On Examining Complex Systems Using the q-Weibull Distribution in Classical and Bayesian Paradigms

Abbas, Nasir

doi:10.2991/jsta.d.200825.001

Cited by 5 publications

(2 citation statements)

References 13 publications

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“…The q-Weibull distribution includes an additional r parameter, and in the cases r = 1 and r = 2 we recover the q-exponential and q-Gaussian distributions, respectively. The q-Weibull distribution also has been used in a variety of contexts in complex systems [56,57,58], and it is closely linked to the Tsallis statistics [59,60,61,62]. We finally propose to fit the I-V curves with the q-Weibull cdf, shown in Eq.…”

Section: Using the Q-weibull Distribution Function: Plasma Potential ...mentioning

confidence: 99%

New procedure to estimate plasma parameters through the q-Weibull distribution by using a Langmuir probe in a cold plasma

Gonzalez

González

Soler

et al. 2022

Plasma Res. Express

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We describe a procedure to obtain the plasma parameters from the {\bf I-V} Langmuir curve by using the Druyvesteyn equation. We propose to include two new parameters, $q$ and $r$, to the usual plasma parameters: plasma potential ($V_p$), floating potential ($V_f$), electron density ($n$), and electron temperature ($T$). These new parameters can be particularly useful to represent non-Maxwellian distributions. The procedure is based on the fit of the {\bf I-V} Langmuir curve with the $q$-Weibull distribution function, and is motivated by recent works which use the $q$-exponential distribution function derived from Tsallis statistics. We obtain the usual plasma parameters employing three techniques: the numerical differentiation using Savitzky Golay (SG) filters, the $q$-exponential distribution function, and the $q$-Weibull distribution function. We explain the limitations of the $q$-exponential function, where the experimental data $V>V_p$ needs to be trimmed beforehand, and this results in a lower accuracy compared to the numerical differentiation with SG. To overcome this difficulty, the $q$-Weibull function is introduced as a natural generalization to the $q$-exponential distribution, and it has greater flexibility in order to represent the concavity change around $V_p$. We apply this procedure to analyze the measurements corresponding to a nitrogen $N_2$ cold plasma obtained by using a single Langmuir probe located at different heights from the cathode. We show that the $q$ parameter has a very stable numerical value with the height. This work may contribute to clarify some advantages and limitations of the use of non-extensive statistics in plasma diagnostics, but the physical interpretation of the non-extensive parameters in plasma physics remains not fully clarified, and requires further research.

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Section: Using the Q-weibull Distribution Function: Plasma Potential ...mentioning

confidence: 99%

New procedure to estimate plasma parameters through the q-Weibull distribution by using a Langmuir probe in a cold plasma

Gonzalez

González

Soler

et al. 2022

Plasma Res. Express

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“…In recent years, the use of Markov Chain Monte Carlo (MCMC) methods has gained much popularity [28][29][30]. Most recently, the author in [31] has considered in detail the q-Weibull distribution for classical and Bayesian analyses, which also serves as a motivation to conduct this study. Keeping in view the extensive literature on the importance of Bayesian analysis and the importance of the Wald distribution, we have attempted to present the Bayesian analysis of the Wald distribution.…”

Section: Introductionmentioning

confidence: 99%

Robust Assessing the Lifetime Performance of Products with Inverse Gaussian Distribution in Bayesian and Classical Setup

Ahmadini¹,

Javed²,

Akhtar³

et al. 2021

Mathematical Problems in Engineering

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The inverse Gaussian (Wald) distribution belongs to the two-parameter family of continuous distributions having a range from 0 to ∞ and is considered as a potential candidate to model diffusion processes and lifetime datasets. Bayesian analysis is a modern inferential technique in which we estimate the parameters of the posterior distribution obtained by formally combining a prior distribution with an observed data distribution. In this article, we have attempted to perform the Bayesian and classical analyses of the Wald distribution and compare the results. Jeffreys' and uniform priors are used as noninformative priors, while the exponential distribution is used as an informative prior. The analysis comprises finding joint posterior distributions, the posterior means, predictive distributions, and credible intervals. To illustrate the entire estimation procedure, we have used real and simulated datasets, and the results thus obtained are discussed and compared. We have used the Bayesian specialized Open BUGS software to perform Markov Chain Monte Carlo (MCMC) simulations using a real dataset.

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On Classical and Bayesian Reliability of Systems Using Bivariate Generalized Geometric Distribution

Abbas¹

2023

J Stat Theory Appl

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The study of system safety and reliability has always been vital for the quality and manufacturing engineers of varying fields for which generally the continuous probability distributions are proposed. Bivariate and multivariate continuous distributions are the candidates while studying more than one characteristic of the system. In this article, an attempt is made to address this issue when the reliability systems generate bivariate and correlated count datasets. The bivariate generalized geometric distribution (BGGD) is believed to serve as a potential candidate to model such types of datasets. Bayesian approach of data analysis has the potential of accommodating the uncertainty associated with the model parameters of interest using uninformative and informative priors. A real life bivariate correlated dataset is analyzed in Bayesian framework and the results are compared with those produced by the classical approach. Posterior summaries including posterior means, highest density regions, and predicted expected frequencies of the bivariate data are evaluated. Different information criteria are evaluated to compare the inferential methods under study. The entire analysis is carried out using Markov chain Monte Carlo (MCMC) set-up of data augmentation implemented through WinBUGS.

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On Examining Complex Systems Using the q-Weibull Distribution in Classical and Bayesian Paradigms

Cited by 5 publications

References 13 publications

New procedure to estimate plasma parameters through the q-Weibull distribution by using a Langmuir probe in a cold plasma

New procedure to estimate plasma parameters through the q-Weibull distribution by using a Langmuir probe in a cold plasma

Robust Assessing the Lifetime Performance of Products with Inverse Gaussian Distribution in Bayesian and Classical Setup

On Classical and Bayesian Reliability of Systems Using Bivariate Generalized Geometric Distribution

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