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Probability density function

About: Probability density function is a research topic. Over the lifetime, 22321 publications have been published within this topic receiving 422885 citations. The topic is also known as: probability function & PDF.


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Journal ArticleDOI
TL;DR: A version of the MED, which adaptively updates the design by “learning” about the unknown response surface sequentially, is proposed and implemented and two potential applications of MED in simulation of complex probability densities and optimization of complex response surfaces are discussed and demonstrated.
Abstract: A new space-filling design, called minimum energy design (MED), is proposed to explore unknown regions of the design space of particular interest to an experimenter. The key ideas involved in constructing the MED are the visualization of each design point as a charged particle inside a box, and minimization of the total potential energy of these particles. It is shown through theoretical arguments and simulations that with a proper choice of the charge function, the MED can asymptotically generate any arbitrary probability density function. A version of the MED, which adaptively updates the design by “learning” about the unknown response surface sequentially, is proposed and implemented. Two potential applications of MED in simulation of complex probability densities and optimization of complex response surfaces are discussed and demonstrated with examples. This article has supplementary material online.

84 citations

Journal ArticleDOI
TL;DR: In this paper, the average probability density P(r,t) of random walks on fractals is revisited within the continuous-time random walks formalism, and corrections to the accepted asymptotic stretched Gaussian decay of the form ralpha are discussed.
Abstract: The average probability density P(r,t) of random walks on fractals is revisited within the continuous-time random walks formalism. Corrections to the accepted asymptotic stretched Gaussian decay of P(r,t) of the form ralpha are discussed. It is shown that P(r,t) obeys a diffusion equation with a fractional time derivative asymptotically, and predictions about the value of alpha are presented.

84 citations

Journal ArticleDOI
TL;DR: In this article, the probability density distributions of one-minute values of global irradiance, conditioned to the optical air mass, considering those as an approximation to the instantaneous distributions, were analyzed.

84 citations

Journal ArticleDOI
TL;DR: In this paper, it is shown that the maximum likelihood estimator is inadmissible with respect to the squared error loss function, and a class of estimators is given which are admissible and minimax for a modified loss function.
Abstract: : The non-central chi-square distribution arises in various statistical analyses. The estimation of the non-centrality parameter of the distribution is of importance in some problems. In this paper it is shown that the maximum likelihood estimator is inadmissible with respect to the squared error loss function. It is trivially minimax since all estimators have unbounded maximum risk. A class of estimators is given which are admissible and minimax for a modified loss function.

83 citations

Journal ArticleDOI
TL;DR: This paper proposes the application of the infinite Gaussian mixture model (GMM) for the calculation of the confidence bounds, thereby relaxing the previous restrictive assumption.
Abstract: Summary. The primary goal of multivariate statistical process performance monitoring is to identify deviations from normal operation within a manufacturing process. The basis of the monitoring schemes is historical data that have been collected when the process is running under normal operating conditions. These data are then used to establish confidence bounds to detect the onset of process deviations. In contrast with the traditional approaches that are based on the Gaussian assumption, this paper proposes the application of the infinite Gaussian mixture model (GMM) for the calculation of the confidence bounds, thereby relaxing the previous restrictive assumption. The infinite GMM is a special case of Dirichlet process mixtures and is introduced as the limit of the finite GMM, i.e. when the number of mixtures tends to oo. On the basis of the estimation of the probability density function, via the infinite GMM, the confidence bounds are calculated by using the bootstrap algorithm. The methodology proposed is demonstrated through its application to a simulated continuous chemical process, and a batch semiconductor manufacturing process.

83 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023382
2022906
2021906
20201,047
20191,117
20181,083