Compound Poisson approximation
Copyright policy )Compound Poisson approximation
Compound Poisson approximation appears naturally in situations where one deals with a large number of rare events. In this paper, results on the topic of compound approximation to the distribution of a sum of (possibly dependent) random variables are reviewed, and a number of open problems and directions of future research are indicated.
- Vilnius University Lithuania
- Vilnius University Lithuania
- University of London United Kingdom
total variation distance, Sums of independent random variables; random walks, Asymptotic distribution theory in statistics, compound Poisson approximation, Central limit and other weak theorems, Gini-Kantorovich distance, Processes with independent increments; Lévy processes, Approximations to statistical distributions (nonasymptotic), Extreme value theory; extremal stochastic processes, Compound Poisson approximation, Inequalities; stochastic orderings, Point processes (e.g., Poisson, Cox, Hawkes processes), Kolmogorov's problem, signed compound Poisson measure
total variation distance, Sums of independent random variables; random walks, Asymptotic distribution theory in statistics, compound Poisson approximation, Central limit and other weak theorems, Gini-Kantorovich distance, Processes with independent increments; Lévy processes, Approximations to statistical distributions (nonasymptotic), Extreme value theory; extremal stochastic processes, Compound Poisson approximation, Inequalities; stochastic orderings, Point processes (e.g., Poisson, Cox, Hawkes processes), Kolmogorov's problem, signed compound Poisson measure
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