Estimation of Asymptotic Confidence Ellipses for Birnbaum-Saunders Distribution

Khanittha Hansoongnern, Bunyanuch Sakonthawichot, Artitaya Sittisareesmer, Wikanda Phaphan


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 ellipses  

Full Text:



Ahmed, S.E., Budsaba, K., Lisawadi, S., & Volodin, A. (2008). Parametric estmation for the Birnbaum-

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,



  • There are currently no refbacks.