Tue, October 1, 2019
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3:00pm [3:00pm] Priyanka Majumder : Indian Institute of Engineering Science and Technology, Shibpur
Probability and Statistics seminar (It will be a talk by videoconference). Speaker: Priyanka Majumder. Affiliation: Indian Institute of Engineering Science and Technology, Shibpur. Date and Time: Tuesday 01 October, 3:00 pm - 4:00 pm. Venue: Ramanujan Hall, Department of Mathematics. Title: On Certain Probabilistic and Inferential Aspects of Reliability Theory. Abstract: Several nonparametric ageing classes have been established in literature based on the various reliability characteristics. The talk will cover certain probabilistic issues such as, reliability bound, moment bound, closure under the formation of weak limits, characterisation theorem, etc., which have been hitherto unknown in the literature, for the New Better than Average Failure Rate (NBAFR) class of life distributions. We further explore the validity of these results in the context of a more general ageing class related to NBAFR family. In the inferential part of my presentation, I will discuss a problem of testing exponentiality against an alternative which is dened based on the Laplace-Stieltjes transform, namely the so-called L-class. The asymptotic distributions of our scale-invariant test statistics are derived and consistency of the test established. General expressions of the local approximate Bahadur eciencies for the test statistics are obtained and evaluated for typical alternatives. The performance of the test is assessed by means of a simulation study and through application to some real life data sets.