Browse > Article

ON THE RATIO X/(X + Y) FOR WEIBULL AND LEVY DISTRIBUTIONS  

ALI M. MASOOM (Department of Mathematical Sciences Ball State University Muncie)
NADARAJAH SARALEES (Department of Statistics University of Nebraska Lincoln)
WOO JUNGSOO (Department of Statistics Yeungnam University Gyongsan)
Publication Information
Journal of the Korean Statistical Society / v.34, no.1, 2005 , pp. 11-20 More about this Journal
Abstract
The distributional properties of R = X/(X + Y) and related estimation procedures are derived when X and Y are independent and identically distributed according to the Weibull or Levy distribution. The work is of interest in biological and physical sciences, econometrics, engineering and ranking and selection.
Keywords
Levy distribution; ratio of random variables; Weibull distribution;
Citations & Related Records
연도 인용수 순위
  • Reference
1 HINKLEY, D. V. (1969). 'On the ratio of two correlated normal random variables' , Biometrika, 56, 635-639   DOI   ScienceOn
2 KORHONEN, P. J. AND NARULA, S. C. (1989). 'The probability distribution of the ratio of the absolute values of two normal variables', Journal of Statistical Computation and Simulation, 33, 173-182   DOI   ScienceOn
3 PROVOST, S. B. (1989). 'On the distribution of the ratio of powers of sums of gamma random variables', Pakistan Journal Statistics, 5, 157-174
4 GRADSHTEYN, I.S. AND RYZHIK, I.M. (1965). Table of Integrals, Series and Products, Academic Press, New York
5 MARSAGLIA, G. (1965). 'Ratios of normal variables and ratios of sums of uniform variables', Journal of the American Statistical Association, 60, 193-204   DOI   ScienceOn
6 BOWMAN, K. O. AND SHENTON, L. R. (1998). 'Distribution of the ratio of gamma variates', Communications in Statistics-Simulation and Computation, 21, 1-19   DOI   ScienceOn
7 PHAM-GIA, T. (2000). 'Distributions of the ratios of independent beta variables and applications' Communications in Statistics-Theory and Methods, 29, 2693-2715   DOI   ScienceOn
8 LEE, R. Y., HOLLAND, B. S. AND FLUECK, J. A. (1979). 'Distribution of a ratio of correlated gamma random variables', SIAM Journal on Applied Mathematics, 36, 304-320   DOI   ScienceOn
9 JOHNSON, N. L., KOTZ, S., AND BALAKRISHNAN, N. (1995). Continuous Univariate Distributions, Volume 2, John Wiley and Sons, New York
10 PRESS, S. J. (1969). 'The t ratio distribution', Journal of the American Statistical Association, 64, 242-252   DOI   ScienceOn
11 HAWKINS, D. I. AND HAN, C. -P (1986). 'Bivariate distributions noncentral chi-square random variables', Communications in Statistics-Theory and Methods, 15, 261-277   DOI
12 MCCOOL, J. I. (1991). 'Inference on P{Y < X} in the Weibull case', Communications in Statistics-Simulation and Computation, 20, 129-148   DOI   ScienceOn
13 O'REILLY, F. J. AND RUEDA, R. (1998). 'A note on the fit for the Levy distribution', Communications in Statistics-Theory and Methods, 27, 1811-1821   DOI   ScienceOn
14 SHCOLNICK, S. M. (1985). 'On the ratio of independent stable random variables', Stability Problems for Stochastic Models (Uzhgorod, 1984), 349-354, Lecture Notes in Mathematics, 1155, Springer, Berlin
15 ALl, M. MASOOM AND Woo, J. (2004a). 'Inference on reliability P(Y < X) in ap-dimensional Rayleigh distribution (with J. Woo)', Mathematical and Computer Modelling (in press)
16 ALl, M. MASOOM AND Woo, J. (2004b). 'Inference on P(Y < X) in the Levy case', Mathematical and Computer Modelling (in press)
17 CHENEY, W. AND KINCAID, D. (1994). Numerical Mathematics and Computing, Third edition, Brooks/Cole Publishing Co. Pacific Grove, California
18 MONTROLL, E. W. AND SHLESINGER, M. F. (1983). 'On the wedding of certain dynamical processes in discorded complex materials to the theory of stable (Levy) distribution functions', In: The Mathematics and Physics of Discarded Media, pp. 109-137, Springer-Verlag, Heidelberg
19 KAPPENMAN, R. F. (1971). 'A note on the multivariate t ratio distribution', Annals of Mathematical Statistics, 42, 349-351   DOI   ScienceOn