الفهرس 
introdutionOnly 14 pages are availabe for public view
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Abstract
In this thesis, the first apart from discretization techniques, we propose and study a new generalization of the basic Lindley distribution. The structural properties of the new distribution are investigated. These include the compounding representation of the distribution, reliability analysis and statistical measures, Expressions for Lorenz and Bonferroni curves and Renyi entropy as ameasure for uncertainty reduction are derived. Maximum likelihood estimation is used to evaluate the parameters. The new model contains twelve lifetime distributions as special cases such as the Lindley, Quasi Lindley, gamma, and exponential distributions, among others. This model has the advantage of being capable of modeling various shapes of aging and failure criteria. Finally, the usefulness of the new model for modeling reliability data is illustrated using a real data set.
The second, A two-parameter transmuted geometric distribution is proposed as a new generalization of the geometric distribution by employing the quadratic transmutation techniques of Shaw and Buckley. The additional parameter plays the role of controlling the tail length. Distributional properties of the proposed distribution are investigated. Maximum likelihood estimation method is discussed along with some data fitting experiments to show its advantages over some existing distributions in literature. The tail flexibility of density of aggregate loss random variable assuming the proposed distribution as primary distribution is outlined and presented along with an illustrative modeling of aggregate claim of a vehicle insurance data. Finally, we present a count regression model based on the proposed distribution and carry out its comparison with some established models.
Keywords: The first, Lindley distribution; mixture; reliability analysis; moment generating function; order statistics; maximum likelihood estimation.
The second, Aggregate claim, count regression, geometric distribution, transmuted distribution.