Bounds on Negative Binomial Approximation to Call Function

* In this paper, we develop Stein's method for negative binomial distribution using call function defined by [f.sub.z](k) = [(k - z).sup.+] = max{k - z, 0}, for k [greater than or equal to] 0 and z [greater than or equal to] 0. We obtain error bounds between E[[f.sub.z]([N.sub.r,p])] and E[[f.s...

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Bibliographic Details
Published inRevstat Vol. 22; no. 1; p. 25
Main Author Kumar, Amit N
Format Journal Article
LanguageEnglish
Published Instituto Nacional de Estatistica 01.01.2024
Instituto Nacional de Estatística | Statistics Portugal
Subjects
call function
CDO
Collateralized debt obligations
error bounds
negative binomial distribution
Stein's method
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Summary:* In this paper, we develop Stein's method for negative binomial distribution using call function defined by [f.sub.z](k) = [(k - z).sup.+] = max{k - z, 0}, for k [greater than or equal to] 0 and z [greater than or equal to] 0. We obtain error bounds between E[[f.sub.z]([N.sub.r,p])] and E[[f.sub.z](V)], where [N.sub.r,p] follows negative binomial distribution and V is the sum of locally dependent random variables, using certain conditions on moments. We demonstrate our results through an interesting application, namely, collateralized debt obligation (CDO), and compare the bounds with the existing bounds. Keywords: * negative binomial distribution; call function; error bounds; Stein's method; CDO. AMS Subject Classification: * Primary: 62E17, 62E20; Secondary: 60F05, 60E05.
ISSN:1645-6726
2183-0371
DOI:10.57805/revstat.v22i1.437