scholarly journals Stein's Method for Compound Geometric Approximation

2010 ◽  
Vol 47 (1) ◽  
pp. 146-156 ◽  
Author(s):  
Fraser Daly
Keyword(s):  
Generating Functions ◽  
Analytical Approach ◽  
Geometric Distribution ◽  
Stein’S Method ◽  
Hitting Times ◽  
Stein's Method ◽  
Geometric Approximation ◽  
Compound Geometric Distribution ◽  
Probabilistic Approximation ◽  
Sequence Patterns

We apply Stein's method for probabilistic approximation by a compound geometric distribution, with applications to Markov chain hitting times and sequence patterns. Bounds on our Stein operator are found using a complex analytical approach based on generating functions and Cauchy's formula.

scholarly journals Stein's Method for Compound Geometric Approximation

2010 ◽  
Vol 47 (01) ◽  
pp. 146-156 ◽  
Author(s):  
Fraser Daly
Keyword(s):  
Generating Functions ◽  
Analytical Approach ◽  
Geometric Distribution ◽  
Stein’S Method ◽  
Hitting Times ◽  
Stein's Method ◽  
Geometric Approximation ◽  
Compound Geometric Distribution ◽  
Probabilistic Approximation ◽  
Sequence Patterns

We apply Stein's method for probabilistic approximation by a compound geometric distribution, with applications to Markov chain hitting times and sequence patterns. Bounds on our Stein operator are found using a complex analytical approach based on generating functions and Cauchy's formula.

scholarly journals Analysis of Statistics for Generalized Stirling Permutations

2011 ◽  
Vol 20 (6) ◽  
pp. 875-910 ◽  
Author(s):  
MARKUS KUBA ◽  
ALOIS PANHOLZER
Keyword(s):  
Generating Functions ◽  
Stein’S Method ◽  
Limiting Distribution ◽  
Permutation Statistics ◽  
Stein's Method ◽  
Urn Models ◽  
Restricted Class

In this work we give a study of generalizations of Stirling permutations, a restricted class of permutations of multisets introduced by Gessel and Stanley [15]. First we give several bijections between such generalized Stirling permutations and various families of increasing trees extending the known correspondences of [20, 21]. Then we consider several permutation statistics of interest for generalized Stirling permutations as the number of left-to-right minima, the number of left-to-right maxima, the number of blocks of specified sizes, the distance between occurrences of elements, and the number of inversions. For all these quantities we give a distributional study, where the established connections to increasing trees turn out to be very useful. To obtain the exact and limiting distribution results we use several techniques ranging from generating functions, connections to urn models, martingales and Stein's method.

On the rate of Poisson process approximation to a Bernoulli process

1997 ◽  
Vol 34 (4) ◽  
pp. 898-907 ◽  
Author(s):  
Aihua Xia
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Discrete Time ◽  
Wasserstein Distance ◽  
Stein’S Method ◽  
Upper Bounds ◽  
Stein's Method ◽  
Bernoulli Process ◽  
Logarithmic Factor ◽  
Process Approximation

This note gives the rate for a Wasserstein distance between the distribution of a Bernoulli process on discrete time and that of a Poisson process, using Stein's method and Palm theory. The result here highlights the possibility that the logarithmic factor involved in the upper bounds established by Barbour and Brown (1992) and Barbour et al. (1995) may be superfluous in the true Wasserstein distance between the distributions of a point process and a Poisson process.

STEIN'S METHOD AND THE BERRY-ESSÉEN THEOREM

1984 ◽  
Vol 26 (1) ◽  
pp. 8-15 ◽  
Author(s):  
A. D. Barbour ◽  
Peter Hall
Keyword(s):  
Stein’S Method ◽  
Stein's Method
Sign in / Sign up

Export Citation Format

Share Document