Goodness of Fit Tests for Composite Hypotheses Based on an Increasing Number of Order Statistics

1976 ◽  
Author(s):  
Ray H. Jakobovits
Keyword(s):  
Order Statistics ◽  
Goodness Of Fit ◽  
Goodness Of Fit Tests ◽  
Composite Hypotheses

scholarly journals Computing the exact distributions of some functions of the ordered multinomial counts: maximum, minimum, range and sums of order statistics

2019 ◽  
Vol 6 (10) ◽  
pp. 190198 ◽  
Author(s):  
Marco Bonetti ◽  
Pasquale Cirillo ◽  
Anton Ogay
Keyword(s):  
New York ◽  
Order Statistics ◽  
Goodness Of Fit ◽  
Multinomial Distribution ◽  
Exact Algorithms ◽  
Statistical Testing ◽  
New York University ◽  
Goodness Of Fit Tests ◽  
Computational Procedures ◽  
Phd Thesis

Starting from seminal neglected work by Rappeport (Rappeport 1968 Algorithms and computational procedures for the application of order statistics to queuing problems. PhD thesis, New York University), we revisit and expand on the exact algorithms to compute the distribution of the maximum, the minimum, the range and the sum of the J largest order statistics of a multinomial random vector under the hypothesis of equiprobability. Our exact results can be useful in all those situations in which the multinomial distribution plays an important role, from goodness-of-fit tests to the study of Poisson processes, with applications spanning from biostatistics to finance. We describe the algorithms, motivate their use in statistical testing and illustrate two applications. We also provide the codes and ready-to-use tables of critical values.

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