Electronic Resource
Springer
Methodology and computing in applied probability
1 (1999), S. 407-421
ISSN:
1387-5841
Keywords:
Stein's method
;
Poisson approximation
;
negative binomial approximation
;
Po´lya distribution
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Bounds on the rate of convergence to the negative binomial distribution are found, where this rate is measured by the total variation distance between probability laws. For an arbitrary discrete random variable written as a sum of indicators, an upper bound of coupling form is expressed as an average of terms each of which measures the difference between the effect of particular indicator being one and the value of a geometrically distributed random variable. When a monotone coupling exists a lower bound can also be shown. Application of these results is illustrated with the example of the Po´lya distribution for which the rate of approach to the negative binomial limit is found.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1010094221471
Permalink
|
Location |
Call Number |
Expected |
Availability |
