A novel asymmetric form of the power half-logistic distribution with statistical inference and real data analysis

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Abstract

This study provided a significant contribution to developing an adaptable trigonometric extension of the power half-logistic distribution. To be more specific, we created an innovative two- parameter lifetime model called the sine power half-logistic distribution (SPHLD) by using features from the sine-generated family of distributions. The novel distribution could be more effective in modeling lifetime phenomena when asymmetric data was presented, which was the primary motivating factor. The SPHLD’s density function plots showed that the distribution adopted several asymmetric shape configurations. Furthermore, the SPHLD’s hazard rate plots displayed both monotonic increases and decreases. The quantile function, moments, incomplete moment, and stress-strength reliability were among the statistical characteristics of the SPHLD that were computed. Statistical inference using sixteen distinct classical estimating techniques was utilized to estimate the SPHLD parameters. A simulation study was done to evaluate the consistency of the different estimates and determine the best estimating approach based on some accuracy measures. Analyses of real data revealed that the SPHLD performed better than a number of alternative distributions.

Keywords

power half logistic distribution / trigonometric distributions / stress-strength reliability / minimum spacing absolute-log distance / Anderson-Darling left tail second order / data analysis

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References

[1] A. Marshall, I. Olkin, A new method for adding a parameter to a family of distributions with applications to the exponential and Weibull families, Biometrika, 84 (1997), 641-652. https://doi.org/10.1093/biomet/84.3.641

[2] N. Eugene, C. Lee, F. Famoye, Beta-normal distribution and its applications, Commun. Stat.-Theory Methods, 31 (2002), 497-512. https://doi.org/10.1081/STA-120003130

[3] A. Alzaatreh, F. Famoye, C. Lee, A new method for generating families of continuous distributions, Metron, 71 (2013), 63-79. https://doi.org/10.1007/s40300-013-0007-y

[4] A. Al-Shomrani, O. Arif, A. Shawky, S. Hanif, M. Q. Shahbaz, Topp-Leone family of distributions: Some properties and application, Pak. J. Stat. Oper. Res., 12 (2016), 443-451. https://doi.org/10.18187/pjsor.v12i3.1458

[5] A. S. Hassan, E. A. El-Sherpieny, S. A. El-Taweel, New Topp Leone-G family with mathematical properties and applications, J. Phys.: Conf. Ser., 12 (2021). https://doi:10.1088/1742-6596/1860/1/012011.

[6] M. A. Badr, I. Elbatal, F. Jamal, C. Chesneau, M. Elgarhy, The transmuted odd Fréchet-G family of distributions: Theory and applications, Mathematics, 8 (2020), 958. https://doi.org/10.3390/math8060958

[7] M. Aslam, Z. Asghar, Z. Hussain, S. F. Shah, A modified T-X family of distributions: Classical and Bayesian analysis, J. Taibah Univ. Sci., 14 (2020), 254-264. https://doi.org/10.1080/16583655.2020.1732642

[8] A. S. Hassan, M. A. H. Sabry, A. M. Elsehtery, A new probability distribution family arising from truncated power Lomax distribution with application to Weibull model, Pak. J. Stat. Oper. Res., 16 (2020), 661-674. https://doi.org/10.1007/s12015-020-09979-4

[9] F. S. Gomes-Silva, A. Percontini, E. de Brito, M. W. Ramos, R. Venâncio, G. M. Cordeiro, The odd Lindley-G family of distributions, Austrian J. Stat., 46 (2017), 65-87. https://doi.org/10.17713/ajs.v46i1.222

[10] A. S. Hassan, S. G. Nassar, Power Lindley-G family of distributions, Ann. Data Sci., 6 (2019), 189-210. https://doi.org/10.1007/s40745-018-0159-y

[11] I. Elbatal, N. Alotaibi, E. M. Almetwally, S. A. Alyami, M. Elgarhy, On odd perks-G class of distributions: properties, regression model, discretization, Bayesian and non-Bayesian estimation, and applications, Symmetry, 14 (2022), 883. https://doi.org/10.3390/sym14050883

[12] A. Z. Afify, G. M. Cordeiro, N. A. Ibrahim, J. M. Elgarhy, M. A. Nasir, The Marshall-Olkin odd Burr III-G family: Theory, estimation, and engineering applications, IEEE Access, 9 (2021), 4376-4387. https://doi.org/10.1109/ACCESS.2020.3044156

[13] C. Chesneau, T. E. Achi, Modified odd Weibull family of distributions: Properties and applications, J. Indian Soc. Probab. Stat., 21 (2020), 259-286. https://doi.org/10.1007/s41096-020-00075-x

[14] J. T. Eghwerido, D. J. Ikwuoche, O. D. AdubisiM, Inverse odd Weibull generated family of distribution, Pak. J. Stat. Oper. Res., 16 (2020), 617-633.

[15] D. Kumar, U. Singh, S. K. Singh, A new distribution using sine function- its application to bladder cancer patients data, J. Stat. Appl. Prob., 4 (2015), 417-427.

[16] Z. Mahmood, C. Chesneau, M.H. Tahir, A new sine-G family of distributions: properties and applications, Bull. Comput. Appl. Math., 7 (2019), 53-81.

[17] N. Balakrishnan, Order statistics from the half logistic distribution. J. Stat. Comput. Simul., 20 (1985), 287-309.

[18] R. S. Rao, P. L. Mamidi, R. R. Kantam, Modified maximum likelihood estimation: Inverse half logistic distribution, J. Math., 5 (2016), 11-19.

[19] H. Torabi, F. L. Bagheri, Estimation of parameters for an extended generalized half logistic distribution based on complete and censored data, J. Iranian Stat. Soc., 9 (2010), 171-195.

[20] G. M. Cordeiro, M. Alizadeh, E. M. M. Ortega, The exponentiated half logistic family of distributions: properties and applications, J. Probab. Stat., 2014 (2014), 864396. https://doi.org/10.1155/2014/864396

[21] J. Oliveira, J. Santos, C. Xavier, D. Trindade, G. M. Cordeiro, The McDonald half-logistic distribution: theory and practice, Commun. Stat. Theory Methods, 45 (2016), 2005-2022. https://doi.org/10.1080/03610926.2013.873131

[22] A. H. Hassan, M. Elgarhy, M. Shakil, Type II half logistic family of distributions with applications, Pak. J. Stat. Oper. Res., 13 (2017), 245-264. https://doi.org/10.18187/pjsor.v13i2.1560

[23] S. D. Krishnarani, On a power transformation of half-logistic distribution, J. Probab. Stat., 20 (2016), 1-10.

[24] R. M. Usman, A. M. Haq, J. Talib, Kumaraswamy half-logistic distribution: properties and applications, J. Stat. Appl. Probab., 6 (2017), 597-609. https://doi.org/10.18576/jsap/060315

[25] D. Yegen, G. Ozel, Marshall-Olkin half logistic distribution with theory and applications, Alphanum. J., 6 (2018), 408-416. https://doi.org/10.17093/alphanumeric.409992

[26] M. Elgarhy, A. S. Hassan, S. Fayomi, Maximum likelihood and Bayesian estimation for two-parameter type I half logistic Lindley distribution, J. Comput. Theor. Nanosci., 15 (2018), 1-9. https://doi.org/10.1166/jctn.2018.7600

[27] A. F. Samuel, O. A. Kehinde, A study on transmuted half logistic distribution: Properties and application, Int. J. Stat. Distribut. Appl., 5 (2019), 54-59.

[28] A. S. Hassan, M. Elgarhy, M. A. Haq, S. Alrajhi, On type II half logistic Weibull distribution with applications, Math. Theory Model., 19(2019), 49-63. https://doi.org/10.21608/esju.2019.268726

[29] M. Anwar, A. Bibi, The half-logistic generalized Weibull distribution, J. Probab. Stat., (2018), 8767826. https://doi.org/10.1155/2018/8767826

[30] A. Algarni, A. M. Almarashi, I. Elbatal, A. S. Hassan, E. M. Almetwally, A. M. Daghistani, et al., Type I half logistic Burr X-G family: Properties, Bayesian, and non-Bayesian estimation under censored samples and applications to COVID-19 data, Math. Probl. Eng., 2021, (2021), 5461130. https://doi.org/10.1155/2021/5461130

[31] G. S. Mohammad, A new two-parameter modified half-logistic distribution: Properties and Applications, Stat. Optim. Inf. Comput., 10 (2022), 589-605. https://doi.org/10.19139/soic-2310-5070-1210

[32] A. S. Hassan, A. Fayomi, A. Algarni, E. M. Almetwally, Bayesian and non-Bayesian inference for unit-exponentiated half-logistic distribution with data analysis, Appl. Sci., 12 (2022), 11253. https://doi.org/10.3390/app122111253

[33] H. Majid, An extended type I half-logistic family of distributions: Properties, applications and different method of estimations, Math. Slovaca, 72 (2022), 745-764. https://doi.org/10.1515/ms-2022-0051

[34] R. M. I. Arshad, M. H. Tahir, C. Chesneau, S. Khan, F. Jamal, The gamma power half-logistic distribution: theory and applications, Sao Paulo J. Math. Sci., 17 (2023), 1142-1169. https://doi.org/10.1007/s40863-022-00331-x

[35] S. M. Alghamdi, M. Shrahili, A. S. Hassan, A. M. Gemeay, I. Elbatal, M. Elgarhy, Statistical inference of the half logistic modified Kies exponential model with modeling to engineering data, Symmetry, 15 (2023), 586. https://doi.org/10.3390/sym15030586

[36] O. D. Adubisi, C. E. Adubisi, Novel distribution for modeling uncensored and censored survival time data and regression model, Reliab. Theory Appl., 3 (2023), 808-824.

[37] R. C. H. Cheng, N. A. K. Amin, Maximum product-of-spacings estimation with applications to the log-normal distribution, University of Wales IST, Math Report, (1979), 79-103.

[38] R. C. H. Cheng, N. A. K. Amin, Estimating parameters in continuous univariate distributions with a shifted origin, J. R. Stat. Soc.: Ser. B (Methodol.) 45 (1983), 394-403. https://doi.org/10.1111/j.2517-6161.1983.tb01268.x

[39] B. Ranneby, The maximum spacing method: An estimation method related to the maximum likelihood method, Scand. J. Stat., 11 (1984), 93-112.

[40] G. M. Cordeiro, T. A. de Andrade, M. Bourguignon, F. G. Silva, The exponentiated generalized standardized half-logistic distribution, Int. J. Stat. Probab., 6 (2017), 24-42. https://doi.org/10.5539/ijsp.v6n3p24

[41] J. I. Seo, S. B. Kang, Notes on the exponentiated half logistic distribution, Appl. Math. Model., 39 (2015), 6491-6500.

[42] M. Muhammad, L. Liu, A new extension of the generalized half logistic distribution with applications to real data, Entropy, 21 (2019), 339. https://doi.org/10.3390/e21040339

[43] R. M. Usman, M. Haq, J. Talib, Kumaraswamy half-logistic distribution: properties and applications, J. Stat. Appl. Probab., 6 (2017), 597-609. https://doi.org/10.18576/jsap/060315

[44] G. M. Cordeiro, R. B. dos Santos, The beta power distribution. Brazil J. Probab. Stat., 26 (2012), 88-112. https://doi.org/10.1214/10-BJPS124

[45] M. V. Aarset, How to identify a bathtub hazard rate, IEEE Trans. Reliab., 36 (1987), 106-108. https://doi.org/10.1109/TR.1987.5222310

[46] E. T. Lee, Statistical methods for survival data analysis, IEEE Trans. Reliab., 35 (1986), 123- 123. https://doi.org/10.1109/TR.1986.4335370

[47] A. Henningsen, O. Toomet, maxLik: A package for maximum likelihood estimation in R, Comput. Stat., 26 (2011), 443-458. https://doi.org/10.1007/s00180-010-0217-1

[48] R Core Team, R: A language and environment for statistical computing, Foundation for Statistical Computing, Vienna, Austria, 2013.

[49] B. Lambert, A student’s guide to Bayesian statistics, in A Student’s Guide to Bayesian Statistics , (2018), 1-520.

[50] K. P. Burnham, D. R. Anderson, Model selection and multimodel inference: a practical information-theoretic approach, Springer, 2002.