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Truncation Models for Pareto and Exponential Distributions with Applications
AdvisorPanorska, Anna K.
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The theme of this work is truncation. We revisit the truncated Pareto(TP) distribution, which is a useful power-law stochastic model for positive data that are subjected to truncation. We extend the standard TP model in the literature, where the main shape parameter α is assumed to be positive, to a more general case with an arbitrary α, and provide an account of its basic properties. We note that within this extended TP family, maximum likelihood estimators of the parameters always exist and are unique, and we account for their exact as well as asymptotic distributions. We also briefly address testing and interval estimation for the parameters, and offer an extension of the model to a regression setting, where the main shape parameter is driven by covariates. We address the issues of parameter estimation and checking goodness-of-fit in the regression setting, and provide multiple data examples illustrating the modeling potential of this new methodology. We present the connection between TP and Truncated Exponential (TE) distribution and build a new bivariate truncated vector (TB) consisting of the sum and maximum of independent and identically distributed (IID) TE random variables.