Abstract
ABSTRACTA new class of continuous distributions with two extra shape parameters is introduced named the generalized odd Burr III (GOBIII) family of distributions. The expression of density can be written as a linear combination of exponentiated densities related to baseline model. The basic properties such as ordinary moments, quantile and generating functions, two entropy measures and order statistics are derived. Three special models of proposed family are presented. Characterizations related to truncated moments and hazard function for GOBIII-G distribution are derived. Method of maximum likelihood is used to estimate the model parameters. We study the behaviour of the estimators by means of simulations. The importance of the new family is illustrated using two real data sets. The real data applications suggest that this family can provide better fits than other competitive distributions. The significance of GOBIII-G family lies in its capability to fit symmetric as well as skewed type of data.
Highlights
Burr III distribution attracts extraordinary consideration since it includes several families of distributions and it incorporates the qualities of different distributions such as exponential and logistic distributions
This section is related to the characterization of generalized odd Burr III (GOBIII)-G family of distributions in two ways: related to truncated moments and related to hazard function
The Maximum Likelihood estimates (MLEs) of GOBIII-Lx model are evaluated for the value of each parameter and for each sample size
Summary
Burr III distribution attracts extraordinary consideration since it includes several families of distributions and it incorporates the qualities of different distributions such as exponential and logistic distributions. The Burr III distribution extensively used in various fields such as survival and reliability analysis, environmental studies, economics, meteorology and water resources, forestry among others. This distribution is applied to wages, income and wealth datasets. The density function (4) permits more flexibility and can be widely applied in numerous areas of real life. It will be manageable when baseline G(x) and g(x) are in closed-form. To make the shape of the proposed distribution more flexible as compared to the baseline model. To provide consistently better fits than other generated distributions having the same or higher number of parameters
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