Masters Degrees (Statistics and Actuarial Science)

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Browsing Masters Degrees (Statistics and Actuarial Science) by Subject "Bayesian estimation"

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    Compounding a class of Rayleigh distributions : an objective Bayesian approach
    (Stellenbosch : Stellenbosch University, 2015-12) Van Rooyen, Renier; Mostert, Paul Johannes; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science
    ENGLISH ABSTRACT: In this work, Bayesian estimation in the context of parametric survival analysis is con- sidered. A class of models derived by compounding and generalising the Rayleigh dis- tribution is regarded. These models are well suited to survival analysis settings where the hazard rate is characterised by a sharp increase over time. An objective Bayesian approach is followed, whereby non-informative prior distribution selection leads to the use of the Je reys, the reference and the probability matching priors. Bayesian point estimators are derived using two symmetric loss functions, namely absolute error and squared error, as well as two asymmetric loss functions, namely linear exponential and general entropy. The resulting models and estimators are showcased in a simulation study by generating right censored lifetime data from the various compound models and utilising the Metropolis-Hastings algorithm to draw realisations from the corresponding posterior distributions, since closed-form expressions for these cannot be found. Obtain- ing the Fisher information plays a crucial part in deriving the non-informative priors. In cases where it cannot be analytically evaluated, an adaptive quadrature routine is used for the numerical approximation of some of the elements in the Fisher information. An application to data sets from practice concludes the exposition of the compound Rayleigh models of interest.