Failure rate of Birnbaum-Saunders distributions: shape, change-point, estimation and robustness. (English) Zbl 1419.62025
For a given symmetric random variable \(Z\) on \(\mathbb{R}\), a random variable \(T\) with the corresponding generalised Birnbaum-Saunders distribution (with parameters \(\alpha\) and \(\beta\)) is defined by \[ T=\beta\left(\frac{\alpha Z}{2}+\sqrt{\left(\frac{\alpha Z}{2}\right)^2+1}\right)^2\,. \] The authors investigate the properties and estimation of the failure rate of this random variable \(T\) in the cases where \(Z\) has either a standard normal, logistic or Student’s-\(t\) distribution. This includes a simulation study and application to real-world data.
Reviewer: Fraser Daly (Edinburgh)
MSC:
62E10 | Characterization and structure theory of statistical distributions |
62F03 | Parametric hypothesis testing |
62F10 | Point estimation |
62F35 | Robustness and adaptive procedures (parametric inference) |
60E05 | Probability distributions: general theory |
62N05 | Reliability and life testing |