A Power Maxwell Distribution with Heavy Tails and Applications

Segovia, Francisco A.; Gómez, Yolanda M.; Venegas, Osvaldo; Gómez, Héctor W.

doi:10.3390/math8071116

Cited by 6 publications

(3 citation statements)

References 20 publications

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“…e failure rate of the Maxwell distribution rises steadily over time, which makes it effective in reliability and in life-testing experiments when the assumption of fixed failure rates, like that of an exponential distribution, is impractical [6]. Among many notable contributions that recommended this distribution in real-world testing investigations are [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

On Neutrosophic Extension of the Maxwell Model: Properties and Applications

Shah

Aslam

Khan

et al. 2022

Journal of Function Spaces

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This work presents the neutrosophic Maxwell distribution (NMD) as a novel probability distribution. The proposed model represents a generalized design of Maxwell distribution that provides more analytical flexibility for data, including all imprecise observations or some degree of vagueness within the dataset. Important reliability characteristics and distributional properties of NMD are developed under the notion of neutrosophy. The neutrosophic forms of some commonly used functions in applied statistics such as mean, variance, moment generating function, and shape coefficients are explored. In view of uncertainties involved in the processing data and indeterminacy in the defined parameters, an estimation framework using the maximum likelihood approach is established. Additionally, the quantile function is developed to validate the distributional properties of NMD. The efficiency of the neutrosophic estimate has been studied through a Monte Carlo simulation. Finally, real data on the incubation period of COVID-19 are considered for numerical illustration, and further extensions of the NMD for future research works are discussed.

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Section: Introductionmentioning

confidence: 99%

On Neutrosophic Extension of the Maxwell Model: Properties and Applications

Shah

Aslam

Khan

et al. 2022

Journal of Function Spaces

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“…Some recent extensions of the MB distribution are discussed, for example, in Sharma et al [4], Vivekanand et al [5], Iriarte et al [6], Dey et al [7], Sharma et al [8] and Segovia et al [9]. Product distributions or independent random variable quotients are of great interest; for example, Shakil et al [10] studied the XY and X/Y distribution, where X and Y are independent random variables that have MB and Rayleigh distributions respectively.…”

Section: Introductionmentioning

confidence: 99%

Scale Mixture of Maxwell-Boltzmann Distribution

Castillo

Gaete²,

Muñoz³

et al. 2023

Mathematics

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This paper presents a new distribution, the product of the mixture between Maxwell-Boltzmann and a particular case of the generalized gamma distributions. The resulting distribution, called the Scale Mixture Maxwell-Boltzmann, presents greater kurtosis than the recently introduced slash Maxwell-Boltzmann distribution. We obtained closed-form expressions for its probability density and cumulative distribution functions. We studied some of its properties and moments, as well as its skewness and kurtosis coefficients. Parameters were estimated by the moments and maximum likelihood methods, via the Expectation-Maximization algorithm for the latter case. A simulation study was performed to illustrate the parameter recovery. The results of an application to a real data set indicate that the new model performs very well in the presence of outliers compared with other alternatives in the literature.

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“…where Γ(•) denotes the gamma function, and F(•; a; b) the cdf of a gamma distribution with shape and rate parameters a and b, respectively. In this paper, an extension of the R distribution is introduced following the general method to obtain distributions with a higher kurtosis coefficient than the slash version of the Rayleigh model proposed by Iriarte et al [10], and applied successfully by other authors: Reyes et al [11] to obtain the Generalized Modified slash model, Reyes et al [12] to get a generalization of Birnbaum-Saunders, Iriarte et al [13] and Segovia [14] to extend the quasi-gamma and power Maxwell distributions, respectively. It will be proven that our proposal admits a representation as a scale mixture of a Rayleigh and a Generalized Gamma distribution.…”

Section: Introductionmentioning

confidence: 99%

Scale Mixture of Rayleigh Distribution

et al. 2020

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In this paper, the scale mixture of Rayleigh (SMR) distribution is introduced. It is proven that this new model, initially defined as the quotient of two independent random variables, can be expressed as a scale mixture of a Rayleigh and a particular Generalized Gamma distribution. Closed expressions are obtained for its pdf, cdf, moments, asymmetry and kurtosis coefficients. Its lifetime analysis, properties and Rényi entropy are studied. Inference based on moments and maximum likelihood (ML) is proposed. An Expectation-Maximization (EM) algorithm is implemented to estimate the parameters via ML. This algorithm is also used in a simulation study, which illustrates the good performance of our proposal. Two real datasets are considered in which it is shown that the SMR model provides a good fit and it is more flexible, especially as for kurtosis, than other competitor models, such as the slashed Rayleigh distribution.

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A Power Maxwell Distribution with Heavy Tails and Applications

Cited by 6 publications

References 20 publications

On Neutrosophic Extension of the Maxwell Model: Properties and Applications

On Neutrosophic Extension of the Maxwell Model: Properties and Applications

Scale Mixture of Maxwell-Boltzmann Distribution

Scale Mixture of Rayleigh Distribution

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