The Maxwell length-biased distribution: Properties and estimation

Saghir, Aamir; Khadim, Aneeqa; Zhang, Lin

doi:10.1080/15598608.2016.1246266

Cited by 12 publications

(6 citation statements)

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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]. For the first time, the Maxwell model was treated as a lifetime distribution and described the Bayesian estimators for the reliability function and the parameter in the study [11].…”

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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“…The TJ distribution of Al-Omari et al (2017) is similar to the Maxwell Length Biased (MLB) distribution of Saghir et al (2016) whose cd f is F (x; α, θ)…”

Section: ) the CD F Of Moeiw Is Given Bymentioning

confidence: 84%

Characterizations and Infinite Divisibility of Certain Recently Introduced Distributions IV

Hamedani¹

2018

IJSP

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“…From Proposition 3, it is clear that θ s is an increasing function with respect to α. The case β = 1, corresponding to the classic LBM distribution, can be found in [12]. From this reference, the following formula is reported:…”

Section: Momentsmentioning

confidence: 99%

“…For this reason, some extensions were developed by applying diverse notorious schemes. We may refer to those presented in [9][10][11][12]. In particular, Modi [11] and Saghir [12] proposed to extend the M distribution through the use of the length-biased scheme, introducing the length-biased Maxwell (LBM) distribution with parameter α > 0.…”

Section: Introductionmentioning

confidence: 99%

“…It is proven that the LBM model offers an interesting alternative to the M model on certain aspects, while keeping the simplicity of one-parameter adjustment. The merits of the LBM distribution are discussed in more detail in [11][12][13][14]. For these reasons, the LBM distribution is a candidate to be at the top of the list of useful one-parameter lifetime distributions, alongside the exponential distribution, Rayleigh distribution, Maxwell distribution, Lindley distribution by [15], Shanker distribution by [16], length-biased exponential (LBE) distribution introduced by [17] and the distribution for instantaneous failures proposed by [18], to name a few.…”

Section: Introductionmentioning

confidence: 99%

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Marshall–Olkin Length-Biased Maxwell Distribution and Its Applications

Mathew¹,

Chesneau

2020

MCA

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It is well established that classical one-parameter distributions lack the flexibility to model the characteristics of a complex random phenomenon. This fact motivates clever generalizations of these distributions by applying various mathematical schemes. In this paper, we contribute in extending the one-parameter length-biased Maxwell distribution through the famous Marshall–Olkin scheme. We thus introduce a new two-parameter lifetime distribution called the Marshall–Olkin length-biased Maxwell distribution. We emphasize the pliancy of the main functions, strong stochastic order results and versatile moments measures, including the mean, variance, skewness and kurtosis, offering more possibilities compared to the parental length-biased Maxwell distribution. The statistical characteristics of the new model are discussed on the basis of the maximum likelihood estimation method. Applications to simulated and practical data sets are presented. In particular, for five referenced data sets, we show that the proposed model outperforms five other comparable models, also well known for their fitting skills.

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The Maxwell length-biased distribution: Properties and estimation

Cited by 12 publications

References 11 publications

On Neutrosophic Extension of the Maxwell Model: Properties and Applications

On Neutrosophic Extension of the Maxwell Model: Properties and Applications

Characterizations and Infinite Divisibility of Certain Recently Introduced Distributions IV

Marshall–Olkin Length-Biased Maxwell Distribution and Its Applications

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