A novel logarithmic approach to generate new probability distributions for data modeling in the engineering sector

Zhao, Yue; Ahmad, Zubair; Alrumayh, Amani; Yusuf, M.; Aldallal, Ramy; Elshenawy, Assem; Riad, Fathy H.

doi:10.1016/j.aej.2022.07.021

Cited by 12 publications

(5 citation statements)

References 30 publications

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“…This subsection provides some rival distributions to verify that the NTF-Weibull distribution can outperform some existing distributions when considering reliability applications. Therefore, we apply the NTF-Weibull distribution to analyze these two mechanical and reliability engineering data sets and compare its results with the original two-parameter Weibull distribution [25], F-Weibull distribution [14], exponentiated Weibull (E-Weibull) distribution [26], new exponential Weibull (NE-Weibull) distribution [27], logarithmic Weibull (L-Weibull) distribution [28], and flexible generalized skew-normal (FGSN) distribution [29]. The PDFs of these selected probability distributions are as follows:…”

Section: The Rival Distributionsmentioning

confidence: 99%

A New Tangent-Generated Probabilistic Approach with Symmetrical and Asymmetrical Natures: Monte Carlo Simulation with Reliability Applications

Alshanbari,

Al-Mofleh,

Seong

et al. 2023

Symmetry

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It is proven evidently that probability distributions have a significant role in data modeling for decision-making. Due to the indispensable role of probability distributions for data modeling in applied fields, a series of probability distributions have been introduced and implemented. However, most newly developed probability distributions involve between one and eight additional parameters. Sometimes the additional parameters lead to re-parametrization problems. Therefore, the development of new probability distributions without additional parameters is an interesting research topic. In this paper, we study a new probabilistic method without incorporating any additional parameters. The proposed approach is based on a tangent function and may be called a new tangent-G (NT-G) family of distributions. Certain properties of the NT-G distributions are derived. Based on the NT-G method, a new flexible probability distribution called a new tangent flexible Weibull (NTF-Weibull) distribution is studied. The parameters of the NTF-Weibull distribution are estimated using seven different estimation methods. Based on these eight estimations, a brief simulation of the NTF-Weibull distribution is also provided. Finally, we prove the applicability of the NTF-Weibull distribution by analyzing two waiting-time data sets taken from the reliability sector. We consider three statistical tests with a p-value to evaluate the performance and goodness of fit of the NTF-Weibull distribution.

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Section: The Rival Distributionsmentioning

confidence: 99%

A New Tangent-Generated Probabilistic Approach with Symmetrical and Asymmetrical Natures: Monte Carlo Simulation with Reliability Applications

Alshanbari,

Al-Mofleh,

Seong

et al. 2023

Symmetry

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“…For example, Ref. [27] proposed the logarithmic-U (Log-U) method. The CDF F(x; δ, λ, Λ Λ Λ) of the Log-U family is…”

Section: Introductionmentioning

confidence: 99%

A New Probability Distribution: Model, Theory and Analyzing the Recovery Time Data

Alshanbari

Odhah

Ahmad

et al. 2023

Axioms

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Probability models are frequently used in numerous healthcare, sports, and policy studies. These probability models use datasets to identify patterns, analyze lifetime scenarios, predict outcomes of interest, etc. Therefore, numerous probability models have been studied, introduced, and implemented. In this paper, we also propose a novel probability model for analyzing data in different sectors, particularly in biomedical and sports sciences. The probability model is called a new modified exponential-Weibull distribution. The heavy-tailed characteristics along with some other mathematical properties are derived. Furthermore, the estimators of the new modified exponential-Weibull are derived. A simulation study of the new modified exponential-Weibull model is also provided. To illustrate the new modified exponential-Weibull model, a practical dataset is analyzed. The dataset consists of seventy-eight observations and represents the recovery time after the injuries in different basketball matches.

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“…To update the flexibility, characteristics, and data fitting of the Weibull model, numerous new versions (extended forms) of the Weibull model has been introduced, studied, and recommended; see Basheer [ 3 ], Shakhatreh et al [ 4 ], Mazucheli et al [ 5 ], Nassar et al [ 6 ], Elgohari and Yousof [ 7 ], Strzelecki [ 8 ], Sindhu and Atangana [ 9 ], Vanem Fazeres-Ferradosa [ 10 ], Ahmad et al [ 11 ], and Zhao et al [ 12 ].…”

Section: Introductionmentioning

confidence: 99%

A new trigonometric modification of the Weibull distribution: Control chart and applications in quality control

et al. 2023

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In the most recent era, the extensions of the probability models via trigonometry methods have received great attention. This paper also offers a novel trigonometric version of the Weibull model called a type-I cosine exponentiated Weibull (for short “TICE-Weibull”) distribution. The identifiability properties for all three parameters of the TICE-Weibull model are derived. The estimators of the TICE-Weibull model are derived by implementing the maximum likelihood approach. To demonstrate the effectiveness of the TICE-Weibull model, two applications from real-world phenomena are analyzed. In addition, the proposed statistical model is established for an attribute control chart based on a time-truncated life test. The advantage of the developed charts is examined based on the average run length (ARL). The necessary tables of shift sizes and various sample sizes are offered for numerous values of the distribution parameters, as well as specified ARL and shift constants. Some numerical examples are discussed for various scheme parameters to study the performance of the new TICE-Weibull attribute control charts. According to our search and a brief study of the statistical literature, there is no published work on the development of a control chart using new probability models that are introduced using the cosine function. This is the key motivation of this work, which fills this amazing and interesting research gap.

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A novel logarithmic approach to generate new probability distributions for data modeling in the engineering sector

Cited by 12 publications

References 30 publications

A New Tangent-Generated Probabilistic Approach with Symmetrical and Asymmetrical Natures: Monte Carlo Simulation with Reliability Applications

A New Tangent-Generated Probabilistic Approach with Symmetrical and Asymmetrical Natures: Monte Carlo Simulation with Reliability Applications

A New Probability Distribution: Model, Theory and Analyzing the Recovery Time Data

A new trigonometric modification of the Weibull distribution: Control chart and applications in quality control

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