The compounding approach is used to introduce a new family of distributions called exponentiated Bell G, analogy to exponentiated G Poisson. Several essential properties of the proposed family are obtained. The special model called exponentiated Bell exponential (EBellE) is presented along with properties. Furthermore, the risk theory related measures including value-at-risk and expected-shortfall are also computed for the special model. Group acceptance sampling plan is designed when a lifetime of a product or item follows an EBellE model taking median as a quality parameter. The parameters of the proposed model are estimated by considering maximum likelihood approach along with simulation analysis. The usefulness of the proposed model is illustrated by practical means which yield better fits as compared to several exponential related extended models.
<abstract><p>In this article, we make mathematical and practical contributions to the Bell-X family of absolutely continuous distributions. As a main member of this family, a special distribution extending the modeling perspectives of the famous Burr XII (BXII) distribution is discussed in detail. It is called the Bell-Burr XII (BBXII) distribution. It stands apart from the other extended BXII distributions because of its flexibility in terms of functional shapes. On the theoretical side, a linear representation of the probability density function and the ordinary and incomplete moments are among the key properties studied in depth. Some commonly used entropy measures, namely Rényi, Havrda and Charvat, Arimoto, and Tsallis entropy, are derived. On the practical (inferential) side, the associated parameters are estimated using seven different frequentist estimation methods, namely the methods of maximum likelihood estimation, percentile estimation, least squares estimation, weighted least squares estimation, Cramér von-Mises estimation, Anderson-Darling estimation, and right-tail Anderson-Darling estimation. A simulation study utilizing all these methods is offered to highlight their effectiveness. Subsequently, the BBXII model is successfully used in comparisons with other comparable models to analyze data on patients with acute bone cancer and arthritis pain. A group acceptance sampling plan for truncated life tests is also proposed when an item's lifetime follows a BBXII distribution. Convincing results are obtained.</p></abstract>
This study captured the performance analysis of European Union (EU) member countries integration and its possible implications for South Asian countries. The primary purpose of this study was to see whether trading/economic bloc of EU has enhanced the performance of its members. The study also analyzed whether the European Union's commercial bloc model can be proposed for other global regions. The data was collected from official sources of EU and it ranged from 2000 to 2021. Descriptive and inferential statistical methods have been applied for data analysis. The results showed that the EU trading groups have not only increased production but also increased the exports and welfare of the entire region of EU. On the basis of findings of this study, it may be suggested that South Asian countries (Sri Lanka, Pakistan, Bhutan, Nepal, Afghanistan, Bangladesh, India and Maldives) needs to construct a South Asian Trading Bloc, rather than SAARC, in order to boost the regional performance and well-being of concerned community.
The compounded Bell generalized class of distributions is proposed in this article as an alternative to the compounded Poisson generalized family of distributions. Some properties and actuarial measures are presented. The properties of a special model named Bell Weibull (BellW) are obtained such as the linear representation of density, rth moment, incomplete moment, moment generating function using Wright generalized hypergeometric function and Meijer’s G function, the pth moment of order statistics, reliability, stochastic ordering, and residual and reversed residual life. Moreover, some commonly used entropy measures, namely, Rényi, Havrda and Charvat, and Arimoto and Tsallis entropy are obtained for the special model. From the inferential side, parameters are estimated using maximum likelihood estimation. The simulation study is performed to highlight the behavior of estimates. Some actuarial measures including expected shortfall, value at risk, tail value at risk, tail variance, and tail variance premium for the BellW model are presented with the numerical illustration. The usefulness of the proposed family is evaluated using insurance claims and COVID-19 datasets. Convincing results are obtained.
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