238 research outputs found

    INFORMATION MEASURES FOR RECORD RANKED SET SAMPLES

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    Salehi and Ahmadi (2014) introduced a new sampling scheme for generating record-breaking data called record ranked set sampling. In this paper, we consider the uncertainty and information content of record ranked set samples (RRSS) in terms of Shannon entropy, Rényi and Kullback-Leibler (KL) information measures. We show that the difference between the Shannon entropy of RRSS and the simple random samples (SRS) is depends on the parent distribution F. We also compare the information content of RRSS with a SRS data in the uniform, exponential, Weibull, Pareto, and gamma distributions. We obtain similar results for RRSS under the Rényi information. Finally, we show that the KL information between the distribution of SRS and distribution of RRSS is distribution-free and increases as the sample size increases.Salehi and Ahmadi (2014) introduced a new sampling scheme for generating record-breaking data called record ranked set sampling. In this paper, we consider the uncertainty and information content of record ranked set samples (RRSS) in terms of Shannon entropy, Rényi and Kullback-Leibler (KL) information measures. We show that the difference between the Shannon entropy of RRSS and the simple random samples (SRS) is depends on the parent distribution F. We also compare the information content of RRSS with a SRS data in the uniform, exponential, Weibull, Pareto, and gamma distributions. We obtain similar results for RRSS under the Rényi information. Finally, we show that the KL information between the distribution of SRS and distribution of RRSS is distribution-free and increases as the sample size increases

    The Odd Inverse Rayleigh Family of Distributions: Simulation & Application to Real Data

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    A new family of inverse probability distributions named inverse Rayleigh family is introduced to generate many continuous distributions. The shapes of probability density and hazard rate functions are investigated. Some Statistical measures of the new generator including moments, quantile and generating functions, entropy measures and order statistics are derived. The Estimation of the model parameters is performed by the maximum likelihood estimation method. Furthermore, a simulation study is used to estimate the parameters of one of the members of the new family. The data application shows that the new family models can be useful to provide better fits than other lifetime models

    A comparison of two symptom selection methods in vibration-based turbomachinery diagnostics

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    Complex diagnostic objects, e.g. critical rotating machines, usually generate a large number of diagnostic symptoms. A procedure is therefore required of selecting those most suitable from the point of view of technical condition evolution representation. A method based on the Singular Value Decomposition has been proposed for this purpose. An alternative is provided by an assessment of information content variation with time. Any symptom, treated as a random variable, may be assigned an information content measure that determines its ‘predictability’. As the end of service life is approached, symptom value is to a growing extent dominated by deterministic (and hence predictable) lifetime consumption processes, which implies decreasing information content. The symptom with the fastest decrease of an information content measure with time should thus be judged the most representative one. Suitability of such approach has already been demonstrated. The aim of this paper is to compare results obtained with both methods

    Random unitaries, Robustness, and Complexity of Entanglement

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    It is widely accepted that the dynamic of entanglement in presence of a generic circuit can be predicted by the knowledge of the statistical properties of the entanglement spectrum. We tested this assumption by applying a Metropolis-like entanglement cooling algorithm generated by different sets of local gates, on states sharing the same statistic. We employ the ground states of a unique model, namely the one-dimensional Ising chain with a transverse field, but belonging to different macroscopic phases such as the paramagnetic, the magnetically ordered, and the topological frustrated ones. Quite surprisingly, we observe that the entanglement dynamics are strongly dependent not just on the different sets of gates but also on the phase, indicating that different phases can possess different types of entanglement (which we characterize as purely local, GHZ-like, and W-state-like) with different degree of resilience against the cooling process. Our work highlights the fact that the knowledge of the entanglement spectrum alone is not sufficient to determine its dynamics, thereby demonstrating its incompleteness as a characterization tool. Moreover, it shows a subtle interplay between locality and non-local constraints.Comment: 14 pages, 11 figures, 1 tabl

    Información cuántica con variables continuas

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    "This thesis identifies the model of simultaneous measurement of the position and momentum observables seminally posed by Arthurs and Kelly as a system described entirely by observables with continuous eigen spectrum; in particular, we treat the model in the regime of Gaussian states by assuming a minimum uncertainty state as the system under measurement. Under this consideration, the mathematical framework used to describe these states in quantum information processing tasks finds applicability. First, we consider the free energies of each quantum system defining the measurement setting in the measurement dynam ics; then, we study how this consideration affects the retrodictive and predictive aspects of accuracy for the simultaneous measurement of the position and momentum observables of the system under examination. We find that the accuracy of the simultaneous measurement is affected by the degree of coupling between the detectors of the measurement apparatus and the system under observation"

    Quantile-Based Generalized Entropy of Order (α, β) for Order Statistics

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    In the present paper, we propose a quantile version of generalized entropy measure for order statistics for residual and past lifetimes and study their properties. Lower and upper bound of the proposed measures are derived. It is shown that the quantile-based generalized information between i-th order statistics and parent random variable is distribution free. The uniform, exponential, generalized Pareto and finite range distributions, which are commonly used in the reliability modeling have been characterized in terms of the proposed entropy measure with extreme order statistics

    Data Science: Measuring Uncertainties

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    With the increase in data processing and storage capacity, a large amount of data is available. Data without analysis does not have much value. Thus, the demand for data analysis is increasing daily, and the consequence is the appearance of a large number of jobs and published articles. Data science has emerged as a multidisciplinary field to support data-driven activities, integrating and developing ideas, methods, and processes to extract information from data. This includes methods built from different knowledge areas: Statistics, Computer Science, Mathematics, Physics, Information Science, and Engineering. This mixture of areas has given rise to what we call Data Science. New solutions to the new problems are reproducing rapidly to generate large volumes of data. Current and future challenges require greater care in creating new solutions that satisfy the rationality for each type of problem. Labels such as Big Data, Data Science, Machine Learning, Statistical Learning, and Artificial Intelligence are demanding more sophistication in the foundations and how they are being applied. This point highlights the importance of building the foundations of Data Science. This book is dedicated to solutions and discussions of measuring uncertainties in data analysis problems

    A New Class of Fractional Cumulative Residual Entropy - Some Theoretical Results, Journal of Telecommunications and Information Technology, 2023, nr 1

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    In this paper, by differentiating the entropy’s generating function (i.e., h(t) = R SX̄F tX (x)dx) using a Caputo fractional-order derivative, we derive a generalized non-logarithmic fractional cumulative residual entropy (FCRE). When the order of differentiation α → 1, the ordinary Rao CRE is recovered, which corresponds to the results from first-order ordinary differentiation. Some properties and examples of the proposed FCRE are also presented
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