TRANSMUTED NEW WEIGHTED EXPONENTIAL DISTRIBUTION: ITS DISTRIBUTIONAL PROPERTIES AND APPLICATIONS TO DATASETS FROM RAINFALL AND BREAST CANCER STUDIES
Abstract
This research paper developed a new distribution referred as transmuted Newweighted exponential distribution. This is an extension of the popular Exponential distribution by using the transmutation map, the probability density function (pdf) and the cumulative distribution function (cdf) of the developed distribution were derived. Some distributional properties of the new distribution were extensively studied. The estimation of the distribution parameters was done using the method of maximum likelihood estimation. The performance of the TNWED has been evaluated using real life datasets from two (2) previous researches and the results show that our proposed distribution fits the datasets more better compared to the fits of the other two distributions (New Weighted Exponential distribution and Exponential distribution) considered in this study.
References
Abdullahi UK, Abba B (2017) On the Inferences and Applications of Odd Generalized Exponential-New Weighted Exponential Distribution. Journal of the Nigeria Association of Mathematical Physics, 43(1):221-228.
Abdullahi J, Abdullahi U.K., Ieren T.G., Kuhe D.A., and Umar A.A. (2018) On the properties and applications of transmuted odd generalized exponential- exponential distribution, Asian Journal of Probability and Statistics, 1(4):1-14. DOI: 10.9734/AJPAS/2018/44073. DOI: https://doi.org/10.9734/ajpas/2018/v1i424552
Abdullahi UK, Ieren TG (2018) On the inferences and applications of transmuted exponential Lomax distribution, International Journal of Advanced Probability and Statistics, 6(1): 30-36, doi:10.14419/ijap.v6i1.8129. DOI: https://doi.org/10.14419/ijasp.v6i1.8129
Azzalini A (1985) A Class of Distributions Which Includes the Normal Ones. Scandinavian Journal of Statistics, 12, 171-178.
Bashir S, Naqvi IB (2016) new Weighted Exponential Distribution and its Applications on Waiting Time Data. International Journal of Scientific Research and Publications, 6 (7): 698-702.
Chen G, Bunce C, Jiang W A (2010) New distribution for extreme value analysis. In Computational Intelligence and Software Engineering (CiSE), 2010 International Conference on, pages 1-4. IEEE, 2010. DOI: https://doi.org/10.1109/CISE.2010.5677106
Elbatal I, Diab LS, Alim NAA (2013). Transmuted generalized linear Exponential Distribution: Intern J Comp Appl 83: 29-37. DOI: https://doi.org/10.5120/14671-2681
Falgore JY, Aliyu Y, Umar AA, Abdullahi UK (2018) Odd Generalized Exponential-Inverse Lomax Distribution: Theory and Application. Journal of the Nigeria Association of Mathematical Physics, 47:147-156.
Gupta RD, Kundu D (1999) Generalized exponential distributions. Australian and New Zealand Journal of Statistics, 41(2) :173–188 DOI: https://doi.org/10.1111/1467-842X.00072
Gupta RD, Kundu D (2009) A new class of weighted exponential distributions. Statistics 43:6, 621-634, DOI: 10.1080/02331880802605346 DOI: https://doi.org/10.1080/02331880802605346
Ieren TG, and Kuhe AD (2018) On the Properties and Applications of Lomax-Exponential Distribution. Asian Journal of Probability and Statistics, 1(4):1-13. DOI: 10.9734/AJPAS/2018/42546 DOI: https://doi.org/10.9734/ajpas/2018/v1i424557
Khan MS, King R, Hudson IL (2017) Transmuted Generalized Exponential Distribution. A Generalization of the Exponential Distribution with Applications to Survival Data. Communication in Statistics: Theory and Method, 46:6, 4377-4398, DOI: 10.1080/03610918.2015.1118503 DOI: https://doi.org/10.1080/03610918.2015.1118503
Lee ET (1992) Statistical Methods for Survival Data Analysis. 2nd Edn., John Wiley and Sons Ltd., New York, USA., ISBN-13: 9780471615927, Pages: 496.
Lawless J F (2003) Statistical models and methods for lifetime data. 2nd ed., John Wiley and Sons, New York. DOI: https://doi.org/10.1002/9781118033005
Maiti SS, Pramanik S (2015) Odds Generalized Exponential-Exponential Distribution. Journal of Data Science, 13: 733-754. DOI: https://doi.org/10.6339/JDS.201510_13(4).0006
Merovci F (2013) Transmuted Rayleigh Distribution. Australian Journal of Statistics, 42,1: 21–31. DOI: https://doi.org/10.17713/ajs.v42i1.163
Nadarajah S (2009) The skew logistic distribution. Advances in Statistical Analysis, 93:187–203, https://doi.org/10.1007/s10182-009-0105-6. DOI: https://doi.org/10.1007/s10182-009-0105-6
Ramos MWA, Cordeiro GM, Marinho PRD, Dias CRB, Hamedani GG (2013) The Zografos-Balakrishnan log-logistic distribution: Properties and applications. Journal of Statistical Theory and Application, 12: 225-244. DOI: https://doi.org/10.2991/jsta.2013.12.3.2
Shaw WT, Buckley IR (2007) The alchemy of probability distributions: beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map. Research Report
Tian Y, Tian M, Zhu Q (2014) Transmuted Linear Exponential Distribution: A new Generalization of the linear Exponential Distribution with Applications to Survival Data. Communication in Statistics: Computation and Simulation, 43:2661-2671. DOI: https://doi.org/10.1080/03610918.2013.763978
Umar AA, David RO, Falgore JY, Abubakar SS, Abdullahi UK, Mohammed, AS, Damisa SA (2018) The Exponentiated New Weighted Weibull Distribution: Theory and Application. Journal of the Nigeria Association of Mathematical Physics, 47:163-172.
Usman A, Ishaq AI, Abdullahi UK (2019) Generalized transmuted-Inverted exponential Distribution: Theory and Application. Nigeria Journal of Scientific Research, 18(4):354-361.
Copyright (c) 2023 FUDMA JOURNAL OF SCIENCES
This work is licensed under a Creative Commons Attribution 4.0 International License.
FUDMA Journal of Sciences
