Phase Transitions for the Uniform Distribution in the Pattern Maximum Likelihood Problem and its Bethe Approximation

2017 ◽  
Vol 31 (1) ◽  
pp. 597-631
Author(s):  
Chun Lam Chan ◽  
Winston Fernandes ◽  
Navin Kashyap ◽  
Manjunath Krishnapur
Keyword(s):  
Phase Transitions ◽  
Maximum Likelihood ◽  
Uniform Distribution ◽  
Bethe Approximation ◽  
Pattern Maximum

scholarly journals A note about the uniform distribution on the intersection of a simplex and a sphere

2017 ◽  
Vol 09 (04) ◽  
pp. 717-738 ◽  
Author(s):  
Sourav Chatterjee
Keyword(s):  
Phase Transitions ◽  
Uniform Distribution ◽  
Probability Distributions ◽  
High Dimensions ◽  
Uniform Probability ◽  
Product Measures

Uniform probability distributions on [Formula: see text] balls and spheres have been studied extensively and are known to behave like product measures in high dimensions. In this note we consider the uniform distribution on the intersection of a simplex and a sphere. Certain new and interesting features, such as phase transitions and localization phenomena emerge.

scholarly journals Marshall-Olkin Discrete Uniform Distribution

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
E. Sandhya ◽  
C. B. Prasanth
Keyword(s):  
Maximum Likelihood ◽  
Uniform Distribution ◽  
Hazard Rate ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
First Order ◽  
New Family ◽  
Discrete Uniform Distribution ◽  
Discrete Uniform ◽  
Family Of Distributions

We introduce and characterize a new family of distributions, Marshall-Olkin discrete uniform distribution. The natures of hazard rate, entropy, and distribution of minimum of sequence of i.i.d. random variables are derived. First order autoregressive (AR (1)) model with this distribution for marginals is considered. The maximum likelihood estimates for the parameters are found out. Also, the goodness of the distribution is tested with real data.

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