A novel Muth generalized family of distributions: Properties and applications to quality control

Alanzi, Ayed R. A.; Rafique, M. Qaisar; Tahir, M. H.; Jamal, Farrukh; Hussain, Muhammad Adnan; Sami, Waqas

doi:10.3934/math.2023331

Cited by 6 publications

(4 citation statements)

References 28 publications

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“…However, it is of interest because it may be preferable to the one-parameter exponential distribution when modeling data with a subordinate increasing hazard rate function (HRF). Among the existing developments based on the T distribution, let us mention the power M distribution studied in [8], transmuted M-generated class of distributions proposed in [9], new Mgenerated class of distributions elaborated in [10], exponentiated power M distribution discussed in [11], inverse power M distribution investigated in [12] and the truncated M generated family of distributions emphasized in [13]. More recently, Krishna et al [14] used the T distribution for creating an intriguing unit distribution, i.e., a distribution with support as [0, 1], the unit T distribution (UTD).…”

Section: Introductionmentioning

confidence: 99%

Inverse Unit Teissier Distribution: Theory and Practical Examples

Alsadat

Elgarhy

Karakaya

et al. 2023

Axioms

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In this paper, we emphasize a new one-parameter distribution with support as [1,+∞). It is constructed from the inverse method applied to an understudied one-parameter unit distribution, the unit Teissier distribution. Some properties are investigated, such as the mode, quantiles, stochastic dominance, heavy-tailed nature, moments, etc. Among the strengths of the distribution are the following: (i) the closed-form expressions and flexibility of the main functions, and in particular, the probability density function is unimodal and the hazard rate function is increasing or unimodal; (ii) the manageability of the moments; and, more importantly, (iii) it provides a real alternative to the famous Pareto distribution, also with support as [1,+∞). Indeed, the proposed distribution has different functionalities but also benefits from the heavy-right-tailed nature, which is demanded in many applied fields (finance, the actuarial field, quality control, medicine, etc.). Furthermore, it can be used quite efficiently in a statistical setting. To support this claim, the maximum likelihood, Anderson–Darling, right-tailed Anderson–Darling, left-tailed Anderson–Darling, Cramér–Von Mises, least squares, weighted least-squares, maximum product of spacing, minimum spacing absolute distance, and minimum spacing absolute-log distance estimation methods are examined to estimate the unknown unique parameter. A Monte Carlo simulation is used to compare the performance of the obtained estimates. Additionally, the Bayesian estimation method using an informative gamma prior distribution under the squared error loss function is discussed. Data on the COVID mortality rate and the timing of pain relief after receiving an analgesic are considered to illustrate the applicability of the proposed distribution. Favorable results are highlighted, supporting the importance of the findings.

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Section: Introductionmentioning

confidence: 99%

Inverse Unit Teissier Distribution: Theory and Practical Examples

Alsadat

Elgarhy

Karakaya

et al. 2023

Axioms

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“…Many researchers in statistics introduced new distributions like the Go-G family [1], MOG family [2], and MOTL-G family [3]. There were also the APRAY-G family [4], MOW-G family [5], TIIEHL-Gom-TL-G family [6], NETLE family [7], Muth-G family [8], and TNH-G family [9].…”

Section: Introductionmentioning

confidence: 99%

A New Generalized Family of Odd Lomax-G Distributions Properties and Applications

2023

Advances in the Theory of Nonlinear Analysis and Its Application

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The motivation for this study is to develop the new family of continuous distributions called Odd Lomax-G (OLG). Also present a new flexible three-parameter distribution according to the developed family called the Odd Lomax-G Exponential (OLE) distribution. Using binomial series expansion, logarithmic, and exponential expansions, the new OLG family and OLE distribution are expanded. We find the derivative of the moments, the mgf , quantity function, ordered statistics and Rényi entropy. Then use the MLE method to estimate the OLE model parameters. Finally, an importance of the new family is made clear experimentally through two real data applications. Then explore the performance of OLE distribution inferred from family OLG based on certain goodness of fit criteria.

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“…Moreover, reference [18] initiated the reciprocal Burr X-G class derived from the T-X approach, describing its capability to fit virtually all types of failure rates. Reference [19] offered the odd Muth-G class using the T-X method and derived various of its properties. Reference [20] presented the exponentiated-exponentiated Weibull-X class, which has the ability to model any complex data.…”

Section: Introductionmentioning

confidence: 99%

A New Odd Beta Prime-Burr X Distribution with Applications to Petroleum Rock Sample Data and COVID-19 Mortality Rate

Suleiman,

Daud,

Singh

et al. 2023

Data

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In this article, we pioneer a new Burr X distribution using the odd beta prime generalized (OBP-G) family of distributions called the OBP-Burr X (OBPBX) distribution. The density function of this model is symmetric, left-skewed, right-skewed, and reversed-J, while the hazard function is monotonically increasing, decreasing, bathtub, and N-shaped, making it suitable for modeling skewed data and failure rates. Various statistical properties of the new model are obtained, such as moments, moment-generating function, entropies, quantile function, and limit behavior. The maximum-likelihood-estimation procedure is utilized to determine the parameters of the model. A Monte Carlo simulation study is implemented to ascertain the efficiency of maximum-likelihood estimators. The findings demonstrate the empirical application and flexibility of the OBPBX distribution, as showcased through its analysis of petroleum rock samples and COVID-19 mortality data, along with its superior performance compared to well-known extended versions of the Burr X distribution. We anticipate that the new distribution will attract a wider readership and provide a vital tool for modeling various phenomena in different domains.

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A novel Muth generalized family of distributions: Properties and applications to quality control

Cited by 6 publications

References 28 publications

Inverse Unit Teissier Distribution: Theory and Practical Examples

Inverse Unit Teissier Distribution: Theory and Practical Examples

A New Generalized Family of Odd Lomax-G Distributions Properties and Applications

A New Odd Beta Prime-Burr X Distribution with Applications to Petroleum Rock Sample Data and COVID-19 Mortality Rate

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