Estimating the Parametric Functions and Reliability Measures for Exponentiated Lifetime Distributions Family

Year 2022, Volume: 35 Issue: 4, 1665 - 1684, 01.12.2022

Hormatollah Pourreza Ezzatallah Baloui Jamkhaneh , Einolah Deiri Harish Garg

https://doi.org/10.35378/gujs.910897

Cited By: 2

https://izlik.org/JA26HF64PD

Abstract

The paper aims are to extend the theory to estimate the parameters of the exponentiated lifetime distribution. For it, in this paper, we derived the probability density function, cumulative density, reliability function and the stress-strength parameter of the distribution. To estimate the parameters of such distribution, we considered the maximum likelihood and uniformly minimum variance unbiased methods. The validity of the proposed work has been conducted over the simulation study of both estimation methods under the special sub model as exponentiated inverse Gompertz distribution. Finally, some real data has been taken to conduct an analysis and to discuss the effectiveness and advantages of the established work by comparing with other methods. 

Keywords

Exponentiated distributions family , Reliability function , Stress-strength parameter

Supporting Institution

-

Project Number

-

Thanks

-

References

• Mudholkar, G. S., Srivastava, D. K.,“Exponentiated Weibull family for analyzing bathtub failure-real data”, IEEE Transaction Reliability, 42:299-302, (1993).
• Mudholkar, G. S., Srivastava, D. K., Freimes, M.,“The exponentiated Weibull family: A reanalysis of the bus-motor-failure data”, Technometrics, 37: 436-445, (1995).
• Nadarajah, S., Kotz, S.,“The Exponentiated Type Distributions”, Acta Applicandae Mathematicae, 92: 97-111, (2006).
• Delgarm, L., Zadkarami, M. R.,“A new generalization of lifetime distributions”, Computational Statistics, 30: 1185-1198, (2015).
• Pourreza, H., Baloui Jamkhaneh, E., Deiri, E.,“A family of Gamma-generated distributions: Statistical properties and applications”, Statistical Methods in Medical Research, 30(8): 1850-1873, (2021).
• Dixit, U. J., Jabbari Nooghabi, M.,“Efficient estimation in the Pareto distribution”, Statistical Methodology, 7(6): 687-691, (2010).
• Bagheri, S. F., Alizadeh, M., Nadarajah, S., Deiri, E.,“Efficient estimation of the PDF and the CDF of the Weibull extension model”, Communications in Statistics-Simulation and Computation, 45(6): 2191-2207, (2014).
• Bagheri, S. F., Alizadeh, M., Nadarajah, S.,“Efficient estimation of the PDF and the CDF of the exponentiated Gumbel distribution”, Communications in Statistics-Simulation and Computation, 45(1): 339-361, (2016).
• Alizadeh, M., Bagheri, S. F., Baloui Jamkhaneh, E., Nadarajah, S.,“Estimates of the PDF and the CDF of the exponentiated Weibull distribution”, Brazilian Journal of Probability and Statistics, 29(3): 695-716, (2015).
• Alizadeh, M., Razaei, S., Bagheri, S. F., Nadarajah, S.,“Efficient estimation for the generalized exponential distribution”, Statistical Papers, 56(4): 1015-1031, (2015).
• Maiti, S. S., Mukherjee, I.,“On estimation of the PDF and CDF of the Lindley distribution”, Communications in Statistics - Simulation and Computation, 47(5): 1370-1381, (2018).
• Ghasemi Cherati, M., Baloui Jamkhaneh, E., Deiri, E.,“Some estimation procedures of the PDF and CDF of the generalized inverted Weibull distribution with comparison”, International Journal of Nonlinear Analysis and Applications, 12(1): 1017-1036, (2021).
• Bekker, A., Roux, J. ,“Reliability characteristics of the Maxwell distribution: a Bayes estimation study”, Communication in Statistics-Theory and Methods, 34: 2169-2178, (2005).
• Krishna, H., Kumar, K.,“Reliability estimation in Lindley distribution with progressively type II right censored sample”, Mathematics and Computer in Simulation, 82: 281-294, (2011).
• Rastogi, M. K., Tripathi, Y. M.,“Parameter and reliability estimation for an exponentiated half-logistic distribution under progressive type II censoring”, Journal of Statistical Computation and Simulation, 84(8): 1711-1727, (2014).
• Abouei Ardakan, M., Mirzaei, Z., Hamadani, Z., Elsayed, A. E.,“Reliability Optimization by Considering Time-Dependent Reliability for Components”, Quality and Reliability Engineering International, 33: 1641-1654, (2017).
• Amirzadi, A., Baloui Jamkhaneh, E., Deiri, E.,“A comparison of estimation methods for reliability function of inverse generalized Weibull distribution under new loss function”, Journal of Statistical Computation and Simulation, 91(13): 2595-2622, (2021).
• Dmitriev, Yu. G., Koshkin, G. M.,“Nonparametric estimation of the reliability function characteristics using auxiliary information”, Russian Physics Journal, 61(12): 2197-2208, (2019).
• Sankaran, P. G., Dileep Kumar, M.,“Reliability properties of proportional hazards relevation transform”, Metrika, 82: 441-456, (2019).
• Roy, A., Gupta, N.,“Reliability of a coherent system equipped with two cold standby components”, Metrika, 83: 677-697, (2020).
• Gu, Y. K., Fan, Ch. J., Liang, L. Q., Zhang, J.,“Reliability calculation method based on the Copula function for mechanical systems with dependent failure”, Annals of Operations Research, 1-18, (2019).
• Zhang, Y., Yu, T., Song, B.,“A reliability allocation method of mechanism considering system performance reliability”, Quality and Reliability Engineering International, 35(7): 2240-2260, (2019).
• Chaturvedi, A., Tomer, S. K.,“UMVU estimation of the reliability function of the generalized life distributions”, Statistical Papers, 44(3): 301-313, (2003).
• Kundu, D., Gupta, R. D.,“Estimation of P[Y
• Turkkan, N., Pham-Gia, T.,“System stress-strength reliability: The multivariate case”, IEEE Transactions on Reliability, 56(1): 115-124, (2007).
• Rezaei, A., Tahmasbi, R., Mahmoodi, M.,“Estimation of P[Y < X] for generalized Pareto distribution”, Journal of Statistical Planning and Inference, 140: 480-494, (2010).
• Al-Mutairi, D. K., Ghitany, M. E., Kundu, D.,“Inferences on stress-strength reliability from Lindley distributions”, Communications in Statistics-Theory and Methods, 42(8): 1443-1463, (2013).
• Nadar, M., Kizilaslan, F., Papadopoulos, A.,“Classical and Bayesian estimation of P(Y < X) for Kumaraswamy’s distribution”, Journal of Statistical Computation and Simulation, 84(7): 1505-1529, (2014).
• Alghamdi, S. M., Percy, D. F.,“Reliability equivalence factors for a series parallel system of components with exponentiated Weibull lifetimes”, IMA Journal of Management Mathematics, 28(3): 339-358, (2017).
• Kizilaslan, F., Nadar, M.,“Estimation of reliability in a multicomponent stress–strength model based on a bivariate Kumaraswamy distribution”, Statistical Papers, 59: 307-340, (2018).
• Rezaei, A., Sharafi, M., Behboodian, J., Zamani, A. ,“Inferences on stress-strength parameter based on GLD5 distribution”, Communications in Statistics - Simulation and Computation, 47(5): 1251-1263, (2018).
• Alzaatreh, A., Lee, C., Famoye, F.,“A new method for generating families of continuous distributions”, Metron, 71 (1): 63-79, (2013).
• Nadarajah, S., Bagheri, S. F., Alizadeh, M., Bahrami Samani, E.,“Estimation of the stress strength parameter for the generalized exponential-Poisson distribution”, Journal of Testing and Evaluation, 46(5): 2184-2202, (2017).
• Gross, A. J., Clark, V. A.,“Survival Distributions: Reliability Applications in the Biomedical Sciences”, New York: John Wiley and Sons, 105-105, (1975).
• Eliwa, M. S., El-Morshedy, M., Ibrahim, M.,“Inverse Gompertz Distribution: Properties and Different Estimation Methods with Application to Complete and Censored Data”, Annals of Data Science, 6: 321-339, (2019).
• El-Gohary, A., Alshamrani, A., Al-Otaibi, A. N.,“The generalized gompertz distribution”, Applied Mathematical Modelling, 37: 13-24, (2013).
• Crowder, M.,“Tests for a family of survival models based on extremes”, In: Limnios N., Nikulin M. (eds.), Recent Advances in Reliability Theory: Statistics for Industry and Technology, Birkhäuser Boston, Boston, MA, 307–321, (2000).