The principal goal of this paper is to extend the classical problem of find the values of α ∈ C for which the mappings, eitherare univalent, whenever f belongs to some subclasses of univalent mappings in D, but in the case of harmonic mappings, considering the shear construction introduced by Clunie and Sheil-Small in [3].The second, and third, and fivth authors were partially supported by Fondecyt Grants #1190756 .
In this article, we study an extension of the sinh Cauchy model in order to obtain asymmetric bimodality. The behavior of the distribution may be either unimodal or bimodal. We calculate its cumulative distribution function and use it to carry out quantile regression. We calculate the maximum likelihood estimators and carry out a simulation study. Two applications are analyzed based on real data to illustrate the flexibility of the distribution for modeling unimodal and bimodal data.
In actuarial statistics, distributions with heavy tails are of great interest to actuaries, as they represent a better description of risk exposure through a type of indicator with a certain probability. These risk indicators are used to determine companies’ exposure to a particular risk. In this paper, we present a distribution with heavy right tail, studying its properties and the behaviour of the tail. We estimate the parameters using the maximum likelihood method and evaluate the performance of these estimators using Monte Carlo. We analyse one set of simulated data and another set of real data, showing that the distribution studied can be used to model income data.
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