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Journal of the American Statistical Association Volume 71, 1976 - Issue 354
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Theory and Method

The Ratio of the Geometric Mean to the Arithmetic Mean for a Random Sample from a Gamma Distribution

Ronald E. Glaser Department of Mathematics, University of California, Davis, CA, 95616, USA
Pages 480-487 | Received 01 Jun 1974, Published online: 05 Apr 2012

References

  • Abramowitz , Milton and Stegun , Irene A. 1970 . Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , Washington , D.C. : National Bureau of Standards .
  • Anderson , T. W. 1958 . An Introduction to Multivariate Statistical Analysis , New York : John Wiley & Sons, Inc. .
  • Barnes , E. W. 1899 . “The Theory of the Gamma Function” . Messenger of Mathematics , 29 : 64 – 128 .
  • Bartlett , M. S. “Properties of Sufficiency and Statistical Tests” . Proceedings of the Royal Society of London, Ser. A . Vol. 160 , May . pp. 268 – 82 .
  • Box , G. E. P. 1949 . “A General Distribution Theory for a Class of Likelihood Ratio Criteria” . Biometrika , 36 December : 317 – 46 .
  • Glaser , Ronald E. 1973 . “Inferences for a Gamma Distributed Random Variable with Both Parameters Unknown, with Applications to Reliability” , Department of Operations Research and Department of Statistics, Stanford University . Technical Report No. 154
  • Glaser , Ronald E. 1974 . “The Ratio of the Geometric Mean to the Arithmetic Mean for a Random Sample from a Gamma Distribution” , Department of Mathematical Sciences, Johns Hopkins University . Technical Report No. 190
  • Glaser , Ronald E. 1974 . “Inferences on the Shape Parameter of a Gamma Distribution” , Department of Mathematical Sciences, Johns Hopkins University . Technical Report No. 198
  • Glaser , Ronald E. 1976 . “Exact Critical Values for Bartlett?s Test for Homogeneity of Variances” . Journal of the American Statistical Association , 71 June : 488 – 90 .
  • Hardy , G. H. , Littlewood , J. E. and Pólya , G. 1952 . Inequalities , Cambridge , , England : Cambridge University Press .
  • Lloyd , David K. and Lipow , Myron . 1962 . Reliability: Management, Methods, and Mathematics , Englewood Cliffs , N.J. : Prentice-Hall, Inc. .
  • Parzen , Emanuel . 1960 . Modern Probability Theory and Its Applications , New York : John Wiley & Sons, Inc. .
  • Pitman , E. J. G. “The ‘Closest’ Estimates of Statistical Parameters” . Proceedings of the Cambridge Philosophical Society . Vol. 33 , April . pp. 212 – 22 .
  • Rice , J. R. 1969 . The Approximation of Functions, Vol. II , Reading , Mass. : Addison-Wesley Publishing Co. .
  • Schoenberg , I. J. 1969 . Approximations with Special Emphasis on Spline Functions , New York : Academic Press, Inc. .

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