scholarly journals A Neyman-Pearson Proper Way to Universal Testing of Multiple Hypotheses Formed by Groups of Distributions

2020 ◽  
pp. 18-33
Author(s):  
Evgueni Haroutunian ◽  
Aram Yesayan
Keyword(s):  
Error Probability ◽  
Probability Distributions ◽  
Single Letter ◽  
Asymptotically Optimal ◽  
Discrete Probability ◽  
Multiple Hypotheses ◽  
Universal Testing ◽  
Error Probabilities ◽  
Discrete Probability Distributions ◽  
The Given

The asymptotically optimal Neyman-Pearson procedures of detection for models characterized by M discrete probability distributions arranged into K, 2 ≤ K ≤ M groups considered as hypotheses are investigated. The sequence of tests based on a growing number of observations is logarithmically asymptotically optimal (LAO) when a certain part of the given error probability exponents (reliabilities) provides positives values for all other reliabilities. LAO tests sequences for some models of objects, including cases, when rejection of decision may be permitted, and when part, or all given error probabilities decrease subexponentially with an increase in the of number of experiments, are desined. For all reliabilities of such tests single-letter characterizations are obtained. A simple case with three distributions and two hypotheses is considered.

scholarly journals On Multiple Hypotheses LAO Testing With Rejection of Decision for Two Dependent Objects

2018 ◽  
pp. 110-114
Author(s):  
Evgueni Haroutunian ◽  
Aram Yesayan ◽  
Narine Harutyunyan
Keyword(s):  
Hypotheses Testing ◽  
Asymptotically Optimal ◽  
Discrete Probability ◽  
Multiple Hypotheses ◽  
Optimal Tests ◽  
The Matrix ◽  
Statistical Hypotheses ◽  
Asymptotically Optimal Tests ◽  
Error Probabilities ◽  
Statistical Hypotheses Testing

Multiple statistical hypotheses testing with possibility of rejecting of decisionis considered for model consisting of two dependent objects characterized by joint discrete probability distribution. The matrix of error probabilities exponents (reliabilities) of asymptotically optimal tests is studied.

scholarly journals Scheduling independent stochastic tasks under deadline and budget constraints

2019 ◽  
Vol 34 (2) ◽  
pp. 246-264 ◽  
Author(s):  
Louis-Claude Canon ◽  
Aurélie Kong Win Chang ◽  
Yves Robert ◽  
Frédéric Vivien
Keyword(s):  
Probability Distributions ◽  
Problem Instance ◽  
Cloud Platform ◽  
Expected Number ◽  
Asymptotically Optimal ◽  
Discrete Probability ◽  
Distribution Laws ◽  
Scheduling Strategies ◽  
Discrete Probability Distributions ◽  
Deadline Constraint

This article discusses scheduling strategies for the problem of maximizing the expected number of tasks that can be executed on a cloud platform within a given budget and under a deadline constraint. The execution times of tasks follow independent and identically distributed probability laws. The main questions are how many processors to enroll and whether and when to interrupt tasks that have been executing for some time. We provide complexity results and an asymptotically optimal strategy for the problem instance with discrete probability distributions and without deadline. We extend the latter strategy for the general case with continuous distributions and a deadline and we design an efficient heuristic which is shown to outperform standard approaches when running simulations for a variety of useful distribution laws.

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.

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
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