Parameter Estimation of Birnbaum-Saunders Distribution under Competing Risks Using the Quantile Variant of the Expectation-Maximization Algorithm

Chanseok Park and Min Wang ()
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Chanseok Park: Applied Statistics Laboratory, Department of Industrial Engineering, Pusan National University, Busan 46241, Republic of Korea
Min Wang: Department of Management Science and Statistics, The University of Texas at San Antonio, San Antonio, TX 78249, USA

Mathematics, 2024, vol. 12, issue 11, 1-17

Abstract: Competing risks models, also known as weakest-link models, are utilized to analyze diverse strength distributions exhibiting multi-modality, often attributed to various types of defects within the material. The weakest-link theory posits that a material’s fracture is dictated by its most severe defect. However, multimodal problems can become intricate due to potential censoring, a common constraint stemming from time and cost limitations during experiments. Additionally, determining the mode of failure can be challenging due to factors like the absence of suitable diagnostic tools, costly autopsy procedures, and other obstacles, collectively referred to as the masking problem. In this paper, we investigate the distribution of strength for multimodal failures with censored data. We consider both full and partial maskings and present an EM-type parameter estimate for the Birnbaum-Saunders distribution under competing risks. We compare the results with those obtained from other distributions, such as lognormal, Weibull, and Wald (inverse-Gaussian) distributions. The effectiveness of the proposed method is demonstrated through two illustrative examples, as well as an analysis of the sensitivity of parameter estimates to variations in starting values.

Keywords: Birnbaum-Saunders distribution; competing risks; EM algorithm; missing data (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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