The research of properties of maximum likelihood estimates of Weibull distribution parameters by left truncated data
Abstract
Left truncated data often arise in problems of reliability analysis, when sampling is carried out under condition that the lifetime is not less than a certain value. This paper is devoted to the research of statistical properties of maximum likelihood estimates (MLE) of Weibull distribution parameters depending on the sample size, truncation level, and the number of truncated observations in a sample. The research is carried out by means of computer simulation technique. The statement of the Fisher information contained in a sample of left truncated observations for distribution parameters has been obtained. The Fisher information losses from truncation and relative efficiency of MLE have been estimated. The results obtained in this paper can be useful for the problems of probabilistic reliability models construction by left truncated data.
References
1. Баталова З.Г. Анализ точности метода максимального правдоподобия для случайно цензурированных выборок. В кн.: Статистические методы обработки результатов наблюдений при контроле качества и надежности машин и приборов. Л., ЛДНТП, 1979. С. 14-17.
2. Баскаков В.Н. Обобщенный метод минимального расстояния для цензурированных данных // Надежность и контроль качества. 1995. № 7. С. 3-7.
3. Лемешко Б.Ю., Гильдебрант С.Я., Постовалов С.Н. К оцениванию параметров надежности по цензурированным выборкам // Заводская лаборатория. Диагностика материалов. 2001. Т. 67, № 1. С. 52-64.
4. Balakrishnan N., Mitra D. Left truncated and right censored Weibull data and likelihood infence with an illusrtation // Computational Statistics and Data Analysis. 2012. V. 56, № 12. P. 4011-4012.
5. Balakrishnan N., Mitra D. Likelihood inference for lognormal data with left truncation and right censoring with an illustration // Journal of Statistical Planning and Inference. 2011. V. 141, № 11. P. 3536-3553.
6. Li J. Cox Model Analysis with the Dependently Left // Mathematics Theses. Georgia State University, Atlanta, GA, 2010. Paper 88.
7. Su Y.-R., Wang J.-L. Modeling left-truncated and right-censored survival data with longitudinal covariates // The Annals of Statistics. 2012. V. 40, № 3. P. 1465-1488.
8. Кокс Д.Р., Оукс Д. Анализ данных типа времени жизни / пер. с англ. О.В. Селезнева. М: Финансы и статистика, 1988. 191 с.
9. Bagdonavicius V., Kruopis J., Nikulin M.S. Nonparametric Tests for Censored Data. London, Wiley (ISTE - 2010). P. 233.
10. Pan W.A., Chappell R. Nonparametric Estimator of Survival Functions // Lifetime Data Analysis. Boston. 1998. № 4. P. 187-202.
11. Cohen A.C. Truncated and censored samples: theory and applications. New York: Marcel Dekker, 1991. 328 p.
12. Balakrishnan N., Cohen A.C. Order Statistics and Inference: Estimation. Boston: Academic Press, 1991.
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Chimitova E..., Ermilova E... The research of properties of maximum likelihood estimates of Weibull distribution parameters by left truncated data. The Herald of the Siberian State University of Telecommunications and Information Science. 2016;(4):47-58. (In Russ.)
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