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A Journal of Theoretical and Applied Statistics
Volume 58, 2024 - Issue 1
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Research Article

On conditional spacings and their properties under coherent system setting

, &
Pages 194-208 | Received 04 Jan 2023, Accepted 15 Jan 2024, Published online: 30 Jan 2024

References

  • Cochran WG. The χ2 test of goodness of fit. Ann Math Stat. 1952;23:315–345. doi: 10.1214/aoms/1177729380
  • Darling DA. The Kolmogorov-Smirnov, Cramér-von Mises tests. Ann Math Stat. 1957;28:823–838. doi: 10.1214/aoms/1177706788
  • Barlow RE, Proschan F. Inequalities for linear combinations of order statistics from restricted families. Ann Math Stat. 1966;37:1574–1592. doi: 10.1214/aoms/1177699149
  • Pledger P, Proschan F. Comparisons of order statistics and of spacings from heterogeneous distributions. In: Rustagi JS, editor. Optimizing methods in statistics. New York: Academic Press; 1971. p. 89–113.
  • Kochar SC, Kirmani S. Some results on normalized spacings from restricted families of distributions. J Stat Plan Inference. 1995;46:47–57. doi: 10.1016/0378-3758(94)00095-D
  • Hu T, Zhuang W. Stochastic properties of p-spacings of generalized order statistics. Probab Eng Inf Sci. 2005;19:257–276. doi: 10.1017/S026996480505014X
  • Hu T, Zhuang W. Stochastic comparisons of m-spacings. J Stat Plan Inference. 2006;136:33–42. doi: 10.1016/j.jspi.2004.06.029
  • Khaledi B, Kochar SC. Stochastic ordering between distributions and their sample spacings. Stat Probab Lett. 1999;44:161–166. doi: 10.1016/S0167-7152(99)00004-8
  • Khaledi B, Kochar SC. Stochastic properties of spacings in a single-outlier exponential model. Probab Eng Inf Sci. 2001;15:401–408.
  • Kochar SC, Korwar R. Stochastic orders for spacings of heterogeneous exponential random variables. J Multivar Anal. 1996;57:69–83. doi: 10.1006/jmva.1996.0022
  • Kochar SC. On stochastic ordering between distributions and their sample spacings. Stat Probab Lett. 1999;42:345–352. doi: 10.1016/S0167-7152(98)00224-7
  • Hu T, Jin W, Khaledi B. Ordering conditional distributions of generalized order statistics. Probab Eng Inf Sci. 2007;21:401–417. doi: 10.1017/S0269964807000046
  • Xie H, Hu T. Ordering conditional distributions of spacings of generalized order statistics. J Iran Stat Soc. 2007;6:155–171.
  • Kochar SC, Rojo J. Some new results on stochastic comparisons of spacings from heterogeneous exponential distributions. J Multivar Anal. 1996;59:272–281. doi: 10.1006/jmva.1996.0065
  • Kochar SC, Xu M. Stochastic comparisons of spacings from heterogeneous samples. In: Wells M, Sen-Gupta A, editors. Advanced in directional and linear statistics. New York: Springer; 2011. p. 113–130.
  • Torrado N, Lillo RE. Likelihood ratio order of spacings from two heterogeneous samples. J Multivar Anal. 2013;114:338–348. doi: 10.1016/j.jmva.2012.08.015
  • Torrado N, Lillo RE, Wiper MP. On the conjecture of Kochar and Korwar. J Multivar Anal. 2010;5:1274–1283. doi: 10.1016/j.jmva.2009.11.006
  • Burkschat M. Multivariate dependence of spacings of generalized order statistics. J Multivar Anal. 2009;100:1093–1106. doi: 10.1016/j.jmva.2008.10.008
  • Khaledi B, Kochar SC. Dependence among spacings. Probab Eng Inf Sci. 2000;14:461–472. doi: 10.1017/S0269964800144055
  • Kim SH, David HA. On the dependence structure of order statistics and concomitants of order statistics. J Stat Plan Inference. 1990;24:363–368. doi: 10.1016/0378-3758(90)90055-Y
  • Shaked M, Tong YL. Stochastic ordering of spacings from dependent random variables. Inequalities Stat Prob. 1984;5:141–149. IMS lecture notes monograph series. doi: 10.1214/lnms/1215465640
  • Alimohammadi M, Esna-Ashari M, Navarro J. Likelihood ratio comparisons and logconvexity properties of p-spacings from generalized order statistics. Probab Engrg Inform Sci. 2023;37:86–105. doi: 10.1017/S0269964821000498
  • Arnold BC, Balakrishnan N, Nagaraja HN. A first course in order statistics. New York: John Wiley & Sons; 1992.
  • Balakrishnan N. Permanents, order statistics, outliers, and robustness. Rev Mat Complut. 2007;20:7–107. doi: 10.5209/rev_REMA.2007.v20.n1.16528
  • Balakrishnan N, Kundu D, Cramer E. Hybrid censoring know-how: designs and implementations. San Diego: Academic Press; 2023.
  • Zhang Z, Yang L, Yang Y. The conditional spacings and their stochastic properties. Stat Probab Lett. 2022;186:Article ID 109466.
  • Shaked M, Shanthikumar JG. Stochastic orders. New York: Springer; 2007.
  • Müller A, Stoyan D. Comparison methods for stochastic models and risks. New York: John Wiley & Sons; 2002.
  • Karlin S, Rinott Y. Classes of orderings of measures and related correlation inequalities I. Multivariate totally positive distributions. J Multivar Anal. 1980;10:467–498. doi: 10.1016/0047-259X(80)90065-2
  • Robertson T, Wright FT. On measuring the conformity of a parameter set to a trend, with applications. Ann Stat. 1982;4:1234–1245.
  • Epstein B. Estimation from life test data. Technometrics. 1960;2:447–454. doi: 10.1080/00401706.1960.10489911

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