Authors:
D. Saridha,R. K. Radha,DOI NO:
https://doi.org/10.26782/jmcms.2024.12.00004Keywords:
Asymmetric Loss Functions,Bayes Estimate,Lindley’s Approximation,MSE,Prior,Abstract
This study focuses on estimating the shape and scale parameters of the Topp-Leone Exponential distribution. Bayes estimators are obtained using Exponential, Gamma, LogNormal, and Weibull distributions as the identical priors under asymmetric loss functions such as LINEX and Entropy and integrated with the Lindley approximation method. The simulation study was employed to determine identical prior and loss functions for the shape and scale parameters. It is observed that LINEX loss function with Exponential-Exponential prior for the shape parameter and the scale parameter Gamma-Gamma prior is most preferred for this distribution.Refference:
I. Al-Shomrani, A., Arif O, Ibrahim, S., Hanif, S., and Shahbaz, M. “Topp–Leone Family of Distributions: Some Properties and Application.” Pakistan Journal of Statistics and Operation Research, vol. 12, no.3, 2016, pp. 443-451, doi.org/10.18187/pjsor.v12i3.1458.
II. Anitta, SA., and Dais George. ‘Bayesian Analysis of Two Parameter Weibull Distribution using Different Loss Functions.” Stochastic Modeling and Applications, vol. 24, no.2, 2020, https://www.mukpublications.com/resources/6_FT13_Final.pdf.
III. Epstein, B., and Sobel M. “Some theorems to life resting form an exponential distribution.” Annals of Mathematical Statistics, vol. 25, no.2, 1954, pp. 373-381, doi: 10.1214/aoms/1177728793.
IV. Metiri, Farouk, Zeghdoudi, Halim, and Riad Remiata, Mohamed .”On Bayes estimates of Lindley distribution under Linex loss function: Informative and Non-informative priors.” Global Journal of Pure and AppliedMathematics, vol. 12,2016, pp. 391- 400, https://api.semanticscholar.org/CorpusID:46201692.
V. Olayode, Fatoki.”The Topp-Leone Rayleigh Distribution with Application.” American Journal of Mathematics and Statistics, vol.9, no.6, 2019, pp. 215-220, 10.5923/j.ajms.20190906.02.
VI. Fithriani, I., Hakim, Arief, and Novita, Mila. “A comparison of the Bayesian method under symmetric and asymmetric loss functions to estimate the shape parameter K of Burr distribution.” Journal of Physics Conference Series, (2019),1218, 2019, 10.1088/1742-6596/1108/1/012053
VII. Genc, A. “Moments of order statistics of Topp Leone distribution.”Statistical Papers, vol.53, no.1,2012, pp.117-131, 10.1007/s00362-010-0320-y.
VIII. Albderia, Kadhim, Jawad , Hind.”Estimate survival function of the Topp-Leone exponential distribution with an application.” International journal Nonlinear Analysis and Applications, vol.12, no.2, 2021, pp: 53-60, 10.22075/ijnaa.2021.5014.
IX. Kawsar, F., and Ahmed, SP. “Bayesian Approach in Estimation of shape parameter of Exponentiated moment Exponential distribution.” Journal of Statistical Theory and Applications, vol. 17, no.2, 2017, pp.359-374, 10.2991/jsta.2018.17.2.13
X. Kotz, S., and Seier, E. “Kurtosis of the Topp Leone distributions.”. Interstat,2007, pp.1-15, https://www.researchgate.net/publication/228417010_Kurtosis_of_the_Topp-Leone_distributions.
XI. Lindley, DV. “Approximate Bayesian methods, Journal of Statistical Computation and Simulation.” Trabajos de Estadistica y de Investigacion Operativa vol. 31, 1980, pp. 223-245, http://eudml.org/doc/40822.
XII. Mohammed, H., and Khan, Ali, Athar, AbuJarad. “Bayesian Survival Analysis of Topp-Leone Generalized Family with Stan.” International Journal of Statistics and Applications, vol. 8, no.5, 2018, pp. 274-290, 10.5923/j.statistics.20180805.06.
XIII. Rasheed, Noman. “Topp–Leone compound Rayleigh distribution: properties and applications.” Research Journal of Mathematical and Statistical Science, vol. 7, no.3,2019, pp. 51–58, https://www.researchgate.net/publication/335987957_Topp-Leone_Compound_Rayleigh_Distribution_Properties_and_Applications
XIV. Nadarajah, S., and Kotz,S. “Moments of some J-shaped distributions.”Journal of Applied Statistics, vol. 30, no.3, 2003, pp. 311-317, 10.1080/0266476022000030084.
XV. Singh, Randhir. “Bayesian estimation of the unknown parameter and reliability of the Exponential distribution with a non-natural conjugate prior.” Journal of Emerging Technologies and Innovative Research, vol 8, 2021, pp. 228-236, https://www.jetir.org/papers/JETIR2109426.
XVI. Singh, SK., Singh, Umesh, and Kumar, Dinesh. “Estimation of parameters and reliability function of Exponentiated Exponential distribution: Bayesian approach under General Entropy loss function.” Pakistan Journal of Statistics and Operation Research, vol. 7,2011, pp.199-216, 10.18187/pjsor.v7i2.239.
XVII. Saridha, D., Radha, RK., and Venkatesan, P. “Bayesian estimation of Topp-Leone Exponential distribution using symmetric loss functions for identical priors.” Sirjana Journal. vol. 54, No.3,2024, pp: 19-26, 10.0015.SRJ.2024.V54I2.0096781.222.
XVIII. Topp. CW., and Leone, FC. “A family of J-shaped frequency functions.”.Journal of the American Statistical Association, vol. 50, 1955, pp.209-219, 10.1080/01621459.1955.10501259.
View Download