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      A New One-Parameter Distribution for Right Censored Bayesian and Non-Bayesian Distributional Validation under Various Estimation Methods

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      Mathematics
      MDPI AG

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          Abstract

          We propose a new extension of the exponential distribution for right censored Bayesian and non-Bayesian distributional validation. The parameter of the new distribution is estimated using several conventional methods, including the Bayesian method. The likelihood estimates and the Bayesian estimates are compared using Pitman’s closeness criteria. The Bayesian estimators are derived using three loss functions: the extended quadratic, the Linex, and the entropy functions. Through simulated experiments, all the estimating approaches offered have been assessed. The censored maximum likelihood method and the Bayesian approach are compared using the BB algorithm. The development of the Nikulin–Rao–Robson statistic for the new model in the uncensored situation is thoroughly discussed with the aid of two applications and a simulation exercise. For the novel model under the censored condition, two applications and the derivation of the Bagdonavičius and Nikulin statistic are also described.

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          Objective comparison of methods to decode anomalous diffusion

          Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a challenging task, which traditionally relies on calculating the trajectory mean squared displacement. However, this approach breaks down for cases of practical interest, e.g., short or noisy trajectories, heterogeneous behaviour, or non-ergodic processes. Recently, several new approaches have been proposed, mostly building on the ongoing machine-learning revolution. To perform an objective comparison of methods, we gathered the community and organized an open competition, the Anomalous Diffusion challenge (AnDi). Participating teams applied their algorithms to a commonly-defined dataset including diverse conditions. Although no single method performed best across all scenarios, machine-learning-based approaches achieved superior performance for all tasks. The discussion of the challenge results provides practical advice for users and a benchmark for developers. Deviations from Brownian motion leading to anomalous diffusion are ubiquitously found in transport dynamics but often difficult to characterize. Here the authors compare approaches for single trajectory analysis through an open competition, showing that machine learning methods outperform classical approaches.
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            A Bootstrap Control Chart for Weibull Percentiles

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              ACQUISITION OF RESISTANCE IN GUINEA PIGS INFECTED WITH DIFFERENT DOSES OF VIRULENT TUBERCLE BACILLI1

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                Author and article information

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                Journal
                Mathematics
                Mathematics
                MDPI AG
                2227-7390
                February 2023
                February 10 2023
                : 11
                : 4
                : 897
                Article
                10.3390/math11040897
                e90217c6-9560-48f6-b958-2604f74eba20
                © 2023

                https://creativecommons.org/licenses/by/4.0/

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