Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-24T21:00:55.155Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Distributions of Ordered Values from Burr and Beta Distributions

Published online by Cambridge University Press:  20 November 2018

D. G. Kabe
D. G. Kabe*
Affiliation:
St. Mary's University, Halifax, Nova Scotia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we use some known transformations available in the Theory of Multiple Integrals to give straightforward, simpler, and elegant proofs of some distributions of ordered values from Burr and beta distributions. The exact distribution (under the null hypothesis) of Wilks' ∧ criterion is obtained by considering it as a certain minimum value distribution problem.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 2 , June 1971 , pp. 167 - 173
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Anderson, T. W., An introduction to multivariate statistical analysis, Wiley, New York, 1958.Google Scholar
2. Burr, I. W., Cumulative frequency functions, Ann. Math. Statist. 13 (1942), 215-232.Google Scholar
3. Erdelyi, A. et al. (Ed.), Higher transcendental functions. Vol. 1, McGraw-Hill, New York, 1953.Google Scholar
4. Gibson, G. A., Advanced calculus, Macmillan, London, England, 1944.Google Scholar
5. Kabe, D. G., Dirichlefs transformation and distributions of linear functions of ordered gamma vari?tes, Ann. Inst. Statist. Math. 18 (1966), 367-374.Google Scholar
6. Kabe, D. G., Some distribution problems of order statistics from exponential and power function distributions, Canad. Math. Bull. 11 (1968), 263-274.Google Scholar
7. Kabe, D. G., On a multiple integral useful in order statistics distribution theory, Canad. Math. Bull. 13(1970), 311-315.Google Scholar
8. Malik, H. J., Exact moments of order statistics from the Pare to distribution, Skand. Aktuarietidskr. 49 (1966), 144-157.Google Scholar
9. Malik, H. J., Exact moments of order statistics from the power function distribution, Skand. Aktuarietidskr. 50 (1967), 64-69.Google Scholar
10. Mathai, A. M. and Saxena, R. K., Distribution of a product and the structural set up of densities, Ann. Math. Statist. 40 (1969), 1439-1448.Google Scholar