The extended odd family of probability distributions with practice to a submodel

In recent advances in distribution theory, the Weibull distribution has often been used to generate new classes of univariate continuous distributions. They find many applications in important disciplines such as medicine, biology, engineering, economics, informatics, and finance; their usefulness is synonymous with success. In this study, a new Weibull-generated-type class is presented, called the weighted odd Weibull generated class. Its definition is based on a cumulative distribution function, which combines a specific weighted odd function with the cumulative distribution function of the Weibull distribution. This weighted function was chosen to make the new class a real alternative in the first-order stochastic sense to two of the most famous existing Weibull generated classes: the Weibull-G and Weibull-H classes. Its mathematical properties are provided, leading to the study of various probabilistic functions and measures of interest. In a consequent part of the study, the focus is on a special three-parameter survival distribution of the new class defined with the standard exponential distribution as a reference. The exploratory analysis reveals a high level of adaptability of the corresponding probability density and hazard rate functions; the curves of the probability density function can be decreasing, reversed N shaped, and unimodal with heterogeneous skewness and tail weight properties, and the curves of the hazard rate function demonstrate increasing, decreasing, almost constant, and bathtub shapes. These qualities are often required for diverse data fitting purposes. In light of the above, the corresponding data fitting methodology has been developed; we estimate the model parameters via the likelihood function maximization method, the efficiency of which is proven by a detailed simulation study. Then, the new model is applied to engineering and environmental data, surpassing several generalizations or extensions of the exponential model, including some derived from established Weibull-generated classes; the Weibull-G and Weibull-H classes are considered. Standard criteria give credit to the proposed model; for the considered data, it is considered the best.

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“…with c = 1/2 and γ = 1. Therefore, the WOW-G class appears to be a subclass of the extended odd-G class championed by [22].…”

Section: Motivations and Contributionsmentioning

confidence: 99%

On a Special Weighted Version of the Odd Weibull-Generated Class of Distributions

Hussain

Chesneau

2021

MCA

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“…To avoid the effect of negative drift and simultaneously relax the normality (symmetry) assumption to achieve accurate results, a transmuted truncated normal distribution is adopted herein, due to its flexibility and its attractive properties. More detail about transmuted distributions can be found in Shahbaz et al [35], Alizadeh et al [36], Bakouch et al [37], Bantan et al [38] and Muhammad et al [39], among others. Additionally, measurement errors usually occur during the observation process in practice [40]; therefore, in this study, we include the effect of the error function in order to achieve more precise life estimation results.…”

Section: Introductionmentioning

confidence: 98%

Reliability Analysis with Wiener-Transmuted Truncated Normal Degradation Model for Linear and Non-Negative Degradation Data

Muhammad

Wang

et al. 2022

Symmetry

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The degradation rates of many engineering systems are always positive in practical applications. In some cases, the degradation process is approximately linear, such as train wheel wear degradation and an increase in the operating current of laser devices. In this paper we introduce a degradation modeling and reliability estimation method based on the Wiener process with a transmuted-truncated normal distribution (TTND). The TTND is employed to characterize unit-to-unit variability due to its flexibility in capturing symmetry and the asymmetrical behavior of the drift variable of the Wiener process. A Wiener process with TTND is applied to model the degradation processes of the deteriorating systems in two cases. In the first case, we assume that the degradation process is unaffected by measurement uncertainties, whereas in the second case, the measurement uncertainties are considered. The exact and explicit expressions of PDFs and the reliability functions are derived based on the concept of first hitting time. The Gibbs sampling technique and the Metropolis–Hastings algorithm are employed to obtain the Bayesian estimates of the model’s parameters. The efficiency and the feasibility of the presented approach are demonstrated through numerical examples, with Monte Carlo simulation and a practical application with laser degradation data. Furthermore, deviance information criteria (DIC) are used to compare the proposed model and some existing models. The result indicated that the proposed approach provided better reliability estimation results.

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“…Jamal et al [37] studied the odd Burr-III family of distributions. Bakouch et al [38] introduced the extended odd family of probability distributions. In practical life problems, truncation arises in many fields, such as industry, biology, hydrology, reliability theory and medicine.…”

Section: Introductionmentioning

confidence: 99%

Statistical Inference of Truncated Weibull-Rayleigh Distribution: Its Properties and Applications

Khalifa¹,

Ramadan²,

El-Desouky³

2021

OJMSi

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In this paper, we derived a new distribution named as truncated Weibull Rayleigh (TW-R) distribution. Its characterization and statistical properties are obtained, such as reliability function, hazard function, reversed hazard rate function, cumulative hazard rate function, quantile function, rth moment, incomplete moments, Rényi and q entropies and order statistic. Parameter estimation is implemented using method of maximum-likelihood estimation and Fisher information matrix is derived. Finally, application of the presented new distribution to a real data representing the failure times of 63 airbcraft Windshield is given and its goodness-of-fit is demonstrated. In addition to, comparisons to other models are implemented to show the flexibility of the presented model.

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The extended odd family of probability distributions with practice to a submodel

Cited by 11 publications

References 13 publications

On a Special Weighted Version of the Odd Weibull-Generated Class of Distributions

On a Special Weighted Version of the Odd Weibull-Generated Class of Distributions

Reliability Analysis with Wiener-Transmuted Truncated Normal Degradation Model for Linear and Non-Negative Degradation Data

Statistical Inference of Truncated Weibull-Rayleigh Distribution: Its Properties and Applications

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