A new one-parameter flexible family with variable failure rate shapes: Properties, inference, and real-life applications

Hisham Mahran; Mahmoud M. Mansour; Enayat M. Abd Elrazik; Ahmed Z. Afify; Hisham Mahran; Mahmoud M. Mansour; Enayat M. Abd Elrazik; Ahmed Z. Afify

doi:10.3934/math.2024582

AIMS Mathematics

2024, Volume 9, Issue 5: 11910-11940. doi: 10.3934/math.2024582

Previous Article Next Article

Research article

A new one-parameter flexible family with variable failure rate shapes: Properties, inference, and real-life applications

1.
Department of Statistics, Mathematics and Insurance, Ain Shams University, Cairo 11566, Egypt
2.
Department of Management Information Systems, Yanbu, Taibah University, Yanbu 46422, Saudi Arabia
3.
Department of Statistics, Mathematics, and Insurance, Benha University, Benha 13511, Egypt

Received: 09 January 2024 Revised: 25 February 2024 Accepted: 06 March 2024 Published: 26 March 2024
MSC : 60E05, 62F10, 62F10, 62N05

We introduced a flexible class of continuous distributions called the generalized Kavya-Manoharan-G (GKM-G) family. The GKM-G family extended the Kavya-Manoharan class and provided greater flexibility to the baseline models. The special sub-models of the GKM-G family are capable of modeling monotone and non-monotone failure rates including increasing, reversed J shape, decreasing, bathtub, modified bathtub, and upside-down bathtub. Some properties of the family were studied. The GKM-exponential (GKME) distribution was studied in detail. Eight methods of estimation were used for estimating the GKME parameters. The performance of the estimators was assessed by simulation studies under small and large samples. Furthermore, the flexibility of the two-parameter GKME distribution was explored by analyzing five real-life data applications from applied fields such as medicine, environment, and reliability. The data analysis showed that the GKME distribution outperforms other competing exponential models.
- Kavya-Manoharan transformation,
- exponential distribution,
- order statistics,
- Anderson-Darling estimation,
- mean residual life,
- entropy
Citation: Hisham Mahran, Mahmoud M. Mansour, Enayat M. Abd Elrazik, Ahmed Z. Afify. A new one-parameter flexible family with variable failure rate shapes: Properties, inference, and real-life applications[J]. AIMS Mathematics, 2024, 9(5): 11910-11940. doi: 10.3934/math.2024582

Related Papers:

Abstract

We introduced a flexible class of continuous distributions called the generalized Kavya-Manoharan-G (GKM-G) family. The GKM-G family extended the Kavya-Manoharan class and provided greater flexibility to the baseline models. The special sub-models of the GKM-G family are capable of modeling monotone and non-monotone failure rates including increasing, reversed J shape, decreasing, bathtub, modified bathtub, and upside-down bathtub. Some properties of the family were studied. The GKM-exponential (GKME) distribution was studied in detail. Eight methods of estimation were used for estimating the GKME parameters. The performance of the estimators was assessed by simulation studies under small and large samples. Furthermore, the flexibility of the two-parameter GKME distribution was explored by analyzing five real-life data applications from applied fields such as medicine, environment, and reliability. The data analysis showed that the GKME distribution outperforms other competing exponential models.

References

[1]	A. W. 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 doi: 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 doi: 10.1081/STA-120003130
[3]	W. T. Shaw, I. R. C. Buckley, The alchemy of probability distributions: Beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map, arXiv, 2007. https://doi.org/10.48550/arXiv.0901.0434
[4]	G. M. Cordeiro, M. de Castro, A new family of generalized distributions, J. Stat. Comput. Simul., 81 (2011), 883–898. https://doi.org/10.1080/00949650903530745 doi: 10.1080/00949650903530745
[5]	M. Bourguignon, R. B. Silva, G. M. Cordeiro, The Weibull-G family of probability distributions, J. Data Sci., 12 (2014), 53–68. https://doi.org/10.6339/JDS.2014.12(1).1210 doi: 10.6339/JDS.2014.12(1).1210
[6]	H. M. Yousof, A. Z. Afify, M. Alizadeh, N. S. Butt, G. Hamedani, M. M. Ali, The transmuted exponentiated generalized-G family of distributions, Pak. J. Stat. Oper. Res., 11 (2015), 441–464. https://doi.org/10.18187/pjsor.v11i4.1164 doi: 10.18187/pjsor.v11i4.1164
[7]	A. Z. Afify, G. M. Cordeiro, H. M. Yousof, A. Alzaatreh, Z. M. Nofal, The Kumaraswamy transmuted-G family of distributions: properties and applications, J. Data Sci., 14 (2016), 245–270. https://doi.org/10.6339/JDS.201604_14(2).0004 doi: 10.6339/JDS.201604_14(2).0004
[8]	Z. M. Nofal, A. Z. Afify, H. M. Yousof, H. G. M. Cordeiro, The generalized transmuted-G family of distributions, Commun. Stat. Theory Methods, 46 (2017), 4119–4136. https://doi.org/10.1080/03610926.2015.1078478 doi: 10.1080/03610926.2015.1078478
[9]	G. M. Cordeiro, M. Alizadeh, G. Ozel, B. Hosseini, E. M. M. Ortega, E. Altun, The generalized odd log-logistic family of distributions: Properties, regression models and applications, J. Stat. Comput. Simul., 87 (2017), 908–932. https://doi.org/10.1080/00949655.2016.1238088 doi: 10.1080/00949655.2016.1238088
[10]	S. M. Zaidi, M. M. AL Sobhi, M. El-Morshedy, A. Z. Afify, A new generalized family of distributions: Properties and applications, AIMS Math., 6 (2021), 456–476. https://doi.org/10.3934/math.2021028 doi: 10.3934/math.2021028
[11]	A. Z. Afify, H. Al-Mofleh, H. M. Aljohani, G. M. Cordeiro, The Marshall-Olkin-Weibull-H family: Estimation, simulations, and applications to COVID-19 data, J. King Saud Univ. Sci., 34 (2022), 102115. https://doi.org/10.1016/j.jksus.2022.102115 doi: 10.1016/j.jksus.2022.102115
[12]	M. S. Shama, F. El Ktaibi, J. N. Al Abbasi, C. Chesneau, A. Z. Afify, Complete study of an original power-exponential transformation approach for generalizing probability distributions, Axioms, 12 (2023), 67. https://doi.org/10.3390/axioms12010067 doi: 10.3390/axioms12010067
[13]	P. Kavya, M. Manoharan, Some parsimonious models for lifetimes and applications, J. Stat. Comput. Simul., 91 (2021), 3693–3708. https://doi.org/10.1080/00949655.2021.1946064 doi: 10.1080/00949655.2021.1946064
[14]	N. Alotaibi, A. F. Hashem, I. Elbatal, S. A. Alyami, A. S. Al-Moisheer, M. Elgarhy, Inference for a Kavya-Manoharan inverse length biased exponential distribution under progressive-stress model based on progressive type-Ⅱ censoring, Entropy, 24 (2022), 1033. https://doi.org/10.3390/e24081033 doi: 10.3390/e24081033
[15]	E. A. Eldessouky, O. H. Hassan, M. Elgarhy, E. A. A. Hassan, I. Elbatal, E. M. Almetwally, A new extension of the Kumaraswamy exponential model with modeling of food chain data, Axioms, 12 (2023), 379. https://doi.org/10.3390/axioms12040379 doi: 10.3390/axioms12040379
[16]	A. H. Al-Nefaie, Applications to bio-medical data and statistical inference for a Kavya-Manoharan log-logistic model, J. Radiat. Res. Appl. Sci., 16 (2023), 100523. https://doi.org/10.1016/j.jrras.2023.100523 doi: 10.1016/j.jrras.2023.100523
[17]	F. H. Riad, A. Radwan, E. M. Almetwally, M. Elgarhy, A new heavy tailed distribution with actuarial measures, J. Radiat. Res. Appl. Sci., 16 (2023), 100562. https://doi.org/10.1016/j.jrras.2023.100562 doi: 10.1016/j.jrras.2023.100562
[18]	O. H. M. Hassan, I. Elbatal, A. H. Al-Nefaie, M. Elgarhy, On the Kavya-Manoharan-Burr X model: Estimations under ranked set sampling and applications, J. Risk Financ. Manag., 16 (2023), 19. https://doi.org/10.3390/jrfm16010019 doi: 10.3390/jrfm16010019
[19]	N. Alotaibi, I. Elbatal, M. Shrahili, A. S. Al-Moisheer, M. Elgarhy, E. M. Almetwally, Statistical inference for the Kavya-Manoharan Kumaraswamy model under ranked set sampling with applications, Symmetry, 15 (2023), 587. https://doi.org/10.3390/sym15030587 doi: 10.3390/sym15030587
[20]	E. L. Lehmann, The power of rank tests, Ann. Math. Stat., 24 (1952), 23–43.
[21]	P. G. Sankaran, V. L. Gleeja, Proportional reversed hazard and frailty models, Metrika, 68 (2008), 333–342. https://doi.org/10.1007/s00184-007-0165-0 doi: 10.1007/s00184-007-0165-0
[22]	R. C. Gupta, R. D. Gupta, P. L. Gupta, Modeling failure time data by Lehman alternatives, Commun. Stat. Theory Methods, 27 (1998), 887–904. https://doi.org/10.1080/03610929808832134 doi: 10.1080/03610929808832134
[23]	A. D. Crescenzo, Some results on the proportional reversed hazards model, Stat. Probab. Lett., 50 (2000), 313–321. https://doi.org/10.1016/S0167-7152(00)00127-9 doi: 10.1016/S0167-7152(00)00127-9
[24]	G. S. Mudholkar, D. K. Srivastava, Exponentiated Weibull family for analyzing bathtub failure-rate data, IEEE Trans. Reliab., 42 (1993), 299–302. https://doi.org/10.1109/24.229504 doi: 10.1109/24.229504
[25]	A. Z. Afify, H. M. Yousof, G. G. Hamedani, G. R. Aryal, The Exponentiated Weibull-Pareto distribution with application, J. Stat. Theory Appl., 15 (2016), 326–344. https://doi.org/10.2991/jsta.2016.15.4.2 doi: 10.2991/jsta.2016.15.4.2
[26]	G. M. Cordeiro, A. Z. Afify, H. M. Yousof, R. R. Pescim, G. R. Aryal, The exponentiated Weibull-H family of distributions: Theory and applications, Mediterr. J. Math., 14 (2017). https://doi.org/10.1007/s00009-017-0955-1 doi: 10.1007/s00009-017-0955-1
[27]	R. D. Gupta, D. Kundu, Generalized exponential distributions, Aust. N. J. Stat., 41 (1999), 173–188.
[28]	A. M. Abouammoh, Alshingiti, Reliability estimation of generalized inverted exponential distribution, J. Stat. Comput. Simul., 79 (2009), 1301–1315. https://doi.org/10.1080/00949650802261095 doi: 10.1080/00949650802261095
[29]	A. Mahdavi, D. Kundu, A new method for generating distributions with an application to exponential distribution, Commun. Stat. Theory Methods, 46 (2017), 6543–6557. https://doi.org/10.1080/03610926.2015.1130839 doi: 10.1080/03610926.2015.1130839
[30]	S. K. Maurya, A. Kaushik, S. K. Singh, U. Singh, A new class of distribution having decreasing, increasing, and bathtub-shaped failure rate, Commun. Stat. Theory Methods, 46 (2017), 10359–10372. https://doi.org/10.1080/03610926.2016.1235196 doi: 10.1080/03610926.2016.1235196
[31]	J. A. Greenwood, J. M. Landwehr, N. C. Matalas, J. R. Wallis, Probability weighted moments: Definition and relation to parameters of several distributions expressible in inverse form, Water Resour. Res., 15 (1979), 1049–1054. https://doi.org/10.1029/WR015i005p01049 doi: 10.1029/WR015i005p01049
[32]	J. Swain, S. Venkatraman, J. Wilson, Least squares estimation of distribution function in Johnsons translation system, J. Stat. Comput. Simul., 29 (1988), 271–297. https://doi.org/10.1080/00949658808811068 doi: 10.1080/00949658808811068
[33]	R. Cheng, N. Amin, Maximum product of spacings estimation with application to the lognormal distribution, Math. Rep., 1979.
[34]	R. Cheng, N. Amin, Estimating parameters in continuous univariate distributions with a shifted origin, J. R. Stat. Soc. Ser. B Stat. Methodol., 45 (1983), 394–403. https://doi.org/10.1111/j.2517-6161.1983.tb01268.x doi: 10.1111/j.2517-6161.1983.tb01268.x
[35]	J. H. K. Kao, Computer methods for estimating Weibull parameters in reliability studies, IRE T. Reliab. Qual. Contr., 13 (1958), 15–22. https://doi.org/10.1109/IRE-PGRQC.1958.5007164 doi: 10.1109/IRE-PGRQC.1958.5007164
[36]	H. Cramér, On the composition of elementary errors, Scand. Actuar. J., 1928, 13–74. https://doi.org/10.1080/03461238.1928.10416862 doi: 10.1080/03461238.1928.10416862
[37]	R. E. Von Mises, Wahrscheinlichkeit statistik und wahrheit, Basel: Springer, 1928.
[38]	D. N. P. Murthy, M. Xie, R. Jiang, Weibull models, Hoboken: Wiley, 2004.
[39]	M. E. Ghitany, B. Atieh, S. Nadarajah, Lindley distribution and its application, Math. Comput. Simul., 78 (2008), 493–506. https://doi.org/10.1016/j.matcom.2007.06.007 doi: 10.1016/j.matcom.2007.06.007
[40]	R. Dumonceaux, C. Antle, Discrimination between the lognormal and the Weibull distributions, Technometrics, 15 (1973), 923–926. https://doi.org/10.2307/1267401 doi: 10.2307/1267401
[41]	P. S. Mann, Introductory statistics, 9 Eds., New York: Wiley, 2016.
[42]	E. T. Lee, J. W. Wang, Statistical methods for survival data snalysis, 3 Eds., Hoboken: Wiley, 2003.
[43]	N. Alsadat, M. Elgarhy, A. H. Tolba, A. S. Elwehidy, H. Ahmad, E. M. Almetwally, Classical and Bayesian estimation for the extended odd Weibull power Lomax model with applications, AIP Adv., 13 (2023). https://doi.org/10.1063/5.0170848 doi: 10.1063/5.0170848
[44]	A. H. Tolba, A. H. Muse, A. Fayomi, H. M. Baaqeel, E. M. Almetwally, The Gull alpha power Lomax distributions: Properties, simulation, and applications to modeling COVID-19 mortality rates, PLoS One, 18 (2023). https://doi.org/10.1371/journal.pone.0283308 doi: 10.1371/journal.pone.0283308
[45]	E. Q. Chinedu, Q. C. Chukwudum, N. Alsadat, O. J. Obulezi, E. M. Almetwally, A. H. Tolba, New lifetime distribution with applications to single acceptance sampling plan and scenarios of increasing hazard rates, Symmetry, 15 (2023). https://doi.org/10.3390/sym15101881 doi: 10.3390/sym15101881
[46]	H. M. Barakat, A new method for adding two parameters to a family of distributions with application to the normal and exponential families, Stat. Methods Appl., 24 (2015), 359–372. https://doi.org/10.1007/s10260-014-0265-8 doi: 10.1007/s10260-014-0265-8
[47]	H. M. Barakat, O. M. Khaled, Toward the establishment of a family of distributions that may fit any dataset, Commun. Stat. Simul. Comput., 46 (2017), 6129–6143. https://doi.org/10.1080/03610918.2016.1197245 doi: 10.1080/03610918.2016.1197245

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)