Abstract
In this article, we introduce a new class of five-parameter model called the Exponentiated Weibull Lomax arising from the Exponentiated Weibull generated family. The new class contains some existing distributions as well as some new models. Explicit expressions for its moments, distribution and density functions, moments of residual life function are derived. Furthermore, Rényi and q–entropies, probability weighted moments, and order statistics are obtained. Three suggested procedures of estimation, namely, the maximum likelihood, least squares and weigthed least squares are used to obtain the point estimators of the model parameters. Simulation study is performed to compare the performance of different estimates in terms of their relative biases and standard errors. In addition, an application to two real data sets demonstrate the usefulness of the new model comparing with some new models.
Highlights
The Lomax or Pareto II distribution is originally used for modeling business failure data, and it has been widely applied in a variety of contexts studies. Atkinson and Harrison (1978) and Harris (1968) applied the Lomax distribution to income and wealth data. Bryson (1974) suggested Lomax distribution as an alternative to the exponential distribution for heavytailed data sets. Myhre and Saunders (1982) applied Lomax distribution in the right censored data
We introduce a new five-parameter model, called the Exponentiated Weibull Lomax distribution based on the Exponentiated Weibull-generated (EW-G) family.The rest of the paper is outlined as follows
An extensive simulation study is conducted to compare the performance of the different estimators in the sense of their relative biases (RBs) and standard errors (SEs) for different sample sizes and for different parameter values.1000 samples of small, moderate and large sample sizes are generated from Exponentiated Weibull Lomax (EWL) distribution with different set of parameters
Summary
The Lomax or Pareto II distribution is originally used for modeling business failure data, and it has been widely applied in a variety of contexts studies. Atkinson and Harrison (1978) and Harris (1968) applied the Lomax distribution to income and wealth data. Bryson (1974) suggested Lomax distribution as an alternative to the exponential distribution for heavytailed data sets. Myhre and Saunders (1982) applied Lomax distribution in the right censored data. AbdElfattah and Alharbey (2010) discussed the estimation problem for the Lomax distribution based on generalized probability weighted moments. The estimation problem of the unknown parameters for the Lomax distribution based on type-II progressively hybrid censored samples has been discussed by Ma and Shi (2013). A recent family of univariate distributions generated by Exponentiated Weibull random variables was suggested by Hassan and Elgarhy (2016) and by Cordeiro et al (2017). We introduce a new five-parameter model, called the Exponentiated Weibull Lomax distribution based on the EW-G family.The rest of the paper is outlined as follows.
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