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Characterization of NH distribution through generalized record values. (English) Zbl 1462.62081

Summary: In this paper, we derive the exact expressions as well as recurrence relations for single and product moment of generalized record values from NH distribution. These relations generalize the results given by S. M. T. K. MirMostafaee et al. [Metron 74, No. 1, 37–59 (2016; Zbl 1394.62059)]. Further, we characterize the given distribution through conditional expectation, recurrence relations and truncated moments.

MSC:

62E10 Characterization and structure theory of statistical distributions
62G30 Order statistics; empirical distribution functions

Citations:

Zbl 1394.62059
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References:

[1] M. Ahsanullah and V. B. Nevzorov, Record via Probability Theory, Atlantis Press, Paris, 2015. · Zbl 1441.62002
[2] M. Ahsanullah, Record Statistics, Nova Science Publishers, New York, 1995. · Zbl 0907.62017
[3] B. C. Arnold, N. Balakrishnan and H. N. Nagaraja, Records, Wiley, New York, 1998. · Zbl 0914.60007
[4] M. Ahsanullah, M. Shakil and G. M. B. Kibria, Characterization of continuous distributions by truncated moment, Journal of Modern Applied Statistical Methods, 15(2016), 316-331.
[5] M. Bieniek and D. Szynal, Recurrence relations for distribution functions and moments ofk-th record values, J. Math. Sci., 111(2002), 3511-3519. · Zbl 1006.62046
[6] K. N. Chandler, The distribution and frequency of record values, J. Roy. Statist. Soc. Ser. B, 14(1952), 220-228. · Zbl 0047.38302
[7] M. A. Chaudhry and S. M. Zubair, Generalized incomplete gamma functions with applications, J. Comput. Appl. Math., 55(1994), 99-124. · Zbl 0833.33002
[8] K. Danielak and M. Z. Raqab, Sharp bounds for expectations ofk-th record increments, Aust. N. Z. J. Stat., 46(2004), 665-673. · Zbl 1061.62075
[9] W. Dziubdziela and B. Kopcoi´nski, Limiting properties of thek-th record value, Appl. Math., 15(1976), 187-190. · Zbl 0337.60023
[10] P. Deheuvels, Spacing, record times and extremal processes. Exchangeability in Probability and Statistics, pp. 233-243. North-Holland, Amsterdam (1982). · Zbl 0493.60077
[11] P. Deheuvels, Strong approximations ofk-th records andk-th record times by Wiener processes, Probab. Theory Related Fields, 77(1988), 195-209. · Zbl 0621.60087
[12] I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series of Products, Academic Press, New York, 2007. · Zbl 1208.65001
[13] Z. Grudzie´n, Characterization of Distribution of Time Limits in Record Statistics as well as Distributions and Moments of Linear Record Statistics from the Samples of Random Numbers, Praca Doktorska, UMCS, Lublin, 1982.
[14] Z. Grudzie´n and D. Szynal, On the expected values ofk-th record values and associated characterizations of distributions, Prob. Statist. Decision Theory, A(1983), 119-127. · Zbl 0586.62071
[15] Z. Grudzie´n and D. Szynal, Characterization of continuous distributions via moments ofk-th record values with random indices, J. Appl. Statist. Sci., 5(1997), 259-266. · Zbl 0888.62009
[16] U. Kamps, A Concept of Generalized Order Statistics, B.G. Teubner Stuttgart, Germany, 1995. · Zbl 0851.62035
[17] M. A. Khan and R. U. Khan,k-th upper record values from modi…ed Weibull distribution and characterization, Int. J. Comp. Theo. Stat., 3(2016), 75-80.
[18] R. U. Khan, M. A. Khan and M. A. R. Khan, Relations for moments of generalized record values from additive-Weibull lifetime distribution and associated inference, Stat. Optim. Inf. Comput., 5(2017), 127-136.
[19] R. U. Khan, A. Kulshrestha and M. A. Khan, Relations for moments ofk-th record values from exponential-Weibull lifetime distribution and a characterization, J. Egyptian Math. Soc., 23(2015), 558-562. · Zbl 1328.62286
[20] A. J. Lemonte, A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function, Comput. Statist. Data Anal., 62(2013), 149-170. · Zbl 1348.62043
[21] G. D. Lin, On a moment problem, Tohoku Math. J., 38(1986), 595-598. · Zbl 0602.42016
[22] S. Minimol and P. Y. Thomos, On some properties of Makeham distribution using generalized record values and its characterization, Braz. J. Probab. Stat., 27(2013), 487-501. · Zbl 1298.62178
[23] S. Minimol and P. Y. Thomos, On characterization of Gompertz distribution by properties of generalized record values, J. Stat. Theory Appl., 13(2014), 38-45.
[24] S. M. T. K. MirMostafee, A. Asgharzadeh and A. Fallah, Record values from NH distribution and associated inference, Metron, 74(2016), 37-59. · Zbl 1394.62059
[25] S. Nadarajah and F. Haghighi, An extension of the exponential distribution, Statistics, 45(2011), 543- 558. · Zbl 1228.62018
[26] V. B. Nevzorov, Records: Mathematical Theory, Translation of Mathematical Monographs, vol. 194. American Mathematical Society, Providence, RI, USA, 2001.
[27] J. Paul and P. Y. Thomas, On generalized upper(k)record values from Weibull distribution, Statistica, LXXV(2015), 313-330. · Zbl 1473.62155
[28] J. Paul and P. Y. Thomas, On generalized upper(k)record values from Pareto distribution, Aligarh J. Statist., 36(2016), 63-78. · Zbl 1392.62048
[29] P. Pawlas and D. Szynal, Relations for single and product moments ofk-th record values from exponential and Gumble distributions, J. Appl. Statist. Sci., 7(1998), 53-62. · Zbl 0901.62023
[30] P. Pawlas and D. Szynal, Recurrence relations for single and product moments ofk-th record values from Pareto, generalized Pareto and Burr distributions, Comm. Statist. Theory Methods, 28(1999), 1699-1709. · Zbl 0932.62015
[31] P. Pawlas and D. Szynal, Recurrence relations for single and product moments ofk-th record values Weibull distributions, and a characterization, J. Appl. Statist. Sci., 10(2000), 17-26. · Zbl 0961.62009
[32] B. Singh, R. U. Khan and M. A. R. Khan, Moments of generalized record values from Kumaraswamylog-logistic distribution and related inferences, Thailand Statistician, 17(2019a), 93-103. · Zbl 1420.62224
[33] B. Singh, R. U. Khan and M. A. Khan, Exact moments and characterizations of the Weibull-Rayleigh distribution based on generalized upper record statistics, Applied Mathematics E-Notes, 19(2019b), 675-688 · Zbl 1435.62170
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