Transmuted Ailamujia Distribution with Applications to Lifetime Observations
Asian Journal of Probability and Statistics,
Page 1-11
DOI:
10.9734/ajpas/2023/v21i1452
Abstract
Background of the Study: Quest to extend existing probability distributions to allow for more flexibility in data modelling is never ending.
Aims: This study extends the Ailamujia distribution using quadratic transmutation map to propose a new 2-paramter lifetime distribution.
Methodology: Shapes of the density function and the hazard rate function of the new propositions are obtained. Some mathematical properties of the new distribution are also obtained.
Results: Application of the distribution to four lifetime datasets reveals that the distribution competes favourably with other related distributions.
Conclusion: The new distribution competes favourably with the existing distributions in data modelling.
Keywords:
- Ailamujia distribution
- quadratic transmutation
- lifetime observations
- reliability functions
- parameter estimation
How to Cite
Adetunji, A. A. (2023). Transmuted Ailamujia Distribution with Applications to Lifetime Observations. Asian Journal of Probability and Statistics, 21(1), 1-11. https://doi.org/10.9734/ajpas/2023/v21i1452
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Shaw WT, Buckley IRC. The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. Res. Rep.; 2007.
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Jan U, Fatima K, Ahmad SP. On weighted ailamujia distribution and its applications to lifetime data. J. Stat. Appl. Probab. 2017;6:619–633.
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doi: 10.1080/09720510.2021.1966206.
Gross AJ, Clark VA. Survival distributions: Reliability applications in the biometrical sciences. New York, USA; 1975.
Aijaz A, Ahmad A, Tripathi R. Transmuted inverse lindley distribution : Statistical properties and applications. Sci. Technol. Dev. 2020; 9(4):1–10.
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Meeker WQ, Escobar LA. Statistical methods for reliability data. New York, USA: John Wiley and Sons Inc.; 1998.
Dumonceaux R, Antle C. Discrimination between the lognormal and weibull distributions. Technometrics. 1973;15: 923–926.
Singh S, Singh U, Sharma V. Bayesian prediction of future observations from inverse weibull distribution based on type-II hybrid censored sample. Int. J. Adv. Stat. Probab. 2013;1(32–43).
Upadhyay S, Peshwani M. Choice between weibull and log-normal models: A simulation-based bayesian study. Commun. Stat. Methods. 2003;32:381–405.
Ghitany ME, Atieh B, Nadarajah S. Lindley distribution and its application. Math. Comput. Simul. 2008;78(4):493–506.
DOI: 10.1016/j.matcom.2007.06.007
DOI: 10.1081/STA-120003130.
Shaw WT, Buckley IRC. The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. Res. Rep.; 2007.
Cordeiro GM, de Castro M. A new family of generalized distributions. J. Stat. Comput. Simul. 2011;81(7): 883–898.
DOI: 10.1080/00949650903530745
Cordeiro GM, Ortega EMM, Cunha DCC. The exponentiated generalized class of distributions. J. Data Sci. 2013;11:1–27.
Mahdavi A, Kundu D. A new method for generating distributions with an application to exponential distribution. Commun. Stat. - Theory Methods. 2017; 46(13):6543–6557.
DOI: 10.1080/03610926.2015.1130839.
Lv HQ, Gao HL, Chen CL. Ailamuja distribution and its application in supportability data analysis. J. Acad. Armored Force Eng. 2002;16(3):48–52.
Jamal F, Chesneau C, Aidi K, Ali A. Theory and application of the power ailamujia distribution. J. Math. Model. 2021;9(3):391–413.
DOI: 10.22124/jmm.2020.17547.1512
Jan U, Fatima K, Ahmad SP. On weighted ailamujia distribution and its applications to lifetime data. J. Stat. Appl. Probab. 2017;6:619–633.
Rather AA, et al. A new size biased distribution with applications in engineering and medical science. Int. journals pf Sci. Res. Math. Stat. Sci. 2018;5:75–85.
Haq MA, Usman RM, Hashmi S, Al-Omeri AI. The marshall-olkin length-biased exponential distribution and its applications. J. King Saud Univ. - Sci. 2019;31(2):246–251.
DOI: 10.1016/j.jksus.2017.09.006
Ekhosuehi N, Kenneth GE, UK K. The weibull length biased exponential distribution: Statistical properties and applications. J. Stat. Econom. Methods. 2020; 9:15–30.
Tahir MH, Cordeiro GM. Compounding of Distributions: a Survey and New Generalized Classes. Journal of Statistical Distributions and Applications. 2016;3(13).
Rahman MM, Al-Zahrani B, Shahbaz SH, Shahbaz MQ. Transmuted probability distributions: A review. Pak J Statistics and Operation Research. 2020;16(1):83–94.
De Jong P, Heller GZ. Generalized Linear Models for Insurance Data. Cambridge University Press; 2008.
R-Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria; 2020.
Available: https://www.r-project.org/
Rather AA, Subramanian C, Al-omari AI, Alanzi ARA. Exponentiated ailamujia distribution with statistical inference and applications of medical data. J. Stat. Manag. Syst. 2022;25(4)L907–925.
doi: 10.1080/09720510.2021.1966206.
Gross AJ, Clark VA. Survival distributions: Reliability applications in the biometrical sciences. New York, USA; 1975.
Aijaz A, Ahmad A, Tripathi R. Transmuted inverse lindley distribution : Statistical properties and applications. Sci. Technol. Dev. 2020; 9(4):1–10.
Alkarni SH. Generalized inverse lindley power series distributions: Modeling and simulation. J. Nonlinear Sci. Appl. 2019;12(12):799–815.
DOI: 10.22436/jnsa.012.12.03
Shehata WAM, Yousof H, Aboraya M. A novel generator of continuous probability distributions for the asymmetric left-skewed bimodal real-life data with properties and copulas. Pakistan J. Stat. Oper. Res. 2021;17(4):943–961.
DOI: 10.18187/pjsor.v17i4.3903
Meeker WQ, Escobar LA. Statistical methods for reliability data. New York, USA: John Wiley and Sons Inc.; 1998.
Dumonceaux R, Antle C. Discrimination between the lognormal and weibull distributions. Technometrics. 1973;15: 923–926.
Singh S, Singh U, Sharma V. Bayesian prediction of future observations from inverse weibull distribution based on type-II hybrid censored sample. Int. J. Adv. Stat. Probab. 2013;1(32–43).
Upadhyay S, Peshwani M. Choice between weibull and log-normal models: A simulation-based bayesian study. Commun. Stat. Methods. 2003;32:381–405.
Ghitany ME, Atieh B, Nadarajah S. Lindley distribution and its application. Math. Comput. Simul. 2008;78(4):493–506.
DOI: 10.1016/j.matcom.2007.06.007
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