scholarly journals Some Moment Relations for the Hipp approximation

1996 ◽  
Vol 26 (1) ◽  
pp. 117-121 ◽  
Author(s):  
Jan Dhaene ◽  
Bjørn Sundt ◽  
Nelson De Pril
Keyword(s):  
Finite Number ◽  
Present Note ◽  
Order Approximation ◽  
Probability Distributions ◽  
Higher Order ◽  
Exact Distribution ◽  
Higher Order Moments ◽  
The Moment

AbstractIn the present note we consider the Hipp approximation to the convolution of a finite number of probability distributions on the non-negative integers. It is shown that the moment up to and including order r of the rth order approximation are equal to the corresponding moments of the exact distribution. We also give a relation between the exact and approximated (r + 1)th order moments and indicate how similar relations can be obtained for higher order moments.

scholarly journals Classroom note: An inductive derivation of Stirling numbers of the second kind and their applications in statistics

1997 ◽  
Vol 1 (2) ◽  
pp. 151-157 ◽  
Author(s):  
Anwar H. Joarder ◽  
Munir Mahmood
Keyword(s):  
Probability Distributions ◽  
Stirling Numbers ◽  
Higher Order ◽  
Inductive Method ◽  
Higher Order Moments ◽  
Discrete Probability ◽  
Discrete Probability Distributions

An inductive method has been presented for finding Stirling numbers of the second kind. Applications to some discrete probability distributions for finding higher order moments have been discussed.

scholarly journals Perceptual insensitivity to higher-order statistical moments of coherent random dot motion

2018 ◽  
Author(s):  
Michael L. Waskom ◽  
Janeen Asfour ◽  
Roozbeh Kiani
Keyword(s):  
Visual Processing ◽  
Probability Distributions ◽  
Higher Order ◽  
Statistical Moments ◽  
Coherent Motion ◽  
It Use ◽  
Higher Order Moments ◽  
Dynamic Stimuli ◽  
Dot Motion ◽  
The Individual

ABSTRACTWhen the visual system analyses distributed patterns of sensory inputs, what features of those distributions does it use? It has been previously demonstrated that higher-order statistical moments of luminance distributions influence perception of static surfaces and textures. Here, we tested whether the brain also represents higher-order moments of dynamic stimuli. We constructed random dot kinematograms where dots moved according to probability distributions that selectively differed in terms of their mean, variance, skewness, or kurtosis. When viewing these stimuli, human observers were sensitive to the mean direction of coherent motion and to the variance of the individual dot displacement angles, but they were insensitive to skewness and kurtosis. Observer behavior accorded with a model of directional motion energy, suggesting that information about higher-order moments is discarded early in the visual processing hierarchy. These results demonstrate that use of higher-order moments is not a general property of visual perception.

scholarly journals Inferring gene regulatory networks from single-cell RNA-seq temporal snapshot data requires higher-order moments

Patterns ◽  
2021 ◽  
Vol 2 (9) ◽  
pp. 100332
Author(s):  
N. Alexia Raharinirina ◽  
Felix Peppert ◽  
Max von Kleist ◽  
Christof Schütte ◽  
Vikram Sunkara
Keyword(s):  
Single Cell ◽  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Higher Order ◽  
Rna Seq ◽  
Higher Order Moments ◽  
Gene Regulatory
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