A New Extended-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>X</mml:mi></mml:math>Family of Distributions: Properties and Applications

Mi, Zichuan; Hussain, Saddam; Iftikhar, Anum; Ilyas, Muhammad; Ahmad, Zubair; Khan, Dost Muhammad; Manzoor, Sadaf

doi:10.1155/2020/4650520

Cited by 14 publications

(4 citation statements)

References 21 publications

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“…The formulation of new generalized classes of probability distributions is a topic that has received a great deal of attention in recent years, particularly when it comes to positive data [1]. To mention a few, we refer the reader to [2][3][4] as extensions of the Weibull distribution and [5,6] for Nadarajah-Haghighi generalizations. Most of these works are introduced aiming to furnish more flexible distributions regarding shape densities and hazard rates.…”

Section: Introductionmentioning

confidence: 99%

The unit ratio-extended Weibull family and the dropout rate in Brazilian undergraduate courses

Peña-Ramírez,

Guerra,

Mafalda

2023

PLoS ONE

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We propose a new family of distributions, so-called the unit ratio-extended Weibull family (U R E W). It is derived from ratio transformation in an extended Weibull random variable. The use of this transformation is a novelty of the work since it has been less explored than the exponential and has not yet been studied within the extended Weibull class. Moreover, we offer a valuable alternative to model double-bounded variables on the unit interval. Five U R E W special models are studied in detail, namely the: i) unit ratio-Gompertz; ii) unit ratio-Burr XII; iii) unit ratio-Lomax; v) unit ratio-Rayleigh, and vi) unit ratio-Weibull distributions. We propose a quantile-parameterization for the new family. The maximum likelihood estimators (MLEs) are presented. A Monte Carlo study is performed to evaluate the behavior of the MLEs of unit ratio-Gompertz and unit ratio-Rayleigh distributions. This last model has closed-form and approximately unbiased MLE for small sample sizes. Further, the U R E W submodels are adjusted to the dropout rate in Brazilian undergraduate courses. We focus on the areas of civil engineering, economics, computer sciences, and control engineering. The applications show that the new family is suitable for modeling educational data and may provide effective alternatives compared to other usual unit models, such as the Beta, Kumaraswamy, and unit gamma distributions. They can also outperform some recent contributions in the unit distribution literature. Thus, the U R E W family can provide competitive alternatives when those models are unsuitable.

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Section: Introductionmentioning

confidence: 99%

The unit ratio-extended Weibull family and the dropout rate in Brazilian undergraduate courses

Peña-Ramírez,

Guerra,

Mafalda

2023

PLoS ONE

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“…ey presented a submodel case of the proposed family by using one parameter exponential distribution, named the alpha power exponential distribution. Since then, using the APT technique, various lifetime models have been developed (see [9][10][11][12]). Some well-known probability models that contributed to the probability theory using COVID-19 data are considered by [13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Modeling COVID‐19 Data with a Novel Extended Exponentiated Class of Distributions

Arif

Khan

Aamir

et al. 2022

Journal of Mathematics

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The COVID-19 epidemic has affected every aspect of daily life since December 2019 and caused massive damage to the world. The coronavirus epidemic has affected more than 150 countries around the world. Many researchers have tried to develop a statistical model which can be utilized to analyze the behavior of the COVID-19 data. This article contributes to the field of probability theory by introducing a novel family of distributions, named the novel extended exponentiated class of distributions. Explicit expressions for numerous mathematical characterizations of the proposed family have been obtained with special concentration on a three-parameter submodel of the new class of distributions, named the new extended exponentiated Weibull distribution. The unknown model parameter estimates are obtained via the maximum likelihood estimation method. To assess the performance of these estimates, a comprehensive simulation study is conducted. Three different sets of COVID-19 data are used to check the applicability of the submodel case. The submodel of the new family is compared with three well-known probability distributions. Using different analytical measures, the results demonstrate that the new extended exponentiated Weibull distribution gives promising results in terms of its flexibility and offers data modeling with increasing decreasing, unimodal, and modified unimodal shapes.

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“…Statistical distributions are utilized quite effectively for modeling such data sets. The distributions that are frequently used include: Exponential, Rayleigh, Weibull, Beta, Gamma, Lognormal, Pareto, Lomax and Burr, for more detail we refer to Zichuan et al (2020). However, these traditional distributions are not flexible enough for countering complex form of data sets.…”

Section: Introductionmentioning

confidence: 99%

Contributions Towards New Families of Distributions: An Investigation, Further Developments, Characterizations and Comparative Study

Ahmad

Mahmoudi

Roozegar

et al. 2022

Pak.j.stat.oper.res.

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In the past couple of years, statistical models have been extensively used in applied areas for analyzing real data sets. However, in numerous situations, the traditional distributions are not ﬂexible enough to cater to different aspects of the real phenomena. For example, (i) in the practice of reliability engineering and biomedical analysis, some distributions provide the best ﬁt to the data having monotonic failure rate function, but fails to provide the best ﬁt to the data having non-monotonic failure rate function, (ii) some statistical distributions provide the best ﬁt for small insurance losses, but fails to provide an adequate ﬁt to large claim size data, and (iii) some distributions do not have closed forms causing difﬁculties in the estimation process. To address the above issues, therefore, several methods have been suggested to improve the ﬂexibility of the classical distributions. In this article, we investigate some of the former methods of generalizing the existing distributions. Further, we propose nineteen new methods of extending the classical distributions to obtain ﬂexible models suitable for modeling data in applied ﬁelds. We also provide certain characterizations of the newly proposed families. Finally, we provide a comparative study of the newly proposed and some other existing well-known models via analyzing three real data sets from three different disciplines such as reliability engineering, medical, and ﬁnancial sciences.

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A New Extended-XFamily of Distributions: Properties and Applications

Cited by 14 publications

References 21 publications

The unit ratio-extended Weibull family and the dropout rate in Brazilian undergraduate courses

The unit ratio-extended Weibull family and the dropout rate in Brazilian undergraduate courses

Modeling COVID‐19 Data with a Novel Extended Exponentiated Class of Distributions

Contributions Towards New Families of Distributions: An Investigation, Further Developments, Characterizations and Comparative Study

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