ArticleOriginal scientific text
Title
Inference on the location parameter of exponential populations
Authors 1, 2, 3, 4
Affiliations
- Universidade dos Açores, DM, and CEAUL
- Universidade da Madeira, CCEE, and CEAUL
- Universidade de Lisboa, DEIO and CEAUL
- Universidade dos Açores, DEG, CEEAplA and CEAUL
Abstract
Studentization and analysis of variance are simple in Gaussian families because X̅ and S² are independent random variables. We exploit the independence of the spacings in exponential populations with location λ and scale δ to develop simple ways of dealing with inference on the location parameter, namely by developing an analysis of scale in the homocedastic independent k-sample problem.
Keywords
studentization, analysis of scale, characterizations, independence of exponential spacings, location-scale families, F-ratio
Bibliography
- A.A. Aspin, An examination and further developments of a formula arising in the problem of comparing two mean values, Biometrika 35 (1948), 88-97.
- A.A. Aspin, Tables for use in comparisons whose accuracy involves two variances, separately estimated, Biometrika 36 (1949), 290-293.
- M.F. Brilhante and S. Kotz, Infinite divisibility of the spacings of a Kotz-Kozubowski-Podgórski generalized Laplace model, Statistics & Probability Letters 78 (2008), 2433-2436.
- M.F. Brilhante, D. Pestana, J. Rocha and S. Velosa, Inferência Estatística Sobre Localização e Escala, Sociedade Portuguesa de Estatística, Ponta Delgada 2001.
- H.A. David and H.N. Nagaraja, Order Statistics, 3rd ed., Wiley, New York 2003.
- R.A. Fisher, Statistical Methods for Research Workers, Oliver and Boyd, Edinburgh 1925.
- N.L. Johnson, S. Kotz and N. Balakrishnan, Continuous Univariate Distributions, vol. 2, 2nd ed., Wiley, New York 1995.
- G.W. Oehlert, A First Course in Design and Analysis of Experiments, Freeman, New York 2000.
- V. Perlo, On the distribution of `Student's' ratio for samples of three drawn from the rectangular distribution, Biometrika 25 (1933), 203-204.
- D. Pestana, F. Brilhante and J. Rocha, The analysis of variance revisited, in Extreme Values and Additive Laws, Lisboa (1999), 73-77.
- D. Pestana and J. Rocha, Análise de escala - modelo exponencial, in A Estatística e o Futuro e o Futuro da Estatística, Salamandra, Lisboa (1993), 295-303.
- J. Rocha, Localização e Escala em Situações não Clássicas, Dissertação de Doutoramento, Universidade dos Açores, Ponta Delgada 1995.
- J. Rocha, Inference on location parameters - internally studentized statistics, Rev. Estat. (2001), 355-356.
- F.E. Satterthwaite, An approximate distribution of estimates of variance components, Biometrics Bulletin 2 (1946), 110-114.
- H. Scheffé, On solutions of the Behrens-Fisher problem based on the t-distribution, Ann. Math. Stat. 14 (1943), 35-44.
- H. Scheffé, A note on the Behrens-Fisher problem, Ann. Math. Stat. 15 (1944), 430-432.
- H. Smith, The problem of comparing the results of two experiments with unequal means, J. Council Sci. Industr. Res. 9 (1936), 211-212.
- Student, The probable error of the mean, (Reprinted in E.S. Pearson and J. Wishart, (1958) 'Student's' Collected Papers, Cambridge Univ. Press, Cambridge), Biometrika 6 (1908), 1-25.
- B.L. Welch, The significance of the difference between two means when the population variances are unequal, Biometrika 29 (1938), 350-361.
- B.L. Welch, On the comparison of several mean values: an alternative approach, Biometrika 38 (1951), 330-336.