Second Order Chebyshev–Edgeworth-Type Approximations for Statistics Based on Random Size Samples

Author:

Christoph Gerd1ORCID,Ulyanov Vladimir V.23ORCID

Affiliation:

1. Department of Mathematics, Otto-von-Guericke University Magdeburg, 39016 Magdeburg, Germany

2. Faculty of Computer Science, HSE University, 101000 Moscow, Russia

3. Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow, Russia

Abstract

This article completes our studies on the formal construction of asymptotic approximations for statistics based on a random number of observations. Second order Chebyshev–Edgeworth expansions of asymptotically normally or chi-squared distributed statistics from samples with negative binomial or Pareto-like distributed random sample sizes are obtained. The results can have applications for a wide spectrum of asymptotically normally or chi-square distributed statistics. Random, non-random, and mixed scaling factors for each of the studied statistics produce three different limit distributions. In addition to the expected normal or chi-squared distributions, Student’s t-, Laplace, Fisher, gamma, and weighted sums of generalized gamma distributions also occur.

Funder

Magdeburg University

Moscow Center for Fundamental and Applied Mathematics, Lomonosov Moscow State University

HSE University

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Reference39 articles.

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