Bayesian analysis of the inverse generalized gamma distribution using objective priors

Ramos, Pedro Luiz; Mota, Ali; Ferreira, Paulo H.; Ramos, Eduardo; Tomazella, Vera; Louzada, Francisco

doi:10.1080/00949655.2020.1830991

Cited by 9 publications

(10 citation statements)

References 47 publications

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“…In this section, a novel composite distribution model is proposed for modeling monostatic RCS statistical characteristics of stealth aircraft. The probability density function (PDF) of the proposed Swerling‐chi/inverse Generalized Gamma composite distribution model is defined as 11,15

f ((), σ) goodbreak= \int_{0}^{\infty} f_{1} (()|, σ, t) f_{2} ((), t) italicdt

where

f_{1} (()|, σ, t)

is the PDF of the conditional Swerling‐chi distribution given by

f_{1} (()|, σ, t) goodbreak= \frac{m^{m} σ^{m - 1}}{{(t Ω)}^{m} normalΓ ((), m)} \exp ((), goodbreak- \frac{mσ}{t normalΩ})

and

f_{2} ((), t)

is the PDF of the inverse Generalized Gamma distribution 13,14 given by

f_{2} ((), t) goodbreak= \frac{{italicβγ}^{italicαβ}}{normalΓ ((), α)} t^{- italicαβ - 1} \exp ((), goodbreak- \frac{γ^{β}}{t^{β}})

where

m, α, β, γ

are the fading parameters,

normalΩ

is mean value of

σ

defined by

normalΩ = E ([], σ)

E ([] \cdot)

is the expectation operator, and

normalΓ ([] \cdot)

is the gamma function.…”

Section: Proposed Swerling‐chi/inverse Generalized Gamma Composite Modelmentioning

confidence: 99%

“…In this letter, inspired by the structures of composite distribution models, a new Swerling‐chi/inverse Generalized Gamma composite mode 13,14 is proposed for modeling the monostatic RCS statistical characteristics of stealth aircrafts. Under some specific conditions, the proposed composite distribution model will be reduced to the Fisher‐Snedecor

normalℱ

distribution 15 model and the Swerling‐chi distribution model.…”

Section: Introductionmentioning

confidence: 99%

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Statistical modeling for the monostatic radar cross‐section characteristics of stealth aircraft using the Swerling‐chi/inverse generalized gamma composite distribution model

Wang

Hua

2021

Micro & Optical Tech Letters

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In this article, a new Swerling-chi/inverse generalized gamma composite distribution model is proposed for modeling the monostatic radar cross-section (RCS) statistical characteristics of stealth aircraft. Under some conditions, the proposed distribution model can be reduced to the Fisher-Snedecor F distribution model and the Swerling-chi distribution model. A typical stealth aircraft without radar absorption materials (RAM) is selected as an application for simulation using the adaptive cross approximation (ACA) technique. Based on the nonlinear least-squares criterion, monostatic RCS statistical characteristics of the front sector of this aircraft are fitted using the proposed composite model. For the comparison purpose, monostatic RCS statistical characteristics of this aircraft are also fitted with the conventional RCS distribution models. Goodness-of-fit tests of the proposed distribution model and the conventional distribution models are analyzed in terms of the error-of-fit results and the R 2 test results. Simulation results validate the efficiency and robustness of the proposed distribution model. K E Y W O R D S composite distribution model, inverse generalized gamma distribution, radar cross-section, RCS statistical characteristics, stealth aircraft 2 | PROPOSED SWERLING-CHI/ INVERSE GENERALIZED GAMMA COMPOSITE MODEL In this section, a novel composite distribution model is proposed for modeling monostatic RCS statistical

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f ((), σ) goodbreak= \int_{0}^{\infty} f_{1} (()|, σ, t) f_{2} ((), t) italicdt

where

f_{1} (()|, σ, t)

is the PDF of the conditional Swerling‐chi distribution given by

f_{1} (()|, σ, t) goodbreak= \frac{m^{m} σ^{m - 1}}{{(t Ω)}^{m} normalΓ ((), m)} \exp ((), goodbreak- \frac{mσ}{t normalΩ})

and

f_{2} ((), t)

is the PDF of the inverse Generalized Gamma distribution 13,14 given by

f_{2} ((), t) goodbreak= \frac{{italicβγ}^{italicαβ}}{normalΓ ((), α)} t^{- italicαβ - 1} \exp ((), goodbreak- \frac{γ^{β}}{t^{β}})

where

m, α, β, γ

are the fading parameters,

normalΩ

is mean value of

σ

defined by

normalΩ = E ([], σ)

E ([] \cdot)

is the expectation operator, and

normalΓ ([] \cdot)

is the gamma function.…”

Section: Proposed Swerling‐chi/inverse Generalized Gamma Composite Modelmentioning

confidence: 99%

normalℱ

distribution 15 model and the Swerling‐chi distribution model.…”

Section: Introductionmentioning

confidence: 99%

Statistical modeling for the monostatic radar cross‐section characteristics of stealth aircraft using the Swerling‐chi/inverse generalized gamma composite distribution model

Wang

Hua

2021

Micro & Optical Tech Letters

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“…Thus, Γ 1 + 1 s ≈ e Ψ(1) sfor large values of s. Therefore, for s → ∞, we have Γ Considering the reference prior given in Corollary 2, the result of Corollary 3, and Condition(20), it follows that the posterior reference distribution is proper if:∞ ds = −2 < ∞. (A5)Therefore, the reference prior leads to a proper posterior distribution.Considering the Jeffreys prior given in Corollary 2, the result of Corollary 3, and Condition(20), it follows that the Jeffreys posterior distribution is proper if: ∞…”

mentioning

confidence: 95%

“…The resulting reference prior affords a posterior distribution that has interesting features, such as consistent marginalization, one-to-one invariance, and consistent sampling properties [12]. Some applications of reference priors can be seen for other distributions in [15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Bayesian Reference Analysis for the Generalized Normal Linear Regression Model

et al. 2021

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This article proposes the use of the Bayesian reference analysis to estimate the parameters of the generalized normal linear regression model. It is shown that the reference prior led to a proper posterior distribution, while the Jeffreys prior returned an improper one. The inferential purposes were obtained via Markov Chain Monte Carlo (MCMC). Furthermore, diagnostic techniques based on the Kullback–Leibler divergence were used. The proposed method was illustrated using artificial data and real data on the height and diameter of Eucalyptus clones from Brazil.

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“…Hence, our goal is to obtain a generalized distribution of the IEx model such that it will extend the IEx distribution and also add more flexible features to this life-time model. Many authors have proposed some inverted models due to their flexibility in modeling various types of datasets in different fields (for instance, [24,25]). The basic motivations for using the odd exponentiated half-logistic inverse exponential (OEHLIEx) distribution in practice are the following:…”

Section: Introductionmentioning

confidence: 99%

A Flexible Extension to an Extreme Distribution

et al. 2021

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The aim of this paper is not only to propose a new extreme distribution, but also to show that the new extreme model can be used as an alternative to well-known distributions in the literature to model various kinds of datasets in different fields. Several of its statistical properties are explored. It is found that the new extreme model can be utilized for modeling both asymmetric and symmetric datasets, which suffer from over- and under-dispersed phenomena. Moreover, the hazard rate function can be constant, increasing, increasing–constant, or unimodal shaped. The maximum likelihood method is used to estimate the model parameters based on complete and censored samples. Finally, a significant amount of simulations was conducted along with real data applications to illustrate the use of the new extreme distribution.

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Bayesian analysis of the inverse generalized gamma distribution using objective priors

Cited by 9 publications

References 47 publications

Statistical modeling for the monostatic radar cross‐section characteristics of stealth aircraft using the Swerling‐chi/inverse generalized gamma composite distribution model

Statistical modeling for the monostatic radar cross‐section characteristics of stealth aircraft using the Swerling‐chi/inverse generalized gamma composite distribution model

Bayesian Reference Analysis for the Generalized Normal Linear Regression Model

A Flexible Extension to an Extreme Distribution

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