Abstract
In this paper, we introduce a new general family of distributions obtained by a subtle combination of two well-established families of distributions: the so-called power Topp–Leone-G and inverse exponential-G families. Its definition is centered around an original cumulative distribution function involving exponential and polynomial functions. Some desirable theoretical properties of the new family are discussed in full generality, with comprehensive results on stochastic ordering, quantile function and related measures, general moments and related measures, and the Shannon entropy. Then, a statistical parametric model is constructed from a special member of the family, defined with the use of the inverse Lomax distribution as the baseline distribution. The maximum likelihood method was applied to estimate the unknown model parameters. From the general theory of this method, the asymptotic confidence intervals of these parameters were deduced. A simulation study was conducted to evaluate the numerical behavior of the estimates we obtained. Finally, in order to highlight the practical perspectives of the new family, two real-life data sets were analyzed. All the measures considered are favorable to the new model in comparison to four serious competitors.
Highlights
Owing to the growing amount of data from various applied fields and unstoppable computer progress, there is increasing motivation on developing efficient and flexible statistical models.Such models can be derived from general families of distributions having desirable properties, such as those constructed from a generator distribution
We provide a simulation study to show the nice behavior of the maximum likelihood estimates (MLEs) for the NPTLILx model presented in the subsection above
We introduced and studied a new general family of distributions, called the new power TL-G (NPTL-G)
Summary
Owing to the growing amount of data from various applied fields and unstoppable computer progress, there is increasing motivation on developing efficient and flexible statistical models. Such models can be derived from general families of distributions having desirable properties, such as those constructed from a generator distribution. The main idea of this construction is to add shape parameter(s) to a baseline distribution with the aim to upgrade its flexibility level. Several researchers used the Topp–Leone (TL) distribution as Entropy 2019, 21, 1177; doi:10.3390/e21121177 www.mdpi.com/journal/entropy
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