Now showing 1 - 3 of 3
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    Pseudo-binomial approximation to (k1,k2)-runs
    (01-10-2018) ;
    Kumar, A. N.
    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.
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    Publication
    On Brascamp–Lieb and Poincaré type inequalities for generalized tempered stable distribution
    (01-10-2022)
    Barman, Kalyan
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    In this article, we obtain a Stein's lemma for generalized tempered stable distribution. In particular, we derive a Stein operator for the class generalized tempered stable distributions and discuss its implications on the existing literature. Using this lemma, we obtain Brascamp–Lieb and Poincaré type inequalities for generalized tempered stable distribution.
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    Publication
    On Stein operators for discrete approximations
    (01-11-2017) ;
    ÄŒius, Vydas ÄŒekanavi
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    Vellaisamy, P.
    In this paper, a new method based on probability generating functions is used to obtain multiple Stein operators for various random variables closely related to Poisson, binomial and negative binomial distributions. Also, the Stein operators for certain compound distributions, where the random summand satisfies Panjer's recurrence relation, are derived. A well-known perturbation approach for Stein's method is used to obtain total variation bounds for the distributions mentioned above. The importance of such approximations is illustrated, for example, by the binomial convoluted with Poisson approximation to sums of independent and dependent indicator random variables.