Limit theorems for multivariate discrete distributions

Metrika ◽  
1998 ◽  
Vol 47 (1) ◽  
pp. 47-69 ◽  
Author(s):  
Frank Krummenauer
Keyword(s):  
Limit Theorems ◽  
Discrete Distributions ◽  
Multivariate Discrete Distributions

Asymptotic analysis and local lattice central limit theorems

1979 ◽  
Vol 16 (03) ◽  
pp. 541-553 ◽  
Author(s):  
P.A.P. Moran
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Stirling Numbers ◽  
Central Limit Theorems ◽  
Discrete Distributions ◽  
Asymptotic Formulae ◽  
Local Lattice ◽  
Exact Bounds ◽  
Direct Numerical Integration ◽  
Positive Coefficients

Methods of evaluating the coefficients of high powers of functions defined by power series with positive coefficients are considered. Such methods, which were originally used by Laplace, can, for example, be used to obtain asymptotic formulae for Stirling numbers. They are equivalent to using local lattice central limit theorems. An alternative method using direct numerical integration on a contour integral giving the required coefficient is described. Exact bounds for the accuracy of this method can often be obtained by considerations of the unimodality of discrete distributions. The results are illustrated using convolutions of the rectangular and logarithmic distributions.

scholarly journals On strong unimodality of multivariate discrete distributions

2009 ◽  
Vol 157 (2) ◽  
pp. 234-246 ◽  
Author(s):  
Ersoy Subasi ◽  
Munevver Mine Subasi ◽  
András Prékopa
Keyword(s):  
Discrete Distributions ◽  
Strong Unimodality ◽  
Multivariate Discrete Distributions

Asymptotic analysis and local lattice central limit theorems

1979 ◽  
Vol 16 (3) ◽  
pp. 541-553 ◽  
Author(s):  
P.A.P. Moran
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Stirling Numbers ◽  
Central Limit Theorems ◽  
Discrete Distributions ◽  
Asymptotic Formulae ◽  
Local Lattice ◽  
Exact Bounds ◽  
Direct Numerical Integration ◽  
Positive Coefficients

Methods of evaluating the coefficients of high powers of functions defined by power series with positive coefficients are considered. Such methods, which were originally used by Laplace, can, for example, be used to obtain asymptotic formulae for Stirling numbers. They are equivalent to using local lattice central limit theorems. An alternative method using direct numerical integration on a contour integral giving the required coefficient is described. Exact bounds for the accuracy of this method can often be obtained by considerations of the unimodality of discrete distributions. The results are illustrated using convolutions of the rectangular and logarithmic distributions.

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