Statistical theory and practice of the inverse power Muth distribution

Chesneau, Christophe; Agiwal, Varun

doi:10.1016/j.jcmds.2021.100004

Cited by 9 publications

(4 citation statements)

References 18 publications

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“…where η is a projection of η. The posterior mean of η provides the objective estimate η under the condition of (27). However, it is simple to implement any additional loss function.…”

Section: Prior Distribution and Loss Functionmentioning

confidence: 99%

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The Unit Alpha-Power Kum-Modified Size-Biased Lehmann Type II Distribution: Theory, Simulation, and Applications

et al. 2023

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In order to represent the data with non-monotonic failure rates and produce a better fit, a novel distribution is created in this study using the alpha power family of distributions. This distribution is called the alpha-power Kum-modified size-biased Lehmann type II or, in short, the AP-Kum-MSBL-II distribution. This distribution is established for modeling bounded data in the interval (0,1). The proposed distribution’s moment-generating function, mode, quantiles, moments, and stress–strength reliability function are obtained, among other attributes. To estimate the parameters of the proposed distribution, estimation methods such as the maximum likelihood method and Bayesian method are employed to estimate the unknown parameters for the AP-Kum-MSBL-II distribution. Moreover, the confidence intervals, credible intervals, and coverage probability are calculated for all parameters. The symmetric and asymmetric loss functions are used to find the Bayesian estimators using the Markov chain Monte Carlo (MCMC) method. Furthermore, the proposed distribution’s usefulness is demonstrated using three real data sets. One of them is a medical data set dealing with COVID-19 patients’ mortality rate, the second is a trade share data set, and the third is from the engineering area, as well as extensive simulated data, which were applied to assess the performance of the estimators of the proposed distribution.

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“…where η is a projection of η. The posterior mean of η provides the objective estimate η under the condition of (27). However, it is simple to implement any additional loss function.…”

Section: Prior Distribution and Loss Functionmentioning

confidence: 99%

“…A few examples of recent developments based on the T distribution include the new M-generated class of distributions elaborated in [25], the exponentiated power M distribution discussed in [26], the inverse power M distribution investigated in [27], and the truncated M-generated family of distributions stressed in [28]. Additionally, refs.…”

Section: Introductionmentioning

confidence: 99%

The Unit Alpha-Power Kum-Modified Size-Biased Lehmann Type II Distribution: Theory, Simulation, and Applications

et al. 2023

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“…Biological sciences, life test concerns, chemical data, and medical sciences are only a few of the sectors where inverted distributions are important. In the literature, several inverted distributions were provided by several researchers, such as the inverse Lindley distribution [18], inverted Kumaraswamy distribution [19], inverse power Lindley distribution [21], inverse Weibull generator [20], inverted Xgamma distribution [22], inverted exponentiated Weibull distribution [23], inverse power Lomax distribution [24], inverse exponentiated Lomax distribution [25], inverted Nadarajah-Haghighi distribution [26], inverse Nakagami-m distribution [27], inverted Topp-Leone distribution [28], inverse power Muth distribution [29], inverse Maxwell distribution [30], inverted unit Teissier distribution [31], inverted power Cauchy distribution [32], inverse power Ramos-Louzada distribution [33] among others.…”

Section: Introductionmentioning

confidence: 99%

Statistical analysis of the inverse power Zeghdoudi model: Estimation, simulation and modeling to engineering and environmental data

Elbatal,

Hassan,

Gemeay

et al. 2024

Phys. Scr.

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In this research, we investigate a brand-new two-parameter distribution as an extension of thepower Zeghdoudi distribution (PZD). Using the inverse transformation technique on the PZD, theproduced distribution is called the inverted PZD (IPZD). Its usefulness in producing symmetric andasymmetric probability density functions makes it the perfect choice for lifetime phenomenon mod-eling. It is also appropriate for a range of real data since the relevant hazard rate function has one ofthe following shapes: increasing, decreasing, reverse j-shape or upside-down shape. Mode, quantiles,moments, geometric mean, inverse moments, incomplete moments, distribution of order statistics,Lorenz, Bonferroni, and Zenga curves are a few of the significant characteristics and aspects exploredin our study along with some graphical representations. Twelve effective estimating techniques areused to determine the distribution parameters of the IPZD. These include the Kolmogorov, leastsquares (LS), a maximum product of spacing, Anderson-Darling (AD), maximum likelihood, mini-mum absolute spacing distance, right-tail AD, minimum absolute spacing-log distance, weighted LS,left-tailed AD, Cram ́er-von Mises, AD left-tail second-order. A Monte Carlo simulation is used toexamine the effectiveness of the obtained estimates. The visual representation and numerical resultsshow that the maximum likelihood estimation strategy regularly beats the other methods in terms ofaccuracy when estimating the relevant parameters. The usefulness of the recommended distributionfor modelling data is illustrated and displayed visually using two real data sets and comparisons withother distributions.

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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

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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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Statistical theory and practice of the inverse power Muth distribution

Cited by 9 publications

References 18 publications

The Unit Alpha-Power Kum-Modified Size-Biased Lehmann Type II Distribution: Theory, Simulation, and Applications

The Unit Alpha-Power Kum-Modified Size-Biased Lehmann Type II Distribution: Theory, Simulation, and Applications

Statistical analysis of the inverse power Zeghdoudi model: Estimation, simulation and modeling to engineering and environmental data

Inverse Unit Teissier Distribution: Theory and Practical Examples

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