Different Estimation Methods and Joint Condence Region for the Inverse Burr Distribution Based on Progressively First-Failure Censored Sample with Application to the Nanodroplet Data


Abstract


In this article, the point and interval estimation of parameters for an in-verse Burr distribution based on progressively rst-failure censored sampleis studied. In point estimation, the maximum likelihood and Bayesian meth-ods are developed for estimating the unknown parameters. An expectation-maximization algorithm is applied for computing the maximum likelihoodestimators. The Bayes estimates relative to both the symmetric and asym-metric loss functions are provided using the Lindley's approximation andthe Metropolis-Hastings algorithm. In interval estimation, approximate andexact condence intervals with the exact condence region for the two parameters have been introduced. Moreover, the proposed methods are carriedout to a real data set contains the spreading of nanodroplet impingementonto a solid surface in order to demonstrate the applicabilities.

DOI Code: 10.1285/i20705948v12n2p341

Keywords: Expectation-Maximization algorithm; Exact condence inter- val; Exact condence region; Metropolis-Hastings Algorithm; Nanodroplet; Progressively rst-failure censoring.

References


Aggarwala, R., Balakrishnan, N. (1998). Some properties of progressive censored order statistics from arbitrary and uniform distribution with application to inference and simulation. Journal of Statistical Planning and Inference. 70:35-49.

Al-Moisheer, A.S. (2016). A mixture of two Burr type III distributions: identifiability and estimation under type ii censoring. Mathematical Problems in Engineering. 6:1-12.

Asadi, S. (2012). Simulation of nanodroplet impact on a solid surface. International Journal of Nano Dimension. 3:19-26.

Burr, I.W. (1942). Cumulative frequency distribution. Ann. Math. Stat. 13: 215-232.

Cordeiro, G.M., Gomes, A.E., da-Silva, C.Q., Ortega, E.M.M. (2017). A useful extension of the Burr III distribution. Journal of Statistical Distributions and Applications. 4:24.

Dube, M., Garg, R., Krishna, H. (2016). On progressively first failure censored Lindley distribution. Computational Statistics. 31:139-163.

Dempster, A.P., Laird, N.M., Rubin, D.B. (1977). Maximum likelihood from incomplete data via the em algorithm. J. R. Stat. Soc. Series B. 39: 1-38.

Hastings, W.K. (1970). Monte Carlo sampling methods using markov chains and their applications. Biometrika. 57: 97-109.

Kumar, D. (2016). Lower generalized order statistics based on inverse Burr distribution. American Journal of Mathematical and Management Sciences. 35:15-35.

Kundu, D., Pradhan, B. (2009). Estimating the parameters of the generalized exponential distribution in presence of hybrid censoring. Comm. Statist. Theory Methods. 38: 2030-2041.

Lindley, D.V. (1980). Approximate Bayesian method. Trabajos de Estadistica. 31: 223-245.

Lio, Y.L., Tsai, T.R. (2012). Estimation of for Burr XII distribution based on the progressively first failure-censored samples. J. Appl. Stat. 39:309-322.

Louis, T.A. (1982). Finding the observed information matrix when using the EM algorithm. J. R. Stat. Soc. Series B. 44: 226-233.

Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E. (1953). Equations of state calculations by fast computing machines. Journal of Chemical Physics. 21:1087-1092.

Mohammed, H.S., Ateya, S.F., AL-Hussaini, E.K. (2016). Estimation based on progressive first-failure censoring from exponentiated exponential distribution. Journal of Applied Statistics. 44:1479-1494.

Ng, T., Chan, C.S., Balakrishnan, N. (2002). Estimation of parameters from progressively censored data using EM algorithm. Comput. Stat. Data Analys. 39: 371- 386.

Sel, S., Jung, M., Chung, Y. (2017). Bayesian and maximum likelihood estimations from parameters of McDonald Extended Weibull model based on progressive type-II censoring. Journal of Statistical Theory and Practice. 1-24.

Panahi, H., Sayyareh, A. (2016). Estimation and prediction for a unified hybrid-censored Burr Type XII distribution. J. Statist. Comput. Simulation. 86: 55-73.

Panahi, H. (2017a). Estimation of the Burr type III distribution with application in unified hybrid censored sample of fracture toughness. Journal of Applied Statistics. 44:2575-2592.

Panahi, H. (2017b). 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.

Precious, M., Broderick, O., Alphonse, A., Huang, S. (2017). The Burr XII modified Weibull distribution: model, properties and applications. Electronic Journal of Applied Statistical Analysis. 10:118-145.

Wang, L., Shi, Y. (2012). Reliability analysis based on progressively first-failure-censored samples for the proportional hazard rate model. Math. Comput. Simul. 82:1383-1395.

Wu, S.J., Kus, C. (2009). On estimation based on progressive first-failure-censored sampling. Computational Statistics & Data Analysis. 53:3659-3670.


Full Text: pdf
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.