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.

INTERACTIVE SIMULATIONS OF DISCRETE PROBABILITY DISTRIBUTIONS

2019 ◽  
Author(s):  
Rubén Darío Santiago Acosta ◽  
Ernesto Manuel Hernández Cooper ◽  
Faustino Yescas Martinez
Keyword(s):  
Probability Distributions ◽  
Discrete Probability ◽  
Discrete Probability Distributions ◽  
Interactive Simulations

scholarly journals Optimal approximate sampling from discrete probability distributions

2020 ◽  
Vol 4 (POPL) ◽  
pp. 1-31 ◽  
Author(s):  
Feras A. Saad ◽  
Cameron E. Freer ◽  
Martin C. Rinard ◽  
Vikash K. Mansinghka
Keyword(s):  
Probability Distributions ◽  
Discrete Probability ◽  
Discrete Probability Distributions
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