Comparison of Some Estimation Methods for the Mixed Exponential Distribution for Heterogeneous Data
DOI:
https://doi.org/10.31272/jae.i145.1283Keywords:
Methodology Mixture, Mixed exponential distribution model, survival, failure rate, Maximum Likelihood Method (ML), Least squares (LS)Abstract
The research dealt with a new idea for mixing: using a new mixing method for some distributions to find a new mixed distribution. Thus, we can obtain a mixed distribution with many parameters, where three identical exponential distributions are mixed to get a new distribution that is more flexible than the classical distributions. The mixed distribution is represented by a new coefficient, the mixing coefficient, which means the percentage of contribution to the mixed distribution. Some characteristics of the mixed distribution were also found, and the (ML, LS) method was used to estimate the parameters of the new mixed distribution. Due to the nonlinear relationship between the parameters, we used the Newton-Raphson numerical algorithm to estimate the parameters, and the results of the least squares (LS) method were the best for all sample sizes used.
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[1] Abid, S. H., Al-Noor, N. H., & Boshi, M. A. A. (2020). The Generalized Gamma–Exponentiated Weibull Distribution with its Properties. Al-Mustansiriyah Journal of Science, 31(2), 30-37. DOI: https://doi.org/10.23851/mjs.v31i2.775
[2] Al-Wakeel, A. A. Monte Carlo Estimation of the Two-Component Mixture Weibull Distribution Parameters.
[3] El-Bassiouny, A. H., Medhat, E. D., Abdelfattah, M., & Eliwa, M. S. (2016). A mixture of exponentiated generalised Weibull-Gompertz distribution and its applications in reliability. J. Stat. Appl. Probab, 5(3), 455-468. DOI: https://doi.org/10.18576/jsap/050310
[4] Erişoğlu, Ü., Erişoğlu, M., & Erol, H. (2011). A mixture model of two different distributions approach to analysing heterogeneous survival data. International Journal of Computational and Mathematical Sciences, 5(2), 75-79.
[5] Erisoglu, U., Erisoglu, M., & Erol, H. (2012). Pak. J. Statist. 2012 Vol. 28 (1), 115-130 MIXTURE MODEL APPROACH TO THE ANALYSIS OF HETEROGENEOUS SURVIVAL DATA. Pak. J. Statist, 28(1), 115-130.
[6] Hussain, J. N., & Shareef, A. M. (2021, May). Parameters estimation of new mixed Weibull Rayleigh and Exponential distribution. In Journal of Physics: Conference Series (Vol. 1879, No. 2, p. 022125). IOP Publishing. DOI: https://doi.org/10.1088/1742-6596/1879/2/022125
[7] Khudhair, M. S., & Aboudi, E. H. (2023). Estimating an Exponentiated Expanded Power Function Distribution Using an Artificial Intelligence Algorithm. Journal Of AL-Turath University College, 2(35).
[8] Mohammed, Y. A., Yatim, B., & Ismail, S. (2013). A simulation study of a parametric mixture model of three distributions to analyse heterogeneous survival data. Modern Applied Science, 7(7), 1-9. DOI: https://doi.org/10.5539/mas.v7n7p1
[9] Mohammed, Y. A., Yatim, B., & Ismail, S. (2014, July). A parametric mixture model of three different distributions: An approach to analyse heterogeneous survival data. In AIP Conference Proceedings (Vol. 1605, No. 1, pp. 1040-1045). American Institute of Physics. DOI: https://doi.org/10.1063/1.4887734
[10] Mohammed, Y. A., Yatim, B., & Ismail, S. (2015). A mixture model of the exponential, gamma and Weibull distributions to analyse heterogeneous survival data. Journal of Scientific Research and Reports, 5(2), 132-139. DOI: https://doi.org/10.9734/JSRR/2015/15014
[11] Muhammad, M. Z. K., & Muhammad, R. S. (2022). Comparison between the estimates of the potential function and Bayes using the exponential distribution of the reliability function (Cascade stress-strength). Journal of Administration and Economics, (132), 248-259.
[12] Razali, A. M., & Salih, A. A. (2009). Combining two Weibull distributions using a mixing parameter. European Journal of Scientific Research, 31(2), 296-305.
[13] Taheer, H. F., & Al-Saffar, R. S. (2023). EXPANDED BETA DISTRIBUTION FOR RISK FUNCTION ESTIMATION WITH APPLICATION. Journal of Higher Education Theory and Practice, 23(1), 794.
[14] Tahir, M., Aslam, M., Abid, M., Ali, S., & Ahsanullah, M. (2020). A 3-component mixture of exponential distribution assuming doubly censored data: properties and Bayesian estimation. Journal of Statistical Theory and Applications, 19(2), 197-211. DOI: https://doi.org/10.2991/jsta.d.200508.002
[15] Türkan, A. H., & ÇALIŞ, N. (2014). Comparison of two-component mixture distribution models for heterogeneous survival datasets: A Review Study. Istatistik Journal of The Turkish Statistical Association, 7(2), 33-42.
[16] Yilmaz, M., & Buyum, B. (2015). Parameter estimation methods for two-component mixed exponential distributions. Istatistik Journal of The Turkish Statistical Association, 8(2), 51.
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