Bayesian Inference for Skew-Symmetric Distributions

Ghaderinezhad, Fatemeh; Ley, Christophe; Loperfido, Nicola

doi:10.3390/sym12040491

Cited by 5 publications

(3 citation statements)

References 51 publications

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“…This is achieved through a variety of methods, as evidenced by the great spectrum of work in the literature. The degree to which the chosen distribution fits the input data greatly influences both the analysis and the empirical results; see [1][2][3]. Bounded data with random variables for rates and proportions are widely used in many fields of knowledge, including economics and medicine.…”

Section: Introductionmentioning

confidence: 99%

“…Given their asymmetry and/or kurtosis, some authors have recently concentrated on generating distributions defined on the bounded interval using any of the parent distribution modification strategies. Moreover, popular flexible distributions known as "skew-symmetric distributions" are useful for modeling non-normal characteristics such as skewness and kurtosis [3]. We refer to recent studies in [4][5][6][7][8] for a better understanding.…”

Section: Introductionmentioning

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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Section: Introductionmentioning

confidence: 99%

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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“…This is one of the reasons for the proposed Fernandez-Steel skew normal (FSSN) CAR model. Skewness is one of the features of skew-symmetric distributions [23]. Compared to the normal and DE distributions, which can only capture data that have a symmetrical pattern, FSSN distribution is able to be more flexible when explaining both symmetrical and asymmetrical data [24].…”

Section: Introductionmentioning

confidence: 99%

Fernandez–Steel Skew Normal Conditional Autoregressive (FSSN CAR) Model in Stan for Spatial Data

2021

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In spatial data analysis, the prior conditional autoregressive (CAR) model is used to express the spatial dependence on random effects from adjacent regions. This paper provides a new proposed approach regarding the development of the existing normal CAR model into a more flexible, Fernandez–Steel skew normal (FSSN) CAR model. This approach is able to capture spatial random effects that have both symmetrical and asymmetrical patterns. The FSSN CAR model is built on the basis of the normal CAR with an additional skew parameter. The FSSN distribution is able to provide good estimates for symmetry with heavy- or light-tailed and skewed-right and skewed-left data. The effects of this approach are demonstrated by establishing the FSSN distribution and FSSN CAR model in spatial data using Stan language. On the basis of the plot of the estimation results and histogram of the model error, the FSSN CAR model was shown to behave better than both models without a spatial effect and with the normal CAR model. Moreover, the smallest widely applicable information criterion (WAIC) and leave-one-out (LOO) statistical values also validate the model, as FSSN CAR is shown to be the best model used.

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