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Annals of Data Science
Published in: Annals of Data Science 4/2023

05-04-2021

The Discrete Analogue of the Weibull G Family: Properties, Different Applications, Bayesian and Non-Bayesian Estimation Methods

Authors: Mohamed Ibrahim, M. Masoom Ali, Haitham M. Yousof

Published in: Annals of Data Science | Issue 4/2023

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Abstract

In this work, we propose and study a new discrete analogue of the Weibull class. Many useful properties such as ordinary moments; moment generating function; cumulant generating function; probability generating function; central moments and dispersion index are derived. Two special discrete versions are discussed theoretically, graphically, and numerically. The hazard rate function of the new family can be "upside down", "increasing", "decreasing", "constant", "J-hazard rate function" and "double upside down" and "increasing-constant". Non-Bayesian estimation methods such as the maximum likelihood estimation; Cramér-von Mises estimation; the ordinary least square estimation and the weighted least square estimation are considered. The Bayesian estimation procedure under the squared error loss function is also presented. The Markov chain Monte Carlo simulations for comparing non-Bayesian and Bayesian estimation are performed using the Gibbs sampler and Metropolis Hastings algorithm. The flexibility of the new family is illustrated by four real datasets. The new family (through two special discrete versions) provided a better fit than sixteen competitive distributions.
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Literature
1.
Roy D (2004) Discrete Rayleigh distribution. IEEE Trans Reliab 53:255–260
2.
Gomez-Déniz E (2010) Another generalization of the geometric distribution. TEST 19:399–415
3.
Jazi AM, Lai DC, Alamatsaz HM (2010) Inverse Weibull distribution and estimation of its parameters. Stat Methods 7:121–132
4.
Gomez-Déniz E, Caldern-Ojeda E (2011) The discrete Lindley distribution: properties and applications. J Stat Comput Simul 81:1405–1416
5.
Nekoukhou V, Bidram H (2015) The exponentiated discrete Weibull distribution. Stat Oper Res Trans 39:127–146
6.
Hussain T, Ahmad M (2014) Discrete inverse Rayleigh distribution. Pak J Stat 30:203–222
7.
Hussain T, Aslam M, Ahmad MA (2016) Two parameter discrete Lindley distribution. Rev Colomb Estadistica 39:45–61
8.
Para BA, Jan TR (2016) Discrete version of log-logistic distribution and its applications in genetics. Int J Mod Math Sci 14:407–422
9.
Para BA, Jan TR (2016) On discrete three-parameter Burr type XII and discrete Lomax distributions and their applications to model count data from medical science. Biom Biostat Int J 4:1–15
10.
11.
AbuJarad MH, Khan AA, Khaleel MA et al (2020) Bayesian reliability analysis of Marshall and Olkin model. Ann Data Sci 7:461–489
12.
Kemp AW (2004) Classes of discrete lifetime distributions. Commun Stat Theor Methods 33(12):3069–3093
13.
Aboraya M, Yousof HM, Hamedani GG, Ibrahim M (2020) A new family of discrete distributions with nathematical properties, characterizations, bayesian and non-bayesian estimation methods. Mathematics 8:1648
14.
Eliwa MS, Alhussain ZA, El-Morshedy M (2020) Discrete Gompertz-G family of distributions for over-and under-dispersed data with properties, estimation, and applications. Mathematics 8(3):358
15.
Brito E, Cordeiro GM, Yousof HM, Alizadeh M, Silva GO (2017) The Topp-Leone odd log-logistic family of distributions. J Stat Comput Simul 87(15):3040–3058
16.
Aryal GR, Yousof HM (2017) The exponentiated generalized-G Poisson family of distributions. Stoch Qual Control 32(1):7–23
17.
Yousof HM, Afify AZ, Hamedani GG, Aryal G (2017) The Burr X generator of distributions for lifetime data. J Stat Theory Appl 16(3):288–305
18.
Yousof HM, Korkmaz MC, Sen S (2019) A new two-parameter lifetime model. Ann Data Sci 8:1–16
19.
Yousof HM, Alizadeh M, Jahanshahiand SMA, Ramires TG, Ghosh I, Hamedani GG (2017) The transmuted Topp-Leone G family of distributions: theory, characterizations and applications. J Data Sci 15(4):723–740
20.
Yousof HM, Altun E, Ramires TG, Alizadeh M, Rasekhi M (2018) A new family of distributions with properties, regression models and applications. J Stat Manag Syst 21(1):163–188
21.
Yousof HM, Majumder M, Jahanshahi SMA, Ali MM, Hamedani GG (2018) A new Weibull class of distributions: theory, characterizations and applications. J Stat Res Iran JSRI 15(1):45–82
22.
Yousof HM, Hamedani GG, Ibrahim M (2020) The Two-parameter Xgamma Fréchet Distribution: characterizations, copulas, mathematical properties and different classical estimation methods. Contrib Math 2(2020):32–41
23.
Yousof HM, Rasekhi M, Alizadeh M, Hamedani GG (2018) The Marshall-Olkin exponentiated generalized G family of distributions: properties, applications and characterizations. J Nonlinear Sci Appl 13(1):34–52
24.
Cordeiro GM, Yousof HM, Ramires TG, Ortega EM (2018) The Burr XII system of densities: properties, regression model and applications. J Stat Comput Simul 88(3):432–456
25.
Merovci F, Alizadeh M, Yousof HM, Hamedani GG (2017) The exponentiated transmuted-G family of distributions: theory and applications. Commun Stat-Theory Methods 46(21):10800–10822
26.
Merovci F, Yousof HM, Hamedani GG (2020) The poisson topp leone generator of distributions for lifetime data: theory, characterizations and applications. Pak J Stat Oper Res 16(2):343–355
27.
Abouelmagd THM, Hamed MS, Hamedani GG, Ali MM, Goual H, Korkmaz MC, Yousof HM (2019) The zero truncated Poisson Burr X family of distributions with properties, characterizations, applications, and validation test. J Nonlinear Sci Appl 12(5):314–336
28.
Abouelmagd THM, Hamed MS, Handique L, Goual H, Ali MM, Yousof HM, Korkmaz MC (2019) A new class of distributions based on the zero truncated poisson distribution with properties and applications. J Nonlinear Sci Appl 12(3):152–164
29.
Alizadeh M, Jamal F, Yousof HM, Khanahmadi M, Hamedani GG (2020) Flexible Weibull generated family of distributions: characterizations, mathematical properties and applications. Univ Politehnica Bucharest Sci Bull-Ser A-Appl Math Phys 82(1):145–150
30.
Alizadeh M, Yousof HM, Jahanshahi SMA, Najibi SM, Hamedani GG (2020) The transmuted odd log-logistic-G family of distributions. J Stat Manag Syst 23(4):761–787
31.
Alizadeh M, Yousof HM, Rasekhi M, Altun E (2018) The odd log-logistic poisson-G family of distributions. J Math Ext 12(1):81–104
32.
Karamikabir H, Afshari M, Yousof HM, Alizadeh M, Hamedani G (2020) The Weibull Topp-Leone generated family of distributions: statistical properties and applications. J Iran Stat Soc 19(1):121–161
33.
Korkmaz MÇ, Alizadeh M, Yousof HM, Butt NS (2018) The generalized odd Weibull generated family of distributions: statistical properties and applications. Pak J Stat Oper Res 14:541–556
34.
Nascimento AD, Silva KF, Cordeiro GM, Alizadeh M, Yousof HM, Hamedani GG (2019) The odd Nadarajah-Haghighi family of distributions: properties and applications. Stud Sci Math Hung 56(2):185–210
35.
36.
Poisson SD (1837) Probabilité des Jugements en Matiére Criminelle et en Matiére Civile, Précédées des RéGles Génerales du Calcul des Probabilitiés. Bachelier, Paris, France, pp 206–207
37.
Olson DL, Shi Y (2007) Introduction to business data mining. McGraw-Hill/Irwin, New York
38.
Shi Y, Tian YJ, Kou G, Peng Y, Li JP (2011) Optimization based data mining: theory and applications. Springer, Berlin
39.
Tien JM (2017) Internet of things, real-time decision making, and artificial intelligence. Ann Data Sci 4(2):149–178
40.
Ishaq AI, Abiodun AA (2020) The Maxwell-Weibull distribution in modeling lifetime datasets. Ann Data Sci 7:639–662
41.
Bebbington M, Lai CD, Wellington M, Zitikis R (2012) The discrete additive Weibull distribution: a bathtub-shaped hazard for discontinuous failure data. Reliab Eng Syst Saf 106:37–44
42.
Lawless JF (2003) Statistical models and methods for lifetime data. Wiley, New York, NY, USA
43.
Chan S, Riley PR, Price KL, McElduff F, Winyard PJ (2009) Corticosteroid-induced kidney dysmorphogenesis is associated with deregulated expression of known cystogenic molecules, as well as Indian hedgehog. Am J Physiol-Ren Physiol 298:346–356
44.
Bodhisuwan W, Sangpoom S (2016) The discrete weighted Lindley distribution. In: Proceedings of the International Conference on Mathematics, Statistics, and Their Applications, Banda Aceh, Indonesia, pp, 4–6
45.
Bourguignon M, Silva RB, Cordeiro GM (2014) The Weibull-G family of probability distributions. J Data Sci 12:53–68
46.
47.
Goual H, Yousof HM, Ali MM (2019) Validation of the odd Lindley exponentiated exponential by a modified goodness of fit test with applications to censored and complete data. Pak J Stat Oper Res 15(3):745–771
48.
Mansour MM, Ibrahim M, Aidi K, Shafique Butt N, Ali MM, Yousof HM, Hamed MS (2020) A new log-logistic lifetime model with mathematical properties, copula, modified goodness-of-fit test for validation and real data modeling. Mathematics 8(9):1508
49.
50.
Mansour M, Korkmaz MC, Ali MM, Yousof HM, Ansari SI, Ibrahim M (2020) A generalization of the exponentiated Weibull model with properties, Copula and application. Eurasian Bull Math 3(2):84–102
51.
Mansour M, Rasekhi M, Ibrahim M, Aidi K, Yousof HM, Elrazik EA (2020) A new parametric life distribution with modified bagdonavicius-nikulin goodness-of-fit test for censored validation, properties, applications, and different estimation methods. Entropy 22(5):592
52.
Yadav AS, Goual H, Alotaibi RM, Ali MM, Yousof HM (2020) Validation of the Topp-Leone-Lomax model via a modified Nikulin-Rao-Robson goodness-of-fit test with different methods of estimation. Symmetry 12(1):57
53.
Goual H, Yousof HM (2020) Validation of Burr XII inverse Rayleigh model via a modified chi-squared goodness-of-fit test. J Appl Stat 47(3):393–423
54.
Eliwa MS, El-Morshedy M (2019) Bivariate Gumbel-G family of distributions: statistical properties, bayesian and non-bayesian estimation with application. Ann Data Sci 6:39–60
55.
Al-babtain AA, Elbatal I, Yousof HM (2020) A new flexible three-parameter model: properties, clayton copula, and modeling real data. Symmetry 12(3):440
56.
Mansour M, Yousof HM, Shehata WA, Ibrahim M (2020) A new two parameter Burr XII distribution: properties, copula, different estimation methods and modeling acute bone cancer data. J Nonlinear Sci Appl 13(5):223–238
57.
Mansour MM, Butt NS, Yousof HM, Ansari SI, Ibrahim M (2020) A generalization of reciprocal exponential model: clayton copula, statistical properties and modeling skewed and symmetric real data sets. Pak J Stat Oper Res 16(2):373–386
58.
Ali MM, Yousof HM and Ibrahim M (2021a) A new version of the generalized rayleigh distribution with copula, properties, applications and different methods of estimation. Optimal decision making in operations research and statistics: methodologies and applications, CRC Press, Forthcoming
59.
Ali MM, Ibrahim M and Yousof HM (2021b) Expanding the burr X model: properties, copula, real data modeling and different methods of estimation. Optimal decision making in operations research and statistics: methodologies and applications, CRC Press, Forthcoming
60.
61.
Salah MM, El-Morshedy M, Eliwa MS, Yousof HM (2020) Expanded Fréchet model: mathematical properties, copula, different estimation methods. Appl Valid Test Math 8(11):1949
62.
Dougherty ER (1992) Probability and statistics for the engineering, computing and physical sciences. Prentice Hall, Englewood Cliffs, NJ, USA, pp 149–152
63.
Hamedani GG, Altun E, Korkmaz MÇ, Yousof HM, Butt NS (2018) A new extended G family of continuous distributions with mathematical properties, characterizations and regression modeling. Pak J Stat Oper Res 14:737–758
64.
Ibrahim M, Yadav AS, Yousof HM, Goual H, Hamedani GG (2019) A new extension of Lindley distribution: modified validation test, characterizations and different methods of estimation. Commun Stat Appl Methods 26(5):473–495
65.
Nakagawa T, Osaki S (1975) The discrete Weibull distribution. IEEE Trans Reliab 24(5):300–301
66.
Nakagawa T, Osaki S (1975) The discrete Weibull distribution. IEEE Trans Reliab 24:300–301
67.
Roy D (2003) The discrete normal distribution. Commun Stat Theor Methods 32(10):1871–1883
68.
Sangpoom S, Bodhisuwan W (2016) The discrete asymmetric Laplace distribution. J Stat Theory Pract 10(1):73–86
69.
70.
Ali MM, Yousof HM and Ibrahim M (2021a) A new version of the generalized rayleigh distribution with copula, properties, applications and different methods of estimation. Optimal decision making in operations research and statistics: methodologies and applications, CRC Press, forthcoming.
Metadata
Title
The Discrete Analogue of the Weibull G Family: Properties, Different Applications, Bayesian and Non-Bayesian Estimation Methods
Authors
Mohamed Ibrahim
M. Masoom Ali
Haitham M. Yousof
Publication date
05-04-2021
Publisher
Springer Berlin Heidelberg
Published in
Annals of Data Science / Issue 4/2023
Print ISSN: 2198-5804
Electronic ISSN: 2198-5812
DOI
https://doi.org/10.1007/s40745-021-00327-y

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