Skip to Main Content
The online home for the publications of the American Statistical Association
Publication Cover

Statistics

A Journal of Theoretical and Applied Statistics
Volume 57, 2023 - Issue 5
66
Views
0
CrossRef citations to date
0
Altmetric
Research Article

On asymptotic properties of spacings

&
Pages 1267-1283
Received 15 Oct 2022
Accepted 12 Sep 2023
Published online: 13 Oct 2023

References

  • Del Pino GE. On the asymptotic distribution of k-spacings with applications to goodness-of-fit tests. Ann Stat. 1979;7:1058–1065. doi: 10.1214/aos/1176344789  [Crossref] [Web of Science ®][Google Scholar]
  • Beirlant J, Zuijlen M. The empirical distribution function and strong laws for functions of order statistics of uniform spacings. J Multivar Anal. 1985;16:300–317. doi: 10.1016/0047-259X(85)90023-5  [Crossref] [Web of Science ®][Google Scholar]
  • Cheng RCH, Amin NAK. Maximum product of spacings estimation with application to the lognormal distribution, Math Report 79-1, Department of Mathematics, UWIST, Cardiff. 1979.  [Google Scholar]
  • Cheng RCH, Amin NAK. Estimating parameters in continuous univariate distributions with a shifted origin. J Roy Statist Soc Ser B. 1983;45:394–403.  [Google Scholar]
  • Ederer F, Meyers MH, Mantel N. A statistical problem in space and time: do leukemia cases come in clusters? Biometrics. 1964;20:626–636. doi: 10.2307/2528500  [Crossref] [Web of Science ®][Google Scholar]
  • Naus JI. Some probabilities, expectations and variances for the side of largest clusters and smallest intervals. J Amer Stat Ass. 1966;61:1191–1199. doi: 10.1080/01621459.1966.10482203  [Taylor & Francis Online] [Web of Science ®][Google Scholar]
  • Glaz J, Balakrishnan N. eds. Scan statistics and applications. Boston: Birkhauser; 1999.  [Crossref][Google Scholar]
  • Balakrishnan N, Koutras MV. Runs and scans with applications. New York: Wiley; 2002.  [Google Scholar]
  • Pyke A. Spacings (with discussions). J R Stat Soc Ser B. 1965;27:395–449.  [Google Scholar]
  • Ahsanullah M. A characterization of the exponential distribution by higher order gap. Metrika. 1984;31:323–326. doi: 10.1007/BF01915219  [Crossref][Google Scholar]
  • Riffi MI. Characterizing the exponential distribution by m-spacings. J Sci Eng Res. 2018;5:211–214.  [Google Scholar]
  • Barakat HM, Nigm EM, Elsawah AM. Asymptotic distributions of the generalized range, midrange, extremal quotient, and extremal product, with a comparison study. Commun Stat Theory Methods. 2015;44(5):900–913. doi: 10.1080/03610926.2012.750356  [Taylor & Francis Online] [Web of Science ®][Google Scholar]
  • Galambos J. The asymptotic theory of extreme order statistics. NY: John Wiley & Sons; 1978.  [Google Scholar]
  • Hall PG. Limit theorems for sums of general functions of m-spacings. Math Proc Cambridge Philos Soc. 1984;96:517–532. doi: 10.1017/S0305004100062459  [Crossref] [Web of Science ®][Google Scholar]
  • Arnold BC, Balakrishnan N, Nagaraja HN. A first course in order statistics. New York: John Wiley & Sons; 1992.  [Google Scholar]
  • Nevzorov V. Records: mathematical theory. Providence (RI): American Mathematical Society; 2001.  [Google Scholar]
  • David HA, Nagaraja HN. Order statistics. 3rd ed.. Hoboken: Wiley; 2003.  [Crossref][Google Scholar]
  • Riffi MI. Distributions of gamma m-spacings. IUG J Nat Stud. 2017;4:01–06.  [Google Scholar]
  • Balakrishnan N, Stepanov A. A note on the number of observations registered near an order statistic. J Stat Plann Inference. 2005;134:1–14. doi: 10.1016/j.jspi.2004.01.018  [Crossref] [Web of Science ®][Google Scholar]
  • Balakrishnan N, Pakes A, Stepanov A. On the number and sum of near record value observations. Adv Appl Probab. 2005;37:765–780. doi: 10.1239/aap/1127483746  [Crossref] [Web of Science ®][Google Scholar]
  • Seneta E. Regularly varying functions. Berlin: Springer–Verlag; 1976. (Lecture Notes in Mathematics; 508).  [Crossref][Google Scholar]
  • Bingham NH, Goldie C, Teugels JF. Regular variation. Cambridge: Cambridge University Press; 1987.  [Crossref][Google Scholar]
  • Dembinska A, Stepanov A. Limit theorems for the ratio of weak records. Stat Probab Lett. 2006;76:1454–1464. doi: 10.1016/j.spl.2006.03.004  [Crossref] [Web of Science ®][Google Scholar]
  • Balakrishnan N, Stepanov A. Asymptotic properties of the ratio of order statistics. Stat Probab Lett. 2008;78:301–310. doi: 10.1016/j.spl.2007.08.001  [Crossref] [Web of Science ®][Google Scholar]
  • Balakrishnan N, Nevzorov VB, Stepanov A. On normal spacings. Statist Probab Lett. 2023;193:109713. doi: 10.1016/j.spl.2022.109713.  [Crossref] [Web of Science ®][Google Scholar]
  • Balakrishnan N, Stepanov A. Generalization of Borel–Cantelli lemma. Math Sci. 2010;35:61–62.  [Google Scholar]
  • Barndorff-Nielsen O. On the rate of growth of the partial maxima of a sequence of independent identically distributed random variables. Math Scand. 1961;9:383–394. doi: 10.7146/math.scand.a-10643  [Crossref][Google Scholar]
  • Balakrishnan N, Stepanov A. A note on the Borel–Cantelli Lemma, arXiv:2112.00741v1 [math.PR]. 2021.  [Google Scholar]
  • Stepanov A, Dembińska A. Limit theorems for the uppermost mth spacing based on weak geometric records. Stat Probab Lett. 2022;183:109351. doi: 10.1016/j.spl.2021.109351  [Crossref] [Web of Science ®][Google Scholar]

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.