Some parametric and semiparametric inference in survival analysis and reliability

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During the past 6 years, my research has focused mainly on Survival Analysis, Reliability Analysis, Ordered Data Analysis and Distribution Theory. I plan to pursue some outstanding problems in all these areas.******SURVIVAL ANALYSIS: Much work has been done on panel count data analysis and efficient nonparametric tests have been developed by assuming the counting process of the recurrent event to be a non-homogeneous Poisson process. However, Poisson process is quite a restrictive model as it is equi-dispersed and I propose to generalize by assuming a weighted Poisson process for the recurrent event incorporating weight functions to capture over- and under-dispersion.******Many flexible cure rate models and associated parametric inference have been studied. I propose to develop cure rate models in a semi-parametric setup through a proportional hazards model and then develop inferential methods under parametric and nonparametric forms of the baseline hazard function.******RELIABILITY ANALYSIS: Likelihood inference for one-shot device test data has been studied for different lifetime distributions. I plan to extend this work in two directions: to develop semi-parametric inference and to consider competing-cause scenario and develop associated inferential methods. I also plan to develop optimal design of tests based on prior information.******Much work has been done on Wiener and gamma degradation models. However, no work has been done on the development of acceptance sampling plans for units whose failures are monitored by some degradation process, and I plan to work on this issue and also develop sample size determination methods that will be useful for reliability engineers.******ORDERED DATA ANALYSIS: The notion of signatures enables a systematic study of coherent reliability systems. Recently, ordered signatures have been introduced based on conditional failure probabilities of systems given the ordered failure times of n systems. I want to explore their use in developing likelihood inference, especially efficient EM-algorithms, as well as exact nonparametric inference for some lifetime parameters of interest, such as quantile, reliability and cumulative hazard, based on system lifetime data.******DISTRIBUTION THEORY: Several new multivariate skewed distributions have been introduced in the literature and their skewness properties and tests for skewness have been studied. I plan to carry out a similar detailed study of multivariate kurtosis measures as well as tests for kurtosis, especially for testing multivariate normality.******Anticipated Outcomes and Benefits to the Field and to Canada: Most post-docs and PhD students I supervised have taken up positions in many institutions across the world, including Calgary, Manitoba and McMaster in Canada. Some others have joined Canadian companies such as Bombardier, BMO, CIBC, RBC, GE Capital and Rogers. I anticipate the proposed work to result in similar benefits.**