| Автор | Olusegun George, E. |
| Автор | Sivaram, Meenakshi. |
| Дата выпуска | 1987 |
| dc.description | An asymptotic expansion of the Student t distribution is derived by expanding the standardized Student t distribution in terms of the normal distribution. This expansion is inverted to obtain corresponding asymptotic expansions for the Student t percentiles as functions of the standard normal percentiles0 Using the first two, three or four terms of these expansions, we get approximations of the Student t percentiles which are generally more accurate than the approximations given by Fisher and Cornish(1960) and Koehler (1983).An approximation of the distribution function obtained from this expansion is compared with the approximations discussed by Ling (1978) andfound to be more accurate for moderate degrees of freedom. |
| Формат | application.pdf |
| Издатель | Marcel Dekker, Inc. |
| Копирайт | Copyright Taylor and Francis Group, LLC |
| Тема | Hermite polynomials |
| Тема | asymptotic expansions |
| Название | A modification of the Fisher-Cornish approximation for the student t percentiles |
| Тип | research-article |
| DOI | 10.1080/03610918708812641 |
| Electronic ISSN | 1532-4141 |
| Print ISSN | 0361-0918 |
| Журнал | Communications in Statistics - Simulation and Computation |
| Том | 16 |
| Первая страница | 1123 |
| Последняя страница | 1132 |
| Аффилиация | Olusegun George, E.; Department of Mathematical Sciences, Memphis State University |
| Аффилиация | Sivaram, Meenakshi.; Department of Mathematical Sciences, Memphis State University |
| Выпуск | 4 |
| Библиографическая ссылка | Fisher, R.A. and Cornish, E.A. 1960. “The percentile points of distributions having known cumulants”. Technometrics, 2: 209–255. |
| Библиографическая ссылка | Gentleman, W.M. and Jenkins, M.A. 1968. “An approximation for Student t-distribution”. Biometrika, 55: 571–572. |
| Библиографическая ссылка | Hill, G.W. and Davis, A.W. 1968. “Generalized asymptotic expansion of Cornish-Fisher type”. Ann. Math. Statist, 39: 1264–1273. |
| Библиографическая ссылка | Johnson, N.L. and Kotz, S. 1970. Distributions in Statistics: Continuous Univariate Distributions, Vol. I, New York: John Wiley. |
| Библиографическая ссылка | Kennedy, W.J. and Gentle, J.E. 1980. Statistical Computing, New York: Marcel Dekker. |
| Библиографическая ссылка | Koehler, K.J. 1983. “A simple approximation for the percentiles of the t distribution”. Technometrics, 25: 103–105. |
| Библиографическая ссылка | Ling, R.F. 1978. “Accuracy of approximations for t, X2 and F probabilities”. Journal of Amer. Statist. Assoc, 73: 274–283. |
