Improved interval estimation for the two-parameter Birnbaum-Saunders distribution

Abstract An improved interval estimation for the two-parameter Birnbaum–Saunders distribution is discussed. The proposed method is based on the recently developed higher-order likelihood-based asymptotic procedure. The probability coverages of confidence intervals are based on the proposed method and those procedures discussed in Ng et al. (Comput. Statist. Data Anal., (2003)) are evaluated using Monte Carlo simulations for small and moderate sample sizes. Two real life examples and some concluding remarks are also presented.

[1]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[2]  O. E. Barndorff-Nielsen,et al.  Infereni on full or partial parameters based on the standardized signed log likelihood ratio , 1986 .

[3]  ScienceDirect Computational statistics & data analysis , 1983 .

[4]  Nancy Reid,et al.  Likelihood and higher‐order approximations to tail areas: A review and annotated bibliography , 1996 .

[5]  E. Kay,et al.  Methods for statistical analysis of reliability and life data , 1974 .

[6]  Sam C. Saunders,et al.  Estimation for a family of life distributions with applications to fatigue , 1969, Journal of Applied Probability.

[7]  O. Barndorff-Nielsen Modified signed log likelihood ratio , 1991 .

[8]  N. Singpurwalla,et al.  Methods for Statistical Analysis of Reliability and Life Data. , 1975 .

[9]  Z. Birnbaum,et al.  A new family of life distributions , 1969 .

[10]  Debasis Kundu,et al.  Modified moment estimation for the two-parameter Birnbaum-Saunders distribution , 2003, Comput. Stat. Data Anal..

[11]  A. Desmond Stochastic models of failure in random environments , 1985 .

[12]  Necip Doganaksoy,et al.  Comparisons of Approximate Confidence Intervals for Distributions Used in Life-Data Analysis , 1993 .

[13]  Lee J. Bain,et al.  Inferences on the Parameters of the Birnbaum-Saunders Fatigue Life Distribution Based on Maximum Likelihood Estimation , 1981 .

[14]  Nancy Reid,et al.  A simple general formula for tail probabilities for frequentist and Bayesian inference , 1999 .