On convergence of the distributions of statistics with random sample sizes to normal variance-mean mixtures

2014/10/04 by V. Yu. Korolev, Korolev, V. Yu., Alexander Zeifman +1
Computer Science · Economics, Econometrics and Finance · #Bayesian Methods and Mixture Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1410.1518

openalex publication_date 2014/10/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove a general transfer theorem for multivariate random sequences with independent random indexes in the double array limit setting. We also prove its partial inverse providing necessary and sufficient conditions for the convergence of randomly indexed random sequences. Special attention is paid to the case where the elements of the basic double array are formed as statistics constructed from samples with random sizes. Under rather natural conditions we prove the theorem on convergence of the distributions of such statistics to normal variance-mean mixtures.

Citations

• The Variance Gamma (V.G.) Model for Share Market Returns
• Normal Variance-Mean Mixtures and z Distributions
• On convergence of the distributions of random sequences with independent random indexes to variance-mean mixtures

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