×
Panahi, Hanieh; Moradi, Nasrin

Estimation of the inverted exponentiated Rayleigh distribution based on adaptive type II progressive hybrid censored sample. (English) Zbl 1434.62207

J. Comput. Appl. Math. 364, Article ID 112345, 17 p. (2020).
Summary: In this paper, the problem of estimating parameters of the inverted exponentiated Rayleigh distribution under adaptive type II progressive hybrid censored sample is discussed. The maximum likelihood estimators (MLEs) are developed for estimating the unknown parameters. The asymptotic normality of the MLEs is used to construct the approximate confidence intervals for the parameters. By applying the Bayesian approach, the estimators of the unknown parameters are derived under symmetric and asymmetric loss functions. The Bayesian estimates are evaluated by using the Lindley’s approximation as well as the Monte Carlo Markov chain (MCMC) technique together with Metropolis-Hastings algorithm. The MCMC samples are further utilized to construct the Bayesian intervals for the unknown parameters. Monte Carlo simulations are implemented and observations are given. Finally, the data of the maximum spreading diameter of nano-droplet impact on hydrophobic surfaces is analyzed to illustrative purposes.

Cited in 9 Documents

MSC:

62N01 Censored data models
62G07 Density estimation
62E15 Exact distribution theory in statistics
62P35 Applications of statistics to physics

Keywords:

adaptive type II progressive hybrid censoring; diameter of nano-droplet; Gibbs sampling; inverted exponentiated Rayleigh distribution; Metropolis-Hastings; symmetric and asymmetric loss functions
Cite Review PDF
Full Text: DOI

References:

[1] Ghitany, M. E.; Tuan, V. K.; Balakrishnan, N., Likelihood estimation for a general class of inverse exponentiated distributions based on complete and progressively censored data, J. Stat. Comput. Simul., 84, 96-106 (2014) · Zbl 1453.62685
[2] Kundu, D.; Howlader, H., Bayesian Inference and prediction of the inverse Weibull distribution for Type-II censored data, Comput. Statist. Data Anal., 54, 1547-1558 (2010) · Zbl 1284.62604
[3] Raqab, M. Z.; Madi, M. T., Bayesian Analysis for the exponentiated Rayleigh distribution, METRON - Int. J. Statist., 3, 269-288 (2009) · Zbl 1416.62572
[4] Mahmoud, M. A.W.; Ghazal, M. G.M., Estimations from the exponentiated Rayleigh distribution based on generalized Type-II hybrid censored data, J. Egypt. Math. Soc., 25, 71-78 (2017) · Zbl 1357.62094
[5] Kayal, T.; Tripathi, Y. M.; Rastogi, M. K., Estimation and prediction for an inverted exponentiated Rayleigh distribution under hybrid censoring, Comm. Statist. Theory Methods, 47, 1615-1640 (2018) · Zbl 1392.62296
[6] Banerjee, A.; Kundu, D., Inference based on type-II hybrid censored data from a Weibull distribution, IEEE Trans. Reliab., 57, 369-378 (2008)
[7] Gupta, P. K.; Singh, B., Parameter estimation of lindley distribution with hybrid censored data, Int. J. Syst. Assur. Eng. Manag., 1, 1-8 (2012)
[8] Balakrishnan, N.; Kundu, D., Hybrid censoring models, inferential results and applications, Comput. Statist. Data Anal., 57, 166-209 (2013) · Zbl 1365.62364
[9] Aggarwala, R.; Balakrishnan, N., Some properties of progressive censored order statistics from arbitrary and uniform distribution with application to inference and simulation, J. Statist. Plann. Inference, 70, 35-49 (1998) · Zbl 1067.62538
[10] Kundu, D.; Joarder, A., Analysis of Type-II progressively hybrid censored data, Comput. Statist. Data Anal., 50, 2509-2528 (2006) · Zbl 1284.62605
[11] Childs, A.; Chandrasekar, B.; Balakrishnan, N., Exact likelihood inference for an exponential parameter under progressive hybrid censoring, (Vonta, F.; Nikulin, M.; Limnios, N.; Huber-Carol, C., Statistical Models and Methods for Biomedical and Technical Systems (2008), Birkhauser: Birkhauser Boston), 319-330
[12] Ng, H. K.T.; Kundu, D.; Chan, P. S., Statistical analysis of exponential lifetimes under an adaptive Type-II progressively censoring scheme, Nav. Res. Logist., 56, 687-698 (2009) · Zbl 1178.62111
[13] Balakrishnan, N.; Kateri, M., On the maximum likelihood estimation of parameters of Weibull distribution based on complete and censored data, Statist. Probab. Lett., 78, 2971-2975 (2008) · Zbl 1148.62081
[14] Mahmoud, M. A.W.; Soliman, A. A.; Abd-Ellah, A. H.; El-Sagheer, R. M., Estimation of generalized pareto under an adaptive type-II progressive censoring, Intell. Inform. Manag., 5, 73-83 (2013)
[15] Ismail, A. A., Inference for a step-stress partially accelerated life test model with an adaptive Type-II progressively hybrid censored data from Weibull distribution, J. Comput. Appl. Math., 260 (2014), 553-542 · Zbl 1293.62218
[16] AL Sobhi, M. M.; Soliman, A. A., Estimation for the exponentiated Weibull model with adaptive Type-II progressive censored schemes, Appl. Math. Model., 40, 2, 1180-1192 (2015) · Zbl 1446.62259
[17] Nassar, M.; Abo-Kasem, O., Estimation of the inverse Weibull parameters under adaptive type-II progressive hybrid censoring scheme, J. Comput. Appl. Math., 315, 228-239 (2017) · Zbl 1356.62174
[18] Nassar, M.; Abo-Kasem, O.; Zhang, C.; Dey, S., Analysis of Weibull distribution under adaptive Type-II progressive hybrid censoring scheme, J. Indian Soc. Probab. Statist., 19, 25-65 (2018)
[19] Lindley, D. V., Approximate Bayesian method, Trab. Estadistica, 31, 223-245 (1980) · Zbl 0458.62002
[20] Ritter, C.; Tanner, M. A., Facilitating the gibbs sampler: The gibbs stopper and the griddy-gibbs sampler, J. Amer. Statist. Assoc., 87, 861-868 (1992)
[21] Gilks, W. R.; Wild, P., Adaptive rejection sampling for gibbs sampling, J. R. Statist. Soc. C, 41, 337-348 (1992) · Zbl 0825.62407
[22] Koch, K. R., Gibbs sampler by sampling-importance-resampling, J. Geod., 81, 581-591 (2007) · Zbl 1133.62316
[23] Shao, W.; Guo, G.; Meng, F.; Jia, S., An efficient proposal distribution for Metropolis-Hastings using a B-splines technique, Comput. Statist. Data Anal., 57, 465-478 (2013) · Zbl 1365.65026
[24] Martino, L.; Elvira, V.; Camps-Valls, G., The recycling gibbs sampler for efficient learning, Digit. Signal Process., 74, 1-13 (2018)
[25] Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M. N.; Teller, A. H.; Teller, E., Equations of state calculations by fast computing machines, J. Chem. Phys., 21, 1087-1092 (1953) · Zbl 1431.65006
[26] Hastings, W. K., Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57, 97-109 (1970) · Zbl 0219.65008
[27] Balakrishnan, N.; Sandhu, R. A., A simple simulational algorithm for generating progressive Type-II censored samples, Amer. Statist., 49, 229-230 (1995)
[28] Hai-Bao, H.; Li-Bin, C.; Lu-Yao, B.; Su-He, H., Molecular dynamics simulations of the nano-droplet impact process on hydrophobic surfaces, Chin. Phys. B, 23, Article 074702 pp. (2014)
[29] Shao, Q.; Wong, H.; Xia, J.; IP, W. C., Models for extremes using the extended three-parameter Burr XII system with application to flood frequency analysis, Hydrol. Sci. J., 49, 685-702 (2004)
[30] Saxena, B. K.; Rao, K. V.S., Comparison of Weibull parameters computation methods and analytical estimation of wind turbine capacity factor using polynomial power curve model: case study of a wind farm, Renew.: Wind Water Solar, 2, 1-11 (2015)
[31] Panahi, H., Estimation of the burr type III distribution with application in unified hybrid censored sample of fracture toughness, J. Appl. Statist., 44, 2575-2592 (2017) · Zbl 1516.62528
[32] Panahi, H., Estimation methods for the generalized inverted exponential distribution under type II progressively hybrid censoring with application to spreading of micro-drops data, Commun. Math. Statist., 5, 159-174 (2017) · Zbl 1373.62486
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.