Characterizing the Relationship between Weibull Location Parameter and the Minimal Observation in a Small Size of Sample Based on Stochastic Simulation
Three-parameter Weibull distribution is one of the preferable distribution models to describe product life. However, it is difficult to estimate its location parameter in the situation of a small size of sample. This paper presents a stochastic simulation method to estimate the Weibull location parameters according to a small size of sample of product life observations and a large amount of statistically simulated life date. Big data technique is applied to find the relationship between the minimal observation in a product life sample of size n (n ≥ 3) and the Weibull location parameter. An example is presented to demonstrate the applicability and the value of the big data based stochastic simulation method. Comparing with other methods, the stochastic simulation method can be applied to very small size of sample such as the sample size of three, and it is easy to apply.
References
[1]
McLain, A.C. and Ghosh, S.K. (2011) Nonparametric Estimation of the Conditional Mean Residual Life Function with Censored Data. Lifetime Data Anal, 17, 514-532. https://doi.org/10.1007/s10985-011-9197-x
[2]
Soliman, A.A., Abd-Ellah, A.H. and Abou-Elheggag, N.A. (2012) Estimation of the Parameters of Life for Gompertz Distribution Using Progressive First-Failure Censored Data. Computational Statistics and Data Analysis, 56, 2471-248. https://doi.org/10.1016/j.csda.2012.01.025
[3]
Zhao, M., Jiang, H. and Liu, X. (2013) A Note on Estimation of the Mean Residual Life Function with Left-Truncated and Right-Censored Data. Statistics and Probability Letters, 83, 2332-2336. https://doi.org/10.1016/j.spl.2013.06.020
[4]
Elmahdy, E.E. (2015) A New Approach for Weibull Modeling for Reliability Life Data Analysis. Applied Mathematics and Computation, 250, 708-720. https://doi.org/10.1016/j.amc.2014.10.036
[5]
Jia, X., Wang, D. and Jiang, P. (2016) Inference on the Reliability of Weibull Distribution with Multiply Type-I Censored Data. Reliability Engineering and System Safety, 150, 171-181. https://doi.org/10.1016/j.ress.2016.01.025
[6]
Ducrosadn, F. and Pamphile, P. (2018) Bayesian Estimation of Weibull Mixture in Heavily Censored Data Setting. Reliability Engineering and System Safety, 180, 453-462. https://doi.org/10.1016/j.ress.2018.08.008
[7]
Ahmed, A.O.M. and Bayesian, N.A.I. (2010) Estimator for Weibull Distribution with Censored Data Using Extension of Jeffrey Prior Information. Procedia Social and Behavioral Sciences, 8, 663-669. https://doi.org/10.1016/j.sbspro.2010.12.092
[8]
Al Sobhi, M.M. and Soliman, A.A. (2016) Estimation for the Exponentiated Weibull Model with Adaptive Type-II Progressive Censored Schemes. Applied Mathematical Modelling, 40, 1180-1192. https://doi.org/10.1016/j.apm.2015.06.022
[9]
Mweleli, R., Orawo, L., Tamba, C. and Okenye, J. (2020) Interval Estimation in a Two Parameter Weibull Distribution Based on Type-2 Censored Data. Open Journal of Statistics, 10, 1039-1056. https://doi.org/10.4236/ojs.2020.106059
[10]
Ng, H.K.T., Luo, L., Hu, Y. and Duan, F. (2012) Parameter Estimation of Three - Parameter Weibull Distribution Based on Progressively Type-II Censored Samples. Journal of Statistical Computation & Simulation, 82, 1661-1678. https://doi.org/10.1080/00949655.2011.591797
[11]
Abbasi, B., Rabelo, L. and Hosseinkouchack, M. (2008) Estimating Parameters of the Three-Parameter Weibull Distribution Using a Neural Network. European Journal of Industrial Engineering, 2, 428-445. https://doi.org/10.1504/EJIE.2008.018438
