Summary
The exact distribution function of the ratio of two sums of gamma variates is derived in this paper. The result applies to ratios of quadratic forms and to a statistic used for testing the equality of scale parameters in two gamma populations.
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References
Ali MM, Obaidullah M (1982) Distribution of linear combination of exponential variates. Commun Statist-Theor Meth 11(13):1453–1463
Bain LJ, Engelhart M (1975) A two-moment chi-square approximation for the statistic log\((\bar x/\bar x)\). Journal of the American Statistical Association 70:948–950
Choi SC, Wette R (1969) Maximum likelihood estimation of the parameters of the gamma distribution and their bias. Technometrics 11:683–690
Gradshteyn IS, Ryzhik IM (1980) Table of integrals series and products, corrected and enlarged edition. Academic Press, New York
Grice JV, Bain JL (1980) Inferences concerning the mean of the gamma distribution. Journal of the American Statistical Association 75:929–933
Linhart H (1965) Approximate confidence limits for the coefficient of variation of gamma distributions. Biometrics 31:733–737
Mathai AM (1983) On linear combinations of independent exponential variables. Commun Statist-Theor Meth 12(6):625–632
Shiue W-K, Bain LJ (1983) A two-sample test of equal gamma distribution scale parameters with unknown common shape parameter. Technometrics 25:377–381
Shorack GR (1972) The best test of exponentiality against gamma alternatives. Journal of the American Statistical Association 67:213–214
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Provost, S.B. The distribution function of a statistic for testing the equality of scale parameters in two gamma populations. Metrika 36, 337–345 (1989). https://doi.org/10.1007/BF02614109
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DOI: https://doi.org/10.1007/BF02614109