Inference for generalized inverse exponential distribution based on generalized hybrid Progressive censored data and its application to plasma spray data

Subject Areas : Statistics

parya parviz ¹ , hanieh panahi ² , saeid Asadi ³

1 - Department of Statistics, Science and Research Unit, Islamic Azad University, Tehran, Iran
2 - Department of Mathematics and Statistics, Lahijan branch, Islamic Azad University, Lahijan, Iran
3 - Department of Mechanical Engineering, Payame Noor University (PNU), Tehran, Iran

Received: 2020-04-19 Accepted : 2021-06-12 Published : 2022-03-21

Keywords: تقریب لیندلی, سانسورهیبرید فزاینده تعمیم یافته نوع دوم, برآورد ماکسیمم درستنمایی, پاشش پلاسمایی, یکتایی, نمونه گیری از نقاط مهم,

Abstract :

In many applied research, the researcher does not have access to all the data for some reasons such as time and cost constraints. So, the statistical inference based on the available data is important. In this paper, estimation of unknown parameters of a generalized inverted exponential distribution is studied under generalized Type II progressive hybrid censoring. The maximum likelihood estimators and their existence and uniqueness are investigated. Based on the Bayesian approach, the estimators of the shape and scale parameters are derived under squared error loss function. Since closed - form expressions for the Bayes estimators cannot be obtained, we use Lindley’s approximation and important sampling procedure for obtaining them. Simulation study for comparing the different classical and Bayesian estimations is presented. Finally, two real data sets contain oblique impact of micro droplets onto surface in plasma spray coating process and repair time for a communication transmitter are analyzed for illustration purposes.

References:

[1] Epstein, B. Truncated life-tests in the exponential case. The Annals of Mathematical Statistics 25.555-564(1954)

 

[2]Childs, A. Chandrasekhar, B. Balakrishnan, N. and Kundu, D. Exact likelihood inference based on type -I and type-II hybrid censored samples from the exponential distribution, Annals of the Institute of Statistical Mathematics, 55, 319–330 (2003)

 

[3]Balakrishnan, N. Kundu, D. Hybrid censoring: models, inferential results and applications. Computational Statistics & Data Analysis, vol. 57, no. 1, 166-209(2013)

 

 [4] Gupta, P.K. Singh, B. Parameter estimation of Lindley distribution with hybrid censored data. International Journal of Systems Assurance Engineering and Management, 4(4), 378-385(2012)

 

[5] Sayyareh, A., Panahi, H. Model Selection Based on Tracking Interval Under Unified Hybrid Censored Samples. Journal of the Iranian Statistical Society, 17 (1), 1-31. Statistical Research of Iran, vol. 8, no. 2, 149-162 (2018)

 

[6]   Habibi, R.A., Izanlo, M. An EM algorithm for estimating the parameter of the generalized exponential distribution under unified hybrid censored data. Journal of Statistical Research of Iran, vol. 8, no. 2, 149-162. (2011)

[7] Childs, A., Chandrasekar B., Balakrishnan, N. Exact likelihood inference for an exponential parameter under progressive hybrid censoring schemes. In: Vonta F, Nikulin M, Limnios N, Huber-Carol C (eds) Statistical models and methods for biomedical and technical systems. Birkh¨auser, 323-334. (2008)

[8] Chan, P., Ng, H., Su, F. Exact likelihood inference for the two-parameter exponential distribution under type II  progressively hybrid censoring,  78, 747–770(2015)

[9] Kundu, D., Joarder, A. Analysis of type-II progressively hybrid censored data. Computational statistics & Data Analysis, 50, 2509-2528. (2006a)

 [10] Hemmati, F., Khorram, E. Statistical analysis of the log-normal distribution under type II progressive hybrid censoring schemes. Communications in Statistics Simulation and Computation, 42, 52-75. (2013)

[11] Panahi, H. Estimation Methods for the Generalized Inverted Exponential   Distribution Under Type II Progressively Hybrid Censoring with Application to Spreading   of Micro-Drops Data. Communications in Mathematics and Statistics, 5, 159-174. (2017)

[12]  Lee, k., Sun, H., Cho, Y. Exact liklihood inference of the exponential  paramater under generalized type II progressive hybrid censoring. Journal of the Korean statistical society. 45: 123-136. (2016)

[13] Cho, Y., Sun, H. and Lee, K. Exact likelihood inference for an exponential parameter under generalized progressive hybrid censoring scheme. Statistical Methodology, 23, 18-34.(2015)

[14] Gorny, J., Cramer, E. Exact likelihood inference for exponential distributions under generalized progressive hybrid censoring schemes. Statistical Methodology, 29, 70-94. (2016)

[15] Koley, A., Kundu, D. On generalized progressive hybrid censoring in presence of competing risks. Metrika, 80, 401-426. (2017)

[16] Mohie El-Din, M.M., Nagy, M., Abu-Moussa, M.H. Estimation and prediction for Gompertz distribution under the generalized progressive hybrid censored data. Annals of Data Science, 1-33. (2019)

[17] Gupta R.D., Kundu, D. Generalized exponential distributions, Aust. N. Z. J. Statist. 41(2), 173–188. (1999)

[18] Abouammoh, A.M. and Alshingiti, M.AReliability estimation of generalized inverted exponential distribution. Journal of statistical computation and simulation, 79, 1301-1315. . (2009)

[19] Krishna, H. and Kumar, K. Reliability estimation in generalized inverted exponential distribution with progressively type II censored sample. journal of statistical computation and simulation, 83, 1007-1019. (2013)

[20] Dey, S. and Dey, T. On progressively censored generalized inverted exponential distribution. Journal of Applied statistics, 41, 2557-2576. (2014)

[21] Samuel, B.R., Balamurali, S. and Aslam, M., Designing of repetitive group sampling plan undertruncated life test based on generalized inverted exponential distribution. journal of statistics and Management systems, 21, 955-970. (2018)

 [22]  Hassan, A.S., Marwa, A., and Nagy, H.F. Estimation of P (Y>X) using record values from the generalized inverted exponential distribution. Pakistan journal of statistics and operation Research, 14, 645-660. (2018)

[23] Ateya, S.f. Estimation under Inverse Weibull Distribution based on Balakrishnan’s Unified Hybrid Censored Scheme. Communications in Statistics Simulation and Computation, 46, 3645-3666. (2015)

[24] Kundu, D. and Pradhan, BBayesian inference and life testing plans for generalized exponential distribution. Science in China Series A: Mathematics, 52:1373-1388. (2009)

[25] Lindley, D.V. Approximate Bayesian methods (with discussions), Trabajos de Estadistica 31, 232–245. (1980)

[26]   Varadhan, R., and Gilbert, P.D.  (2009), BB: An R Package for Solving a Large System of Nonlinear Equations and for Optimizing a High-Dimensional Nonlinear Objective Function, J. Statistical Software, 32:4, http://www.jstatsoft.org/v32/i04/.

[27] Von Alven, W. H. (ed.). Reliability Engineering by ARINC. Upper Saddle River, NJ, USA: Prentice. (1964)

[28] Delignette-Muller ML and Dutang C fitdistrplus: An R Package for Fitting Distributions. Journal of Statistical Software, 64(4), 1-34. (2015)

[29] Kang, C.W., Ng, H.W. Splat morphology and spreading behavior due to oblique impact of droplets onto substrates in plasma spray coating process, Surface and Coatings Technology, 200, 5462-5477. 2006),

[30] اسدی، س.، پسندیده فرد، م.، مقیمان، م.، (1386). مطالعه برخورد مایل قطره با سطح جامد در فرآیند لایه نشانی پاششی با استفاده از شبیه­سازی عددی و مدل تحلیلی، نشریه علمی و پژوهشی علوم و مهندسی سطح ایران، دوره 3، شماره 4.