Beyond the Sin-G family: The transformed Sin-G family

Jamal, Farrukh; Chesneau, Christophe; Bouali, Dalal Lala; Hassan, Mahmood Ul

doi:10.1371/journal.pone.0250790

Cited by 21 publications

(9 citation statements)

References 35 publications

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“…The transformed sine G (TSG) family: Jamal et al 48 introduced a new distribution called transformed Sine G family of distributions (TSG) which serves as an extension to the Sine G family using a new polynomial-trigonometrical function along with additional parameters to provide more versatility.…”

Section: Sine Topp-leone Exponentiated Exponential (Stlee) Distributionmentioning

confidence: 99%

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2021

BBIJ

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For the past few years, various forms of statistical distributions based on trigonometrical transformation were proposed by researchers to model data and thereby finding the suitable distribution to predict the possibilities, and application of it in real life. This article aims to review the recent developments and contributions brought about by the various families of trigonometric functions in statistical distribution and its application in data modelling. Several generalised trigonometric distributions are reviewed and compared along with their properties and uses.

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Section: Sine Topp-leone Exponentiated Exponential (Stlee) Distributionmentioning

confidence: 99%

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2021

BBIJ

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“…Another contribution work towards the trigonometric family of distributions is due to Jamal et al [ 17 ]. They introduced a generalized version of the sin- G method called the transformed sin- G (TS- G ) family of distributions.…”

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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“…Numerous pioneering authors have contributed to the development of novel families of distributions designed to overcome the limitations of their predecessors. Notable examples include the skew normal-G family [1] (G stands for generated), Marshall-Olkin-G family [2], exponentiated-G family [3], Kumaraswamy-G family [4], beta-G family [5], odd log-logistic-G family [6], exponentiated-generalized-G family [7], odd Weibull-G family [8], odd generalized exponential family [9], logistic-G family [10], Topp-Leone-G family [11], weighted-G family [12], Marshall-Olkin odd Lindley-G family [13], and sin-G family [14]. These extended distributions exhibit enhanced flexibility and resilience compared with their original counterparts.…”

Section: Introduction 1contextmentioning

confidence: 99%

A Transmuted Modified Power-Generated Family of Distributions with Practice on Submodels in Insurance and Reliability

et al. 2023

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In this article, we propose a new transmuted modified power-generalized family of distributions constructed from the transmuted-generated and modified power-generated families. The proposed approach is flexible and provides a tradeoff between the two baseline families. For a prime study, we identify the main characteristics of the new transmuted modified power family, such as the asymptotic results, quantile function, series representation, and the various kinds of moment measures. By using the exponential distribution as the baseline, a new three-parameter lifetime distribution is constructed. The associated probability functions (density and hazard rate) are flexible and have a variety of asymmetric shapes, which make them attractive for statistical purposes. In particular, for the related probability density function, reversed-J, unimodal, and right-skewed shapes are observed. Measures relating to risk theory are also computed, such as the value at risk and the expected shortfall. By using both simulation analysis and the maximum likelihood approach, the estimation of the model parameters is evaluated. The effectiveness of the proposed model is demonstrated by two real-world cases (one in insurance and the other in reliability), and we show that it yields better fits when compared to other extended models connected to the exponential model.

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Beyond the Sin-G family: The transformed Sin-G family

Cited by 21 publications

References 35 publications

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

A Transmuted Modified Power-Generated Family of Distributions with Practice on Submodels in Insurance and Reliability

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