Objective Bayesian analysis for the Lomax distribution

Ferreira, Paulo H.; Ramos, Eduardo; Ramos, Pedro Luiz; Gonzales, Jhon Franky Bernedo; Tomazella, Vera; Ehlers, Ricardo S.; Silva, Eveliny B.; Louzada, Francisco

doi:10.1016/j.spl.2019.108677

Cited by 11 publications

(8 citation statements)

References 26 publications

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“…Corollary 3.3. The prior (12) has the asymptotic power-law behavior given by π 4 (φ) ∝ φ→0 + φ − 1 2 and the obtained posterior is improper for all n ∈ N + .…”

Section: Some Common Objective Priors With Power-law Asymptotic Behaviormentioning

confidence: 99%

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Power laws distributions in objective priors

Ramos¹,

Rodrigues²,

Ramos³

et al. 2020

Preprint

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The use of objective prior in Bayesian applications has become a common practice to analyze data without subjective information. Formal rules usually obtain these priors distributions, and the data provide the dominant information in the posterior distribution. However, these priors are typically improper and may lead to improper posterior. Here, we show, for a general family of distributions, that the obtained objective priors for the parameters either follow a power-law distribution or has an asymptotic power-law behavior. As a result, we observed that the exponents of the model are between 0.5 and 1. Understand these behaviors allow us to easily verify if such priors lead to proper or improper posteriors directly from the exponent of the power-law. The general family considered in our study includes essential models such as Exponential, Gamma, Weibull, Nakagami-m, Haf-Normal, Rayleigh, Erlang, and Maxwell Boltzmann distributions, to list a few. In summary, we show that comprehending the mechanisms describing the shapes of the priors provides essential information that can be used in situations where additional complexity is presented.

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“…Corollary 3.3. The prior (12) has the asymptotic power-law behavior given by π 4 (φ) ∝ φ→0 + φ − 1 2 and the obtained posterior is improper for all n ∈ N + .…”

Section: Some Common Objective Priors With Power-law Asymptotic Behaviormentioning

confidence: 99%

“…Notice that for (12) is only necessary to know the behavior π 4 (φ) when φ → 0 + that provided enough information to very that the posterior is improper.…”

Section: Some Common Objective Priors With Power-law Asymptotic Behaviormentioning

confidence: 99%

Power laws distributions in objective priors

Ramos¹,

Rodrigues²,

Ramos³

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The posterior distribution obtained using this prior has interesting properties, such as invariance and consistency in marginalization and sample properties [ 18 ]. Some recent reference priors were obtained for the Pareto [ 19 ], Poisson-exponential [ 20 ], extended exponential-geometric [ 21 ], inverse Weibull [ 22 ], generalized half-normal [ 23 ] and Lomax [ 24 ] distributions.…”

Section: Background and Literaturementioning

confidence: 99%

Improved objective Bayesian estimator for a PLP model hierarchically represented subject to competing risks under minimal repair regime

et al. 2021

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In this paper, we propose a hierarchical statistical model for a single repairable system subject to several failure modes (competing risks). The paper describes how complex engineered systems may be modelled hierarchically by use of Bayesian methods. It is also assumed that repairs are minimal and each failure mode has a power-law intensity. Our proposed model generalizes another one already presented in the literature and continues the study initiated by us in another published paper. Some properties of the new model are discussed. We conduct statistical inference under an objective Bayesian framework. A simulation study is carried out to investigate the efficiency of the proposed methods. Finally, our methodology is illustrated by two practical situations currently addressed in a project under development arising from a partnership between Petrobras and six research institutes.

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“…It finds numerous applications in reliability engineering and life testing. The theory, inference and applications of the Lomax distribution have been the subjects of the following inevitable references: [20][21][22][23][24][25][26]. The PL distribution proposed by [17] is obtained by making use of the power transformation to the Lomax distribution, aiming to increase its capabilities on several functional aspects.…”

Section: Introductionmentioning

confidence: 99%

On the Accuracy of the Sine Power Lomax Model for Data Fitting

2021

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Every day, new data must be analysed as well as possible in all areas of applied science, which requires the development of attractive statistical models, that is to say adapted to the context, easy to use and efficient. In this article, we innovate in this direction by proposing a new statistical model based on the functionalities of the sinusoidal transformation and power Lomax distribution. We thus introduce a new three-parameter survival distribution called sine power Lomax distribution. In a first approach, we present it theoretically and provide some of its significant properties. Then the practicality, utility and flexibility of the sine power Lomax model are demonstrated through a comprehensive simulation study, and the analysis of nine real datasets mainly from medicine and engineering. Based on relevant goodness of fit criteria, it is shown that the sine power Lomax model has a better fit to some of the existing Lomax-like distributions.

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Objective Bayesian analysis for the Lomax distribution

Cited by 11 publications

References 26 publications

Power laws distributions in objective priors

Power laws distributions in objective priors

Improved objective Bayesian estimator for a PLP model hierarchically represented subject to competing risks under minimal repair regime

On the Accuracy of the Sine Power Lomax Model for Data Fitting

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