New generalized-X family: Modeling the reliability engineering applications

Statistical distributions have great applicability for modeling data in almost every applied sector. Among the available classical distributions, the inverse Weibull distribution has received considerable attention. In the practice of distribution theory, numerous methods have been studied and suggested/introduced to increase the flexibility level of the traditional probability distributions. In this paper, we implement different distribution methods to obtain five new different versions of the inverse Weibull model. The new modifications of the inverse Weibull model are called the logarithm transformed-inverse Weibull, a flexible reduced logarithmic-inverse Weibull, the weighted TX-inverse Weibull, a new generalized-inverse Weibull, and the alpha power transformed extended-inverse Weibull distributions. To illustrate the flexibility and applicability of the new modifications of the inverse Weibull model, a biomedical data set is analyzed. The data set consists of 108 observations and represents the mortality rate of the COVID-19-infected patients. The practical application shows that the new generalized-inverse Weibull is the best modification of the inverse Weibull distribution.

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“…where m(x; ψ) � d/dxM(x; ψ). Wang et al [36] studied a NG-X (new generalized-X) family with DF R(x; ψ, θ), provided by…”

Section: Introductionmentioning

confidence: 99%

New Statistical Approaches for Modeling the COVID‐19 Data Set: A Case Study in the Medical Sector

et al. 2022

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“…In order to provide a close fit to such type of engineering data sets, numerous updated versions of the Weibull distribution have been produced and implemented. For example, (i) Ahmad et al [11] studied a new Weibull-Weibull distribution for analyzing the strength of the alumina material; (ii) Zhao et al [12] introduced TIHT-Weibull distribution for modeling the failure time of coating machines; (iii) Wang et al [13] implemented the NG-Weibull distribution for analyzing the failure time of the electronic machine. For more recent modifications of the Weibull distribution, we refer to Klakattawi [14]; Wang et al [15]; Tianshuai et al [16]; Al-Sobhi [17]; Gonzalez et al [18]; Emam and Tashkandy [19]; Prataviera [20]; and Rehman et al [21].…”

Section: Introductionmentioning

confidence: 99%

A Novel Generalized-M Family: Heavy-Tailed Characteristics with Applications in the Engineering Sector

El-Morshedy

Almaspoor

Abbas³

et al. 2022

Mathematical Problems in Engineering

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The Weibull distribution has prominent applications in the engineering sector. However, due to its monotonic behavior of the hazard function, the Weibull model does not provide the best fit for data in many cases. This paper introduces a new family of distributions to obtain new flexible distributions. The proposed family is called a novel generalized- M family. Based on this approach, an updated version of the Weibull distribution is introduced. The updated version of the Weibull distribution is called a novel generalized Weibull distribution. The proposed distribution is able to capture four different patterns of the hazard function. Some mathematical properties of the proposed method are obtained. Furthermore, the maximum likelihood estimators of the proposed family are also obtained. Moreover, a simulation study is conducted for evaluating these estimators. For illustrating the proposed model, two data sets from the engineering sector are analyzed. Based on some well-known analytical measures, it is shown that the novel generalized Weibull distribution is the best competing distribution for analyzing the engineering data sets.

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“…such that β > 0 can be considered as an extra parameter. Wang et al [22] developed another method called, a NG-X (new generalized-X) family by the following DF:…”

Section: Introductionmentioning

confidence: 99%

A New Flexible Logarithmic‐X Family of Distributions with Applications to Biological Systems

et al. 2022

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Probability distributions play an essential role in modeling and predicting biomedical datasets. To have the best description and accurate prediction of the biomedical datasets, numerous probability distributions have been introduced and implemented. We investigate a novel family of lifetime probability distributions to represent biological datasets in this paper. The proposed family is called a new flexible logarithmic- X (NFLog- X ) family. The suggested NFLog- X family is obtained by applying the T- X method together with the exponential model having the PDF m t = e − t . Based on the NFLog- X approach, a three parameters probability distribution, namely, a new flexible logarithmic-Weibull (NFLog-Wei) distribution is introduced. The method of maximum likelihood estimation is adopted for estimating the parameters of the NFLog- X family. In the end, we examine three different biological datasets in order to give a thorough numerical research that illustrates the NFLog-Wei distribution. Comparisons are made between the analytical goodness-of-fit metrics of the suggested distribution. We made comparison with the (i) alpha power transformed Weibull, (ii) exponentiated Weibull, (iii) Weibull, (iv) flexible reduced logarithmic-Weibull, and (v) Marshall–Olkin Weibull distributions. After performing the analyses, we observe that the proposed method outclassed other competitive distributions.

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New generalized-X family: Modeling the reliability engineering applications

Cited by 13 publications

References 23 publications

New Statistical Approaches for Modeling the COVID‐19 Data Set: A Case Study in the Medical Sector

New Statistical Approaches for Modeling the COVID‐19 Data Set: A Case Study in the Medical Sector

A Novel Generalized-M Family: Heavy-Tailed Characteristics with Applications in the Engineering Sector

A New Flexible Logarithmic‐X Family of Distributions with Applications to Biological Systems

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