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In this work, we propose a three-parameter generalized Lindley distribution using the cubic rank transmutation map approach by Granzotto et al. (2017). We derive expressions for several mathematical properties including moments and moment generating function, mean deviation, probability weighted moments, quantile function, reliability analysis, and order statistics. We conducted a simulation study to assess the performance of the maximum likelihood estimation procedure for estimating model parameters. The flexibility of the proposed model is illustrated by analyzing two real data sets. [ABSTRACT FROM AUTHOR]

A three-parameter generalization of the Pareto distribution is presented with density function having a flexible upper tail in modeling loss payment data. This generalized Pareto distribution will be referred to as theOdd Paretodistribution since it is derived by considering the distributions of the odds of the Pareto and inverse Pareto distributions. Basic properties of the Odd Pareto distribution (OP) are studied. Model parameters are estimated using both modified and regular maximum likelihood methods. Simulation studies are conducted to compare the OP with the exponentiated Pareto, Burr, and Kumaraswamy distributions using two different test statistics based on the ml method. Furthermore, two examples from the Norwegian fire insurance claims data-set are provided to illustrate the upper tail flexibility of the distribution. Extensions of the Odd Pareto distribution are also considered to improve the fitting of data. [ABSTRACT FROM PUBLISHER]