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

Gerd Christoph () and Vladimir V. Ulyanov
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Gerd Christoph: Department of Mathematics, Otto-von-Guericke University Magdeburg, 39016 Magdeburg, Germany
Vladimir V. Ulyanov: Faculty of Computer Science, HSE University, 101000 Moscow, Russia

Mathematics, 2023, vol. 11, issue 8, 1-18

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.

Keywords: second order Chebyshev–Edgeworth expansions; negative binomially distributed sample sizes; Pareto-like distributed sample sizes; asymptotically normally distributed statistics; asymptotically chi-square distributed statistics; scaled Student’s t-distribution; normal distribution; discrete Pareto distribution; generalized Laplace distribution; weighted sums of generalized gamma distributions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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