Topic
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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172 citations
TL;DR: In this paper, the authors extended the Koksma-Hlawka inequality to the case of non-uniform distributions and proposed a new strategy of representative point set determination via rearrangement, which is then applied to stochastic dynamical response analysis of strong nonlinear structures by incorporating into the probability density evolution method.
171 citations
TL;DR: In this article, the load probability density function (pdf) in the distribution network shows a number of variations at different nodes and cannot be represented by any specific distribution, and an approach to utilise the loads as pseudo-measurements for the purpose of distribution system state estimation (DSSE).
Abstract: This study presents an approach to utilise the loads as pseudo-measurements for the purpose of distribution system state estimation (DSSE). The load probability density function (pdf) in the distribution network shows a number of variations at different nodes and cannot be represented by any specific distribution. The approach presented in this study represents all the load pdfs through the Gaussian mixture model (GMM). The expectation maximisation (EM) algorithm is used to obtain the parameters of the mixture components. The standard weighted least squares (WLS) algorithm utilises these load models as pseudo-measurements. The effectiveness of WLS is assessed through some statistical measures such as bias, consistency and quality of the estimates in a 95-bus generic distribution network model.
170 citations
TL;DR: In this article, a localized spectral analysis based on wavelet bases rather than on periodic-ones has been applied to decompose the instantaneous clearness index signal into a set of orthonormal subsignals.
170 citations
TL;DR: The core of the methodology is a novel concept of “probabilistically constrained rectangle”, which permits effective pruning/validation of nonqualifying/qualifying data and a new index structure called the U-tree for minimizing the query overhead.
Abstract: In an uncertain database, every object o is associated with a probability density function, which describes the likelihood that o appears at each position in a multidimensional workspace. This article studies two types of range retrieval fundamental to many analytical tasks. Specifically, a nonfuzzy query returns all the objects that appear in a search region rq with at least a certain probability tq. On the other hand, given an uncertain object q, fuzzy search retrieves the set of objects that are within distance eq from q with no less than probability tq. The core of our methodology is a novel concept of “probabilistically constrained rectangle”, which permits effective pruning/validation of nonqualifying/qualifying data. We develop a new index structure called the U-tree for minimizing the query overhead. Our algorithmic findings are accompanied with a thorough theoretical analysis, which reveals valuable insight into the problem characteristics, and mathematically confirms the efficiency of our solutions. We verify the effectiveness of the proposed techniques with extensive experiments.
170 citations