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DISTRIBUTION THEORY

Asymptotic Distribution for Symmetric Spacing Statistics

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Pages 37-46 | Received 20 Jan 2006, Accepted 07 Apr 2006, Published online: 18 Feb 2007

References

  • Aras , G. , Jammalamadaka , S. R. , Zhou , X. ( 1989 ). Limit distribution of spacings statistics when the sample size is random . Statist. Probab. Lett. 8 : 451 – 456 .
  • Beirlant , J. , Janssen , P. , Veraverbeke , N. ( 1989 ). On the asymptotic normality of functions of uniform spacings . Canad. J. Statist. 19 : 93 – 101 .
  • Cheng , R. C. H. , Amin , N. A. K. ( 1983 ). Estimating parameters in continuous univariate distributions with a shifted origin . J. R. Statist. Soc. B 45 : 394 – 403 .
  • Cressie , N. ( 1976 ). On the logarithms of high-order spacings . Biometrika 63 : 343 – 355 .
  • Czekala , F. ( 1993 ). Asymptotic distributions of statistics based on logarithm of spacings . Zastos. Mat. 21 : 511 – 519 .
  • Darling , D. A. ( 1953 ). On a class of problems related to the random division of an interval . Ann. Math. Statist. 24 : 239 – 253 .
  • Durrett , R. ( 1991 ). Probability: Theory and Examples . California : Wadsworth .
  • Ekstrom , M. ( 2001 ). Consistency of generalized maximum spacing estimates . Scand. J. Statist. 28 : 343 – 355 .
  • Gebert , J. R. , Kale , B. K. ( 1969 ). Goodness-of-fit tests based on discriminatory information . Statist. Hefte. 3 : 192 – 200 .
  • Greenwood , M. ( 1946 ). The statistical study of infectious diseases . J. R. Statist. Soc. A 109 : 85 – 110 .
  • Hall , P. ( 1984 ). Limit-theorems for sums of general functions of M-spacings . Math. Proc. Comb. Phil. Soc. 96 : 517 – 532 .
  • Hall , P. ( 1986 ). Asymptotic normality of sum-fuctions of spacings . Ann. Probab. 17 : 1066 – 1072 .
  • Holst , L. ( 1979 ). On powerful distributional tests based on sample spacings . J. Multi. Anal. 19 : 201 – 224 .
  • Holst , L. , Rao , J. S. ( 1981 ). Asymptotic spacings theory with applications to sample problem . Canad. J. Statist. 9 : 79 – 89 .
  • Jammalamadaka , S. R. , Ghosh , K. ( 2001 ). A general estimation method using spacings . J. Statist. Plann. Infer. 93 : 71 – 82 .
  • Kimball , B. F. ( 1950 ). On the asymptotic distribution of the sum of powers of unit frequency differences . Ann. Math. Statist. 21 : 263 – 271 .
  • Kuo , M. , Rao , J. S. ( 1984 ). Asymptotic results on the Greenwood statistic and some of its generalizations . J. R. Statist. Soc. B 27 : 395 – 449 .
  • LeCam , L. ( 1958 ). Une théoreme sur la division d'une intervalle par des points prés au hasard . Pub. Inst. Statist. Univ. Paris 18 : 473 – 494 .
  • Moran , P. ( 1947 ). Random division of an interval . J. R. Statist. Soc. B 9 : 92 – 98 .
  • Pyke , R. ( 1965 ). Spacings (with discussion) . J. R. Statist. Soc. B 27 : 395 – 449 .
  • Pyke , R. ( 1972 ). Spacings revisited . Sixth Berkeley Symp. Math. Statist. Probab . Vol. 1 . University of California Press , pp. 417 – 427 .
  • Ranneby , B. ( 1984 ). The maximum spacing method. An estimation method related to the maximum likelihood method . Scand. J. Statist. 11 : 93 – 112 .
  • Ranneby , B. , Ekstrom , M. ( 1997 ). Maximum spacing estimates based on different metrics . Research Report, No. 5, Dept. of Mathematical Statistics, Umea University .
  • Rao , J. S. , Sethuraman , J. ( 1975 ). Weak convergence of empirical distribution function of random variables subject to perturbations and scale factors . Ann. Statist. 3 ( 2 ): 299 – 313 .
  • Sethuraman , J. , Rao , J. S. (1970). Pitman efficiencies of tests based on spacings. In: Puri , M. L. , ed. Non Parametric Techniques in Statistical Inferences . Cambridge : Cambridge University Press, pp. 404–415.
  • Shao , Y. , Hahn , M. G. ( 1995 ). Limit theorems for the logarithm of sample spacings . Statist. Probab. Lett. 24 : 121 – 132 .
  • Sherman , B. ( 1950 ). A random variable related to the spacing of sample values . Ann. Math. Statist. 21 : 339 – 361 .
  • Weiss , L. ( 1957 ). Asymptotic power of certain tests of fit based on sample spacings . Ann. Math. Statist. 28 : 778 – 782 .
  • Weiss , L. ( 1965 ). Discussion of Pyke . J. R. Statist. Soc. B 27 : 443 .

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