Numerical Methods on the Triple Informative Prior Distribution for the Failure Rate Basic Gompertz Model

Al-Obedy, Nadia J. Fezaa; Mohammed, Amal A.; Abraheem, Sudad K.

doi:10.37652/juaps.2022.172394

Document Type : Research Paper

Authors

¹ Department of Mathematics /College of Science / Mustansiriyah University, Baghdad, Iraq

² Department of Wayys&Transportation / College of Engineering / Mustansiriyah University,

³ Department of Mathematics /College of Science / Mustansiriyah University, Iraq

https://doi.org/10.37652/juaps.2022.172394

Abstract

In this paper, it has been dealt with basic Gompertz distribution. The maximum likelihood, Bayes methods of estimation were used to estimate the unknown shape parameter. The failure rate (hazard) function with the least loss was found using different priors (Gamma, exponential, chi-square and triple prior) under symmetric loss function (Degroot loss function). A comparison was made about the performance of these estimators with the numerical solution that was found using expansion methods (Bernstein polynomial and power function) which was applied to find the failure rate function numerically. The proficiency test of the proposed methods was conducted with a number of test examples. Finally, for computations the Matlab (R2015b) is used.

Keywords

Main Subjects

Mathematical

References

[1] Gompertz, B. (1825), On the Nature of the Function Expressive of the Law of Human Mortality and on the New Mode of Determining the Value of Life Contingencies, Phil, Trans. R. Soc. A., Gupta, R. C., Vol.115, pp. 380-513.

[2] Wetterstrand, W. (1981), Parametric Models for Life Insurance Mortality Data Gompertz’s Law over time, Transactions of the Society of Actuaries, Vol.33, pp. 159-175.

[3] Rasheed, H. A. and Hasanain, W., Nadia, J. (2018), Comparing Some Estimators of two Parameter of Basic Gompertz Distribution, Journal of Iraqi Al-Kwarizmi Society (JIKHS), Vol.2, pp. 178-187.

[4] Lenart, A. (2012), The Moments of the Gompertz Distribution and Maximum Likelihood Estimation of its Parameters, Scandinavian Actuarial Journal, Vol.3, pp. 255-277.

[5] Sanku Dey, Fernando, A. and Devendra, K. (2018), Statistical Properties and Different Methods of Estimation of Gompertz Distribution with Application, Journal of Statistics and Management System, Vol.21(5), pp. 839-876.

[6] Hanaa, H. and Nouf, M. (2019), Classical and Bayesian Estimation of Parameters for the Beta Exponentiated Gompertz Distribution with Real Data Application, Jour. of Adv. Research in dynamical and control Systems, Vol.11, pp. 446-453.

[7] Garg, M., Rao, B. and Redmond, C. (1970), Maximum Likelihood Estimation of Parameters of the Gompertz Survival Function, Journal of the Royal Statistical Society, Series C, Vol.19(2), pp. 152-159.

[8] Mohammed, A. A. (2006), Approximate Solutions for a System of Linear Fractional Order Integro-Differential Equations of Volterra Types. Ph.D. Thesis, Mustansiriyha University.

[9] Shihab, S. N. and Mohammed, A. A. (2012), An Efficient Algorithm for n^th Order Integro-Differential Equations Using New Haar Wavelets Matrix Designation, International Journal of Emerging Technologies in Computational and Applied Sciences (IJETCAS), Vol.2(1), Aug. Nov., pp. 32-35.

[10] Atkinson, K. E. (1997), The Numerical Solution of Integral Equations of the Second Kind, Cambridge University Press.

[11] Mohammed, A. A., Ibraheem, S. K. and Al-Obedy, N. J. (2018), Bayesian Estimation of Reliability Burr Type XII Under Al-Bayyatis' Suggest Loss Function with Numerical Solution. IOP Conf. Series: Journal of Phsics: Conf. Series (JPCS), 012041, doi :10.1088/1742-6596/1003/1/012041, Vol.1003, pp. 1-16.

[12] Ibraheem, S. K., Al-Obedy, N. J. and Mohammed, A. A. (2020), A Comparative Study on the Double Prior for Reliability Kumaraswamy Distribution with Numerical Solution. Baghdad Science Journal, Vol.17, pp. 159-165.

[13] Soliman, A. A. and Al Sobhi, M. M. (2015), Bayesian MCMC Inference for the Gompertz Distribution Based on Progressive First-Failure Censoring Data, The 2^nd ISM International Statistical Conference (ISM-II), AIP Conf. Proc,1643, pp. 125-134.

[14] Kadilar, C. and Karasoy, D. S. (2007), A New Bayes Estimate of the Charge Point in the Hazard Function, Computational Statistics and Data Analysis, Vol.51, pp. 2993-3001.

[15] Griffin, J. E. and Brown, P. J. (2010), Inference with Normal Gamma Prior Distributions in regression Problems, Bayesian Analysis, Vol.5(1), pp. 171-188.

[16] Mohammed, S. F. and Batul, R. (2015), Bayesian Estimation of Shift Point in Shape Parameter of Inverse Gaussion Distribution Under Different Loss Function, Journal of Optimization in Industrial Engineering, Vol.18, pp. 1-12.

[17] Patel, R. M. and Patel, A. C. (2017), The Double Prior Selection for the Parameter of Exponential Life Time Model Under Type II Censoring, Journal of Modern Applied Statistical Methods, doi:10.22237/Jmasm/1493598180, Vol.16(1), pp. 406-427.

[18] DeGroot, M. H. (2005), Optimal Statistical Decision, John Wilely&Sons, Vol.82.

[19] Akbar, A. K., Mohammed, A., Zawar, H. and Muhammad, T. (2016), Comparison of Loss Functions for Estimating the Scale Parameter of Log-Normal Distribution Using Non-Informative Prior, Haccttepe Journal of Mathematics and Statistics, Vol.45(6), pp. 1831-1845.

Journal of University of Anbar for Pure Science

Numerical Methods on the Triple Informative Prior Distribution for the Failure Rate Basic Gompertz Model

References

References

Volume 14, Issue 2
August 2020
Page 88-94

Numerical Methods on the Triple Informative Prior Distribution for the Failure Rate Basic Gompertz Model

References

References

Volume 14, Issue 2August 2020Page 88-94

Volume 14, Issue 2
August 2020
Page 88-94