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Annals of Data Science

25-11-2024 | Original Article

On the xgamma k-record values and associated inference

Authors: Masoud Bazari Jamkhaneh, S. M. T. K. MirMostafaee, Marziye Jadidi

Published in: Annals of Data Science

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Abstract

The xgamma distribution was first introduced by Sen et al. [1] as an alternative distribution to the exponential model. The xgamma distribution exhibits a bathtub-shaped hazard rate function, so it is suitable for many lifetime phenomena. In this paper, we consider the upper k-record values from the xgamma distribution. We obtain exact explicit expressions for the moments of k-record values. We compute the means, variances, and covariances of the upper k-records. Using these computed values, we can find the best linear unbiased estimators (BLUEs) and the best linear invariant estimators (BLIEs) of the location and scale parameters of the xgamma model. In addition, we work on the prediction of a future k-record value. We find the best linear unbiased predictor (BLUP) and the best linear invariant predictor (BLIP) of a future k-record value. Another linear predictor is also discussed. A simulation study is performed to assess the proposed estimators and predictors. We also present a real data example in order to illustrate the application of the theoretical results of the paper. At the end of the paper, we will provide several concluding remarks.

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Sen S, Maiti SS, Chandra N (2016) The xgamma distribution: Statistical properties and application. J Mod Appl Stat Methods 15(1):774–788. https://doi.org/10.22237/jmasm/1462077420CrossRef

Raqab MZ (2002) Inferences for generalized exponential distribution based on record statistics. J Statist Plann Inference 104(2):339–350. https://doi.org/10.1016/S0378-3758(01)00246-4CrossRef

Ahmadi J, MirMostafaee SMTK (2009) Prediction intervals for future records and order statistics coming from two parameter exponential distribution. Statist Probab Lett 79(7):977–983. https://doi.org/10.1016/j.spl.2008.12.002CrossRef

MirMostafaee SMTK, Asgharzadeh A, Fallah A (2016) Record values from NH distribution and associated inference. Metron 74(1):37–59. https://doi.org/10.1007/s40300-015-0069-0CrossRef

Fallah A, Asgharzadeh A, MirMostafaee SMTK (2018) On the Lindley record values and associated inference. J Stat Theory Appl 17(4):686–702. https://doi.org/10.2991/jsta.2018.17.4.10CrossRef

Yousaf F, Ali S, Shah I (2019) Statistical inference for the Chen distribution based on upper record values. Ann Data Sci 6(4):831–851. https://doi.org/10.1007/s40745-019-00214-7CrossRef

Tripathi A, Singh U, Singh SK (2021) Inferences for the DUS-exponential distribution based on upper record values. Ann Data Sci 8(2):387–403. https://doi.org/10.1007/s40745-019-00231-6CrossRef

Etemad Golestani B, Ormoz E, MirMostafaee SMTK (2024) Statistical inference for the inverse Lindley distribution based on lower record values. REVSTAT. https://revstat.ine.pt/index.php/REVSTAT/article/view/559

Arnold BC, Balakrishnan N, Nagaraja HN (1998) Records. John Wiley & Sons, New YorkCrossRef

10.

Nevzorov VB (2001) Records: Mathematical theory. American Mathematical Society, Providence, Rhode Island

11.

Ahsanullah M (2004) Record values-theory and applications. University Press of America, Dallas

12.

Glick N (1978) Breaking records and breaking boards. Amer Math Monthly 85(1):2–26. https://doi.org/10.2307/2978044CrossRef

13.

Dziubdziela W, Kopociński B (1976) Limiting properties of the \(k\)-th record values. Appl Math 15(2):187–190. https://doi.org/10.4064/am-15-2-187-190CrossRef

14.

Olson DL, Shi Y (2007) Introduction to business data mining. McGraw-Hill/Irwin, New York

15.

Shi Y, Tian YJ, Kou G, Peng Y, Li J (2011) Optimization based data mining: theory and applications. Springer, LondonCrossRef

16.

Shi Y (2022) Advances in Big Data analytics: Theory, algorithm and practices. Springer, SingaporeCrossRef

17.

Ahmadi J, MirMostafaee SMTK, Balakrishnan N (2012) Bayesian prediction of \(k\)-record values based on progressively censored data from exponential distribution. J Stat Comput Simul 82(1):51–62. https://doi.org/10.1080/00949655.2010.526609CrossRef

18.

MirMostafaee SMTK, Mahdizadeh M, Aminzadeh M (2016) Bayesian inference for the Topp-Leone distribution based on lower \(k\)-record values. Japan J Indust Appl Math 33(3):637–669. https://doi.org/10.1007/s13160-016-0222-zCrossRef

19.

Wang L, Tripathi YM, Wu SJ, Zhang M (2020) Inference for confidence sets of the generalized inverted exponential distribution under \(k\)-record values. J Comput Appl Math 380:112969. https://doi.org/10.1016/j.cam.2020.112969CrossRef

20.

Jafari AA, Bafekri S (2021) Inferences on the performance index of Weibull distribution based on \(k\)-record values. J Comput Appl Math 382:113060. https://doi.org/10.1016/j.cam.2020.113060CrossRef

21.

Vishwakarma GK, Gupta S, Elsawah AM (2023) Shrinkage estimation of location parameter for uniform distribution based on \(k\)-record values. Sankhya B 85(2):405–419. https://doi.org/10.1007/s13571-023-00313-9CrossRef

22.

Pramanik S, Maiti S (2023) Different estimation methods for the parameter of xgamma distribution and their comparison. Reliab Theory Appl 18(4(76)):229-241. https://doi.org/10.24412/1932-2321-2023-476-229-241

23.

Sen S, Al-Mofleh H, Maiti SS (2021) On discrimination between the Lindley and xgamma distributions. Ann Data Sci 8(3):559–575. https://doi.org/10.1007/s40745-020-00243-7CrossRef

24.

Elshahhat A, Elemary BR (2021) Analysis for xgamma parameters of life under type-II adaptive progressively hybrid censoring with applications in engineering and chemistry. Symmetry 13(11):2112. https://doi.org/10.3390/sym13112112CrossRef

25.

Kumar S (2022) Classical and the Bayesian estimation of process capability index \(C_{py}\): A comparative study. J Reliab Stat Stud 15(1):153-186. https://doi.org/10.13052/jrss0974-8024.1517

26.

Pathak A, Kumar M, Singh SK, Singh U, Tiwari MK, Kumar S (2024) E-Bayesian inference for xgamma distribution under progressive type II censoring with binomial removals and their applications. Int J Model Simul 44(3):136–155. https://doi.org/10.1080/02286203.2022.2161744CrossRef

27.

Sen S, Chandra N, Maiti SS (2018) Survival estimation in xgamma distribution under progressively type-II right censored scheme. Model Assist Stat Appl 13(2):107–121. https://doi.org/10.3233/MAS-180423CrossRef

28.

Yadav AS, Saha M, Singh SK, Singh U (2019) Bayesian estimation of the parameter and the reliability characteristics of xgamma distribution using Type-II hybrid censored data. Life Cycle Reliab Saf Eng 8(1):1–10. https://doi.org/10.1007/s41872-018-0065-5CrossRef

29.

Saha M, Yadav AS (2021) Estimation of the reliability characteristics by using classical and Bayesian methods of estimation for xgamma distribution. Life Cycle Reliab Saf Eng 10(3):303–317. https://doi.org/10.1007/s41872-020-00162-9CrossRef

30.

Yadav AS (2023) Bayesian estimation for xgamma distribution under type-I hybrid censoring scheme using asymmetric loss function. Pak J Stat Oper Res 19(1):27-49. https://doi.org/10.18187/pjsor.v19i1.2808

31.

Khoshkhoo Amiri Z, MirMostafaee SMTK (2023) Analysis for the xgamma distribution based on record values and inter-record times with application to prediction of rainfall and COVID-19 records. Stat Transit new series 24(5):89-108. https://doi.org/10.59170/stattrans-2023-065

32.

Ranjbar V (2024) Statistical inference for x-gamma distribution under progressive type II censoring. São Paulo J Math Sci. https://doi.org/10.1007/s40863-024-00428-5CrossRef

33.

Chacko M, Shy Mary M (2013) Estimation and prediction based on \(k\)-record values from normal distribution. Statistica (Bologna) 73(4):505–516. https://doi.org/10.6092/issn.1973-2201/4495CrossRef

34.

Chacko M, Shy MM (2014) Estimation and prediction based on \(k\)-record values from logistic distribution. Calcutta Statist Assoc Bull 66(3–4):137–160. https://doi.org/10.1177/0008068320140302CrossRef

35.

Thomas PY, Paul J (2014) On generalized lower(k)record values from the Fréchet distribution. J Japan Statist Soc 44(2):157-178. https://doi.org/10.14490/jjss.44.157

36.

Paul J, Thomas PY (2015) On generalized upper(k)record values from Weibull distribution. Statistica (Bologna) 75(3):313–330. https://doi.org/10.6092/issn.1973-2201/6100CrossRef

37.

Minimol S, Thomas PY (2013) On some properties of Makeham distribution using generalized record values and its characterization. Braz J Probab Stat 27(4):487-501. https://www.jstor.org/stable/43601264

38.

Minimol S, Thomas PY (2014) On characterization of Gompertz distribution by properties of generalized record values. J Stat Theory Appl 13(1):38–45. https://doi.org/10.2991/jsta.2014.13.1.4CrossRef

39.

Khan RU, Kulshrestha A, Khan MA (2015) Relations for moments of \(k\)-th record values from exponential-Weibull lifetime distribution and a characterization. J Egyptian Math Soc 23(3):558–562. https://doi.org/10.1016/j.joems.2014.11.003CrossRef

40.

Khan RU, Khan MA, Khan MAR (2017) Relations for moments of generalized record values from additive Weibull distribution and associated inference. Stat Optim Inf Comput 5(2):127-136. https://doi.org/10.19139/soic.v5i2.237

41.

Singh B, Khan R, Khan MA (2019) Exact moments and characterizations of the Weibull-Rayleigh distribution based on generalized upper record statistics. Appl Math E-Notes 19:675–688

42.

Singh B, Khan R, Khan MAR (2019) Moments of generalized record values from Kumaraswamy-log-logistic distribution and related inferences. Thail Stat 17(1):93-103. https://ph02.tci-thaijo.org/index.php/thaistat/article/view/163214

43.

Alam M, Khan MA, Khan R (2020) Characterization of NH distribution through generalized record values. Appl Math E-Notes 20:406–414

44.

Alam M, Khan MA, Khan RU (2021) On upper \(k\)-record values from the generalized linear exponential distribution. J Stat Theory Appl 20(2):289–303. https://doi.org/10.2991/jsta.d.210216.001CrossRef

45.

Alam M, Vidovic Z (2023) K-th record moments and characterization of inverted Nadarajah-Haghighi distribution. Pakistan J Statist 39(2):99–113

46.

Anwar Z, Khan AN, Khan R (2023) Moments of generalized record values from modified Fréchet distribution and its characterization. Reliab Theory Appl 18(2(73)), 429-440. https://doi.org/10.24412/1932-2321-2023-273-429-440

47.

Gradshteyn IS, Ryzhik IM (2007) Table of Integrals, Series, and Products. Edited by A. Jeffrey & D. Zwillinger, 7th Edition, Elsevier/Academic Press, Amsterdam

48.

Lloyd EH (1952) Least-squares estimation of location and scale parameters using order statistics. Biometrika 39(1–2):88–95. https://doi.org/10.2307/2332466CrossRef

49.

Mann NR (1969) Optimum estimators for linear functions of location and scale parameters. Ann Math Stat 40(6):2149-2155. https://www.jstor.org/stable/2239527

50.

Kaminsky KS, Nelson PI (1975) Best linear unbiased prediction of order statistics in location and scale families. J Amer Statist Assoc 70(349):145–150. https://doi.org/10.2307/2285390CrossRef

51.

Chouia S, Zeghdoudi H (2021) The XLindley distribution: Properties and application. J Stat Theory Appl 20(2):318–327. https://doi.org/10.2991/jsta.d.210607.001CrossRef

52.

Chesneau C, Tomy L, Gillariose J (2021) A new modified Lindley distribution with properties and applications. J Stat Manag Syst 24(7):1383–1403. https://doi.org/10.1080/09720510.2020.1824727CrossRef

53.

R Core Team (2021) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.r-project.org

54.

Hasselman B (2018) nleqslv: Solve systems of nonlinear equations, R package version 3.3.2, https://CRAN.R-project.org/package=nleqslv

Title: On the xgamma k-record values and associated inference
Authors: Masoud Bazari Jamkhaneh
S. M. T. K. MirMostafaee
Marziye Jadidi
Publication date: 25-11-2024
Publisher: Springer Berlin Heidelberg
Published in: Annals of Data Science
Print ISSN: 2198-5804
Electronic ISSN: 2198-5812
DOI: https://doi.org/10.1007/s40745-024-00582-9

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