC |
| Тема | 33A30 |
| Тема | 60E10 |
| Тема | 62G99 |
| Название | A COMPREHENSIVC GENERALIZED MEAN VALUE BASED ON THE DIRICHLET DISTRIBUTION |
| Тип | research-article |
| DOI | 10.1080/16073606.1985.9631923 |
| Electronic ISSN | 1727-933X |
| Print ISSN | 1607-3606 |
| Журнал | Quaestiones Mathematicae |
| Том | 8 |
| Первая страница | 343 |
| Последняя страница | 360 |
| Аффилиация | Dickey, James M.; Department of Mathematics and Statistics, State University of New York at Albany |
| Выпуск | 4 |
| Библиографическая ссылка | Carlson, B. C. 1963. Lauricella's hypergeometric functions F<sub>D</sub> . J. Math. Anal. Appl., 7: 452–470. |
| Библиографическая ссылка | Carlson, B. C. 1965. A hypergeometric mean Value.. Procs. Amer. Math. Soc., : 759–766. 16, No. 4 |
| Библиографическая ссылка | Carlson, B. C. 1966. Procs. Amer. Math. Soc. Vol. 17, 32–39. Some inequalities for hypergeometric functions. Vol., No. 1 |
| Библиографическая ссылка | Carlson, B. C. 1977. Special Functions of Applied Mathematics New York: Academic Press. |
| Библиографическая ссылка | Carlson, B. C. and Tobey, M. D. 1968. A property of the hypergeometric mean value.. Procs. Amer. Math. Soc., : 255–262. 19, No. 2 |
| Библиографическая ссылка | deFinetti, Bruno. 1931. Sul concetto di media.. Giornale dell' Instituto Italiano degli Attuari, 2: 369–396. |
| Библиографическая ссылка | deFinetti, Bruno. 1974. Theory of Probability Vol. 1, New York: Wiley. |
| Библиографическая ссылка | Dickey, James M. 1983. Multiple hypergeometric functions, probabilistic interpretations and statistical uses.. J. Amer. Statist. Assoc., 78: 626 |
| Библиографическая ссылка | Feller, William. 1966. An Introduction to Probability Theory and Its Applications, Vol II. New York: Wiley. |
| Библиографическая ссылка | Gini, C. 1938. Di una formula comprensjva delle medie.. Metron, 13: 3–22. |
| Библиографическая ссылка | Hardy, G. H., Littlewood, J. E. and Polya, G. 1934. Inequalities Cambridge. (Revised second edition 1952).: Cambridge University Press. |
| Библиографическая ссылка | Kolmogoroff, A. 1930. Sur la notion de la moyenne.. Atti della R. Accademia Nazionale dei Lincei, 12: 389–391. |
| Библиографическая ссылка | Landsberg, P. T. 1980. J. Math Anal. Appl. Vol. 76, 209–212. A generalized mean. Vol |
| Библиографическая ссылка | Mays, Michael E. 1983. Functions which parameterize means.. Amer. Math. Monthly, 90: 677–683. |
| Библиографическая ссылка | Nagumo, M. 1930. Über eine Klasse von Mittelwerte.. Japanese Jour. Math., 7: 71–79. |
