Characterizations of geometric distributions based on kth record values

References

• Nevzorov VB. Records: mathematical theory. Providence (RI): American Mathematical Society; 2000. (Translations of mathematical monographs; vol. 194).
   Google Scholar
• Arnold BC, Balakrishnan N, Nagaraja HN. Records. New York (NY): Wiley; 1998.
   Google Scholar
• Raqab MZ, Rychlik T. Sharp bounds for the mean of kth record value. Commun Statist Theory Methods. 2002;31:1927–1937. doi: 10.1081/STA-120015011
   Web of Science ®Google Scholar
• Raqab MZ, Rychlik T. Sharp bounds on the expectations of second record values from symmetric populations. Statistics. 2004;38:49–57. doi: 10.1080/0233188032000158808
   Web of Science ®Google Scholar
• Klimczak M, Rychlik T. Maximum variance of kth records. Statist Probab Lett. 2004;69:421–430. doi: 10.1016/j.spl.2004.06.038
   Web of Science ®Google Scholar
• Klimczak M, Rychlik T. Reconstruction of previous failure times and records. Metrika. 2005;61:277–290. doi: 10.1007/s001840400344
   Web of Science ®Google Scholar
• Charalambides ChA, Rychlik T. Distributions and moments of record values in a sequence of maximally dependent random variables. J Statist Plann Inference. 2008;138:2253–2266. doi: 10.1016/j.jspi.2007.09.014
   Web of Science ®Google Scholar
• Goroncy A, Rychlik T. Lower bounds on the expectations of upper record values. J Statist Plann Inference. 2011;141:2726–2737. doi: 10.1016/j.jspi.2011.02.023
   Web of Science ®Google Scholar
• Jasiński K. On maximum variance of kth records. Commun Statist Theory Methods. 2016;45:2392–2401. doi: 10.1080/03610926.2013.879895
   Web of Science ®Google Scholar
• Kozyra PM, Rychlik T. Sharp bounds on the expectations of linear combinations of kth records expressed in the Gini mean difference units. Probab Math Statist. 2018;38:39–59.
   Web of Science ®Google Scholar
• Kozyra PM, Rychlik T. Upper and lower bounds on the variances of linear combinations of the kth records. Statistics. 2018;52:177–204. doi: 10.1080/02331888.2017.1343828
   Web of Science ®Google Scholar
• López-Blázquez F, Salamanca Miño B, Dembińska A. A note on the distribution of kth records from discrete distributions. Statist Probab Lett. 2005;75:325–330. doi: 10.1016/j.spl.2005.06.008
   Web of Science ®Google Scholar
• Dembińska A, López-Blázquez F. A characterization of geometric distribution through kth weak records. Commun Statist Theory Methods. 2005;34:2345–2351. doi: 10.1080/03610920500313692
   Web of Science ®Google Scholar
• Dembińska A, López-Blázquez F. kth records from discrete distributions. Statist Probab Lett. 2005;71:203–214. doi: 10.1016/j.spl.2004.11.001
   Web of Science ®Google Scholar
• Dembińska A. A review on characterizations of discrete distributions based on records and kth records. Commun Statist Theory Methods. 2007;36:1381–1387. doi: 10.1080/03610920601077113
   Web of Science ®Google Scholar
• Dembińska A. Characterizations of discrete distributions based on record values. In: Ahsanullah M, Kirmani S, editors. Extreme value distributions. New York (NY): Nova Science Publishers; 2007. p. 63–75.
   Google Scholar
• Dembińska A. kth records from geometric distribution. Statist Probab Lett. 2008;78:1662–1670. doi: 10.1016/j.spl.2008.01.009
   Web of Science ®Google Scholar
• Dembińska A, Danielak K. On moments of k-records from discrete distributions. Commun Statist Theory Methods. 2008;37:2516–2531. doi: 10.1080/03610920802040381
   Web of Science ®Google Scholar
• Oncel SY, Aliev F. Characterizations of geometric and discrete Pareto distributions based on the conditional distribution of kth records. J Statist Theory Appl. 2016;15:367–372. doi: 10.2991/jsta.2016.15.4.4
   Web of Science ®Google Scholar
• Jasiński K. Relations for product moments and covariances of kth records from discrete distributions. Metrika. 2018;81:125–141. doi: 10.1007/s00184-017-0637-9
   Web of Science ®Google Scholar
• Aliev FA. New characterizations of discrete distributions through weak records. Theory Probab Appl. 1999;44:756–761. doi: 10.1137/TPRBAU000044000004000756000001
   Web of Science ®Google Scholar
• Danielak K, Dembińska A. Some characterizations of discrete distributions based on weak records. Statist Papers. 2007;48:479–489. doi: 10.1007/s00362-006-0349-0
   Web of Science ®Google Scholar
• Danielak K, Dembińska A. On characterizing discrete distributions via conditional expectations of weak record values. Metrika. 2007;66:129–138. doi: 10.1007/s00184-006-0100-9
   Web of Science ®Google Scholar
• Ahsanullah M, Aliev F. A characterization of geometric distribution based on weak records. Statist Probab Lett. 2011;52:651–655.
   Google Scholar
• Karczewski R, Wesołowski J. linearity of regression for weak records, revisited. Statistics. 2017;51:878–887. doi: 10.1080/02331888.2017.1301940
   Web of Science ®Google Scholar
• Feller W. An introduction to probability theory and its applications, Vol. I. 2nd ed. New York (NY): Wiley; 1957.
   Google Scholar