Pseudo-binomial approximation to (k1,k2)-runs

The distribution of (k1,k2)-runs is well-known (Dafnis et al., 2010), under independent and identically distributed (i.i.d.) setup of Bernoulli trials but is intractable under non i.i.d. setup. Hence, it is of interest to find a suitable approximate distribution for (k1,k2)-runs, under non i.i.d. se...

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Bibliographic Details
Published in:	Statistics & probability letters Vol. 141; pp. 19 - 30
Main Authors:	Upadhye, N.S., Kumar, A.N.
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01-10-2018
Subjects:	[formula omitted]-runs Coupling Pseudo-binomial distribution Stein operator Stein’s method secondary Pseudo-binomial distribution Stein’s method (k1,k2)-runs Stein operator Coupling primary
Online Access:	Get full text
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Summary:	The distribution of (k1,k2)-runs is well-known (Dafnis et al., 2010), under independent and identically distributed (i.i.d.) setup of Bernoulli trials but is intractable under non i.i.d. setup. Hence, it is of interest to find a suitable approximate distribution for (k1,k2)-runs, under non i.i.d. setup, with reasonable accuracy. In this paper, pseudo-binomial approximation to (k1,k2)-runs is considered using total variation distance. The approximation results derived are of optimal order and improve the existing results.
ISSN:	0167-7152 1879-2103
DOI:	10.1016/j.spl.2018.05.016