×
Lemonte, Artur J.; Simas, Alexandre B.; Cribari-Neto, Francisco

Bootstrap-based improved estimators for the two-parameter Birnbaum-Saunders distribution. (English) Zbl 1367.62037

J. Stat. Comput. Simulation 78, No. 1, 37-49 (2008).
Summary: We consider the two-parameter Birnbaum-Saunders distribution proposed by Z. W. Birnbaum and S. C. Saunders, J. Appl. Probab. 6, 319–327 (1969; Zbl 0209.49801)], which is commonly used for modeling the lifetime of materials and equipment. We consider different strategies of bias correction of the maximum-likelihood estimators for the parameters that index the distribution via bootstrap (parametric and nonparametric). The numerical evidence favors a particular bootstrap estimator based on parametric resampling. Finally, an example with real data is presented and discussed.

Cited in 33 Documents

MSC:

62E15 Exact distribution theory in statistics
62H10 Multivariate distribution of statistics
62N02 Estimation in survival analysis and censored data

Keywords:

bootstrap; bias correction; Birnbaum-Saunders distribution; maximum-likelihood estimation

Citations:

Zbl 0209.49801

Software:

Ox
Cite Review PDF
Full Text: DOI

References:

[1] DOI: 10.2307/3212003 · Zbl 0209.49801 · doi:10.2307/3212003
[2] DOI: 10.2307/3315148 · Zbl 0581.60073 · doi:10.2307/3315148
[3] DOI: 10.1109/TR.1986.4335393 · Zbl 0592.62089 · doi:10.1109/TR.1986.4335393
[4] DOI: 10.2307/2285692 · Zbl 0299.62013 · doi:10.2307/2285692
[5] Mann N. R., Methods for Statistical Analysis of Reliability and Life Data (1974) · Zbl 0339.62070
[6] DOI: 10.1109/24.257832 · Zbl 0789.62077 · doi:10.1109/24.257832
[7] DOI: 10.1080/03610929408831420 · Zbl 0850.62109 · doi:10.1080/03610929408831420
[8] DOI: 10.1109/24.690913 · doi:10.1109/24.690913
[9] DOI: 10.1080/03610929508831581 · Zbl 0937.62564 · doi:10.1080/03610929508831581
[10] DOI: 10.1080/03610929908832416 · Zbl 0935.62020 · doi:10.1080/03610929908832416
[11] Johnson N., Continuous Univariate Distributions 2, 2. ed. (1995) · Zbl 0821.62001
[12] DOI: 10.2307/3212004 · Zbl 0216.22702 · doi:10.2307/3212004
[13] DOI: 10.2307/1267788 · Zbl 0462.62077 · doi:10.2307/1267788
[14] DOI: 10.1016/S0167-9473(02)00254-2 · Zbl 1429.62451 · doi:10.1016/S0167-9473(02)00254-2
[15] DOI: 10.1214/aos/1176344552 · Zbl 0406.62024 · doi:10.1214/aos/1176344552
[16] DOI: 10.1016/S0165-1765(97)00276-0 · Zbl 0899.90043 · doi:10.1016/S0165-1765(97)00276-0
[17] DOI: 10.2307/2289528 · Zbl 0719.62053 · doi:10.2307/2289528
[18] DOI: 10.1016/S0304-4076(97)00099-7 · Zbl 0961.62111 · doi:10.1016/S0304-4076(97)00099-7
[19] DOI: 10.1016/S0167-9473(02)00102-0 · Zbl 1103.62307 · doi:10.1016/S0167-9473(02)00102-0
[20] Davison A. C., Bootstrap Methods and Their Application (1997) · Zbl 0886.62001 · doi:10.1017/CBO9780511802843
[21] Efron B., An Introduction to the Bootstrap (1993) · Zbl 0835.62038
[22] DOI: 10.1023/A:1023902027800 · Zbl 1047.62119 · doi:10.1023/A:1023902027800
[23] Doornik J. A., Ox: An Object-Oriented Matrix Language, 4. ed. (2001)
[24] Mittelhammer R. C., Econometric Foundations (2000) · Zbl 0961.62110
[25] McCool, J. I. 1974. ”Inferential techniques for Weibull populations”. Dayton, OH: Wright–Patterson Air Force Base. Aerospace Research Laboratories Report ARL TR74-0180 · Zbl 0305.62066
[26] Cohen A. C., Journal of Quality Technology 16 pp 159– (1984)
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.