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On the Unit-Chen distribution with associated quantile regression and applications

  • Mustafa Ç. Korkmaz EMAIL logo , Emrah Altun , Christophe Chesneau and Haitham M. Yousof
From the journal Mathematica Slovaca

Abstract

In this paper, a new distribution defined on (0, 1) is introduced. It is obtained by the transformation of a positive random variable following the Chen distribution with respect to the inverted exponential function. Basic distributional properties of the newly defined distribution are studied. Then, as a statistical model, we examine different methods of estimation for related parameters. We assess the performance of the obtained estimators by a complete simulation study. Subsequently, the quantile regression model based on the proposed distribution is introduced. Applications of the proposed models to real data sets show that they have better modeling capabilities than fair competitors.

  1. (Communicated by Gejza Wimmer)

References

[1] Altun, E.: The log-weighted exponential regression model: alternative to the beta regression model, Comm. Statist. Theory Methods (2021), https://doi.org/10.1080/03610926.2019.1664586.10.1080/03610926.2019.1664586Search in Google Scholar

[2] Altun, E.—Cordeiro, G. M.: The unit-improved second-degree Lindley distribution: inference and regression modeling, Comput. Statist. 35 (2020), 259–279.10.1007/s00180-019-00921-ySearch in Google Scholar

[3] Altun, E.—Hamedani, G. G.: The log-xgamma distribution with inference and application, J. SFdS 159 (2018), 40–55.Search in Google Scholar

[4] Anderson, T. W.—Darling, D. A.: Asymptotic theory of certain ``Goodness of fit'' criteria based on stochastic processes, Ann. Math. Statist. 23 (1952), 193–212.10.1214/aoms/1177729437Search in Google Scholar

[5] Ampadu, C.B.: A Chen type generated Family of distributions, Ann. Biostat. Biom. Appl. 4 (2020), 1–2.Search in Google Scholar

[6] Anzagra, L.—Sarpong, S.—Nasiru, S. Odd Chen-G Family of distributions, Ann. Data. Sci. (2020), https://doi.org/10.1007/s40745-020-00248-2.10.1007/s40745-020-00248-2Search in Google Scholar

[7] Chen, G.—Balakrishnan, N.: A general purpose approximate goodness-of-fit test, J. Qual. Technol. 27 (1995), 154–161.10.1080/00224065.1995.11979578Search in Google Scholar

[8] Chen, Z.: A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function, Statist. Probab. Lett. 49 (2000), 155–161.10.1016/S0167-7152(00)00044-4Search in Google Scholar

[9] Cheng, R. C. H.—Amin, N. A. K.: Maximum product of spacings estimation with application to the lognormal distribution. Math. Report, 79-1, Deparment of Mathematics, UWIST, Cardiff, UK, 1979.Search in Google Scholar

[10] Cheng, R. C. H.—Amin, N. A. K.: Estimating parameters in continuous univariate distributions with a sh1ifted origin, J. Royal Stat. Soci. Series B (Methodological) 45 (1983), 394–403.Search in Google Scholar

[11] Cordeiro, G. M.—Silva, R. B.—NASCIMENTO, A. D. C.: Recent Advances in Lifetime and Reliability Models, Bentham Books, 2020.10.2174/97816810834521200101Search in Google Scholar

[12] David, H. A.—Nagaraja, H.: Order Statistics, 3rd edition, John Wiley and Sons, New York, 2003.10.1002/0471722162Search in Google Scholar

[13] Falk, M.: On the estimation of the quantile density function, Statist. Probab. Lett. 4 (1986), 69–73.10.1016/0167-7152(86)90020-9Search in Google Scholar

[14] G෼ndÜZ, S.—Korkmaz, M. Ç.: A new unit distribution based on the unbounded Johnson distribution rule: The unit Johnson SU distribution, Pak. J. Stat. Oper. Res. 16 (2020), 471–490.10.18187/pjsor.v16i3.3421Search in Google Scholar

[15] Korkmaz, M. Ç.: A new heavy-tailed distribution defined on the bounded interval: the logit slash distribution and its application, J. App. Stat. 47 (2020a), 2097–2119.10.1080/02664763.2019.1704701Search in Google Scholar PubMed PubMed Central

[16] Korkmaz, M. Ç.: The unit generalized half normal distribution: A new bounded distribution with inference and application, UPB Scientific Bulletin, Series A: Applied Mathematics and Physics 82 (2020b), 133–140.Search in Google Scholar

[17] Korkmaz, M. Ç.—Chesneau, C.: On the unit Burr-XII distribution with the quantile regression modeling and applications, J. Comput. Appl. Math. 40 (2021), 1–26.10.1007/s40314-021-01418-5Search in Google Scholar

[18] Korkmaz, M. Ç.—Chesneau, C.—Korkmaz, Z. S.: On the arcsecant hyperbolic normaldistribution. Properties, quantile regression modeling and applications, Symmetry 13(117) (2021a), 1–24.10.3390/sym13010117Search in Google Scholar

[19] Korkmaz, M. Ç.—Chesneau, C.—Korkmaz, Z. S.: Transmuted unit Rayleigh quantile regression model: Alternative to beta and Kumaraswamy quantile regression models, Univ. Politehc. Bucharest Sci. Bull. Ser. A-App. Math. and Phys. (2021b), to appear.Search in Google Scholar

[20] KOTZ, S.—Lumelskii, Ya.—Pensky, M.: The Stress-Strength Model and its Generalization: Theory and Applications, World Scientific, Singapore, 2003.10.1142/5015Search in Google Scholar

[21] Kumaraswamy, P.: A generalized probability density function for double-bounded random processes, J. Hydrol. 46 (1980), 79–88.10.1016/0022-1694(80)90036-0Search in Google Scholar

[22] Mazucheli, J.—Menezes, A. F. B.—Fernandes, L. B.—de Oliveira, R. P.—Ghitany, M.: The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates, J. Appl. Stat. 47 (2020), 954–974.10.1080/02664763.2019.1657813Search in Google Scholar PubMed PubMed Central

[23] Mazucheli, J.—Menezes, A. F. B.—Chakraborty, S.: On the one parameter unit-Lindley distribution and its associated regression model for proportion data, J. Appl. Stat. 46 (2019a), 700–714.10.1080/02664763.2018.1511774Search in Google Scholar

[24] Mazucheli, J.—Menezes, A. F. B.—Dey, S.: Unit-Gompertz distribution with applications, Statistica 79 (2019b), 25–43.Search in Google Scholar

[25] Mazucheli, J.—Menezes, A. F. B.—Dey, S.: The unit-Birnbaum-Saunders distribution with applications, Chil. J. Stat. 9 (2018), 47–57.Search in Google Scholar

[26] Mazucheli, J.—Menezes, A. F. B.—Ghitany, M. E.: The unit-Weibull distribution and associated inference, J. Appl. Prob. Stat. 13 (2018), 1–22.Search in Google Scholar

[27] Murhty, D. P.—Xie, M.—Jiang, R.: Weibull models, Vol. 505, John Wiley & Sons, 2004.Search in Google Scholar

[28] Mitnik, P. A.—Baek, S.: The Kumaraswamy distribution: median-dispersion re-parameterizations for regression modeling and simulation-based estimation, Statist. Papers 54 (2013), 177–192.10.1007/s00362-011-0417-ySearch in Google Scholar

[29] Pourdarvish, A.—Mirmostafaee, S. M. T. K.—Naderi, K.: The exponentiated Topp-Leone distribution: Properties and application, J. Appl. Environ. Biol. Sci. 5 (2015), 251–256.Search in Google Scholar

[30] Ranneby, B.: The maximum spacing method. An estimation method related to the maximum likelihood method, Scand. J. Stat. 11 (1984), 93–112. %varSearch in Google Scholar

[31] Surles, J. G.—Padgett, W. J.: Inference for reliability and stress-strength for a scaled Burr-type X distribution, Lifetime Data Anal. 7 (2001), 187–200.10.1023/A:1011352923990Search in Google Scholar PubMed

[32] Topp, C. W.—Leone, F. C.: A family of J-shaped frequency functions, J. Amer. Stat. Assoc. 50 (1955), 209–219.10.1080/01621459.1955.10501259Search in Google Scholar

[33] Van-Dorp, J. R.—Kotz, S.: The standard two-sided power distribution and its properties: with applications in financial engineering, Amer. Statist. 56 (2002), 90–99.10.1198/000313002317572745Search in Google Scholar

[34] Zacks, S.: Introduction to Reliability Analysis Probability Models and Statistical Methods, Springer-Verlag, New York, 1992.10.1007/978-1-4612-2854-7Search in Google Scholar

Received: 2020-12-14
Accepted: 2021-05-06
Published Online: 2022-06-11
Published in Print: 2022-06-27

© 2022 Mathematical Institute Slovak Academy of Sciences

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