Estimation of Asymptotic Confidence Ellipses for Birnbaum-Saunders Distribution
Abstract
The objective of this research is to propose the maximum likelihood estimators of parameter and also construct asymptotic confidence ellipse for Birnbaum-Saunders distribution. This distribution has been used in extensive of applications, reliability analysis and biological model. The performance of the asymptotic confidence ellipses is evaluated by considering the coverage probabilities and compared with the confidence coefficient of 0.98 for sample sizes = 30, 100, 500 and 1,000; parameter =1, 3, 5, 10, 15 and 20 and parameter = 2. The program R version 3.4.3 is used for Monte Carlo simulation study with 10,000 iterations. The research results find that as the sample size is increasing, the coverage probability is also increasing and closes to the confidence coefficient of 0.98. Moreover, different values of lead to difference of coverage probability values. If the parameter equals to 15 with =500, it gives the maximum of the coverage probability with 0.9083.Keywords : Birnbaum-Saunders distribution, Fisher information matrix, Asymptotic confidence ellipsesReferences
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saunders lifetime distribution based on new parametrization. Thailand Statistician, 6(2), 213-240.
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distribution based on scale-mixture of normal and the em-algorithm. SORT, 33(2), 171-192.
Birnbaum, Z. W., & Saunders, S. C. (1969a). A new family of lifetime distribution. Applied Probability, 6, 319-327.
Birnbaum, Z. W., & Saunders, S. C. (1969b). Estimation for a family of life distribution with applications
to fatigue. Applied Probability, 6, 328-347.
Bowonrattanaset, P., & Budsaba, K. (2011). Some Properties of the Three-Parameter Crack Distribution. Thailand Statistician, 9(2), 195-203.
Duangchana, N. & Budsaba, K. (2014) Asymptotic confidence ellipses of parameters for the inverse Gaussian
distribution. Thammasat International Journal of Science and Technology, 19(2), 22-29.
Kundu, D., Balakrishnan, N., & Jamalizadeh, A. (2010) Bivariate Birnbaum-saunders distribution and
associated inference. Journal of Multivariate Analysis, 101, 113-125.
Jorgensen, B., Seshadri, V., & Whitmore, G. A. (1991) On the mixture of the inverse Gaussian distribution
with its complementary reciprocal. Scad J Statist, 18, 77-89.
Seshadri, V. (1994) The Inverse Gaussian Distribution (A Case Study in Exponential Families), Clarendon Press,
Oxford.
saunders lifetime distribution based on new parametrization. Thailand Statistician, 6(2), 213-240.
Balakrishnan, N., Leiva, V., Sanhueza, A., & Vilca, F. (2009). Estimation in the Birnbaum-saunders
distribution based on scale-mixture of normal and the em-algorithm. SORT, 33(2), 171-192.
Birnbaum, Z. W., & Saunders, S. C. (1969a). A new family of lifetime distribution. Applied Probability, 6, 319-327.
Birnbaum, Z. W., & Saunders, S. C. (1969b). Estimation for a family of life distribution with applications
to fatigue. Applied Probability, 6, 328-347.
Bowonrattanaset, P., & Budsaba, K. (2011). Some Properties of the Three-Parameter Crack Distribution. Thailand Statistician, 9(2), 195-203.
Duangchana, N. & Budsaba, K. (2014) Asymptotic confidence ellipses of parameters for the inverse Gaussian
distribution. Thammasat International Journal of Science and Technology, 19(2), 22-29.
Kundu, D., Balakrishnan, N., & Jamalizadeh, A. (2010) Bivariate Birnbaum-saunders distribution and
associated inference. Journal of Multivariate Analysis, 101, 113-125.
Jorgensen, B., Seshadri, V., & Whitmore, G. A. (1991) On the mixture of the inverse Gaussian distribution
with its complementary reciprocal. Scad J Statist, 18, 77-89.
Seshadri, V. (1994) The Inverse Gaussian Distribution (A Case Study in Exponential Families), Clarendon Press,
Oxford.
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Published
2018-07-20
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