Compound Poisson approximation
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Publication:2135729
DOI10.1214/22-PS8zbMath1489.60029OpenAlexW4285283751MaRDI QIDQ2135729
Vydas Čekanavičius, Serguei Novak
Publication date: 9 May 2022
Published in: Probability Surveys (Search for Journal in Brave)
Full work available at URL: https://projecteuclid.org/journals/probability-surveys/volume-19/issue-none/Compound-Poisson-approximation/10.1214/22-PS8.full
compound Poisson approximationtotal variation distancesigned compound Poisson measureKolmogorov's problemGini-Kantorovich distance
Processes with independent increments; Lévy processes (60G51) Asymptotic distribution theory in statistics (62E20) Inequalities; stochastic orderings (60E15) Central limit and other weak theorems (60F05) Extreme value theory; extremal stochastic processes (60G70) Sums of independent random variables; random walks (60G50) Approximations to statistical distributions (nonasymptotic) (62E17) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)
Cites Work
- Two Uniform Limit Theorems for Sums of Independent Random Variables
- On the Approximation of Polynomial Distributions by Infinitely Divisible Laws
- Approximation of Binomial Distributions by Infinitely Divisible Ones
- On the Rate of Convergence in Kolmogorov’s Second Uniform Limit Theorem
- On the Accuracy of Approximation of Distributions of Sums of Independent Random Variables—Which are Nonzero with a Small Probability—By Means of Accompanying Laws
- Approximation of sums by compound Poisson distributions with respect to stop-loss distances
- On Negative Binomial Approximation to k-Runs
- Rate of Convergence to Poisson Law in Terms of Information Divergence
- A Poisson-Type Limit Theorem for the Number of Pairs of Matching Sequences
- Some notes on poisson limits for empirical point processes
- The Monge–Kantorovich Mass Transference Problem and Its Stochastic Applications
- Approximation in Variation of the Distribution of a Sum of Independent Bernoulli Variables with a Poisson Law
- Maxima and exceedances of stationary Markov chains
- On the Uniform Approximation of Distributions of Sums of Independent Random Variables
- Approximation of quadratic forms of independent random vectors by accompanying laws
- On the Approximation of n-Fold Convolutions of Distributions having Non-Negative Characteristic Functions with Accompanying Laws
- Some Properties of N-Fold Convolutions of Distributions
- On the limit of the Markov binomial distribution
- On the Convergence Rate in Kolmogorov’s Uniform Limit Theorem. II
- On the Rate of Approach of the Distributions of Sums of Independent Random Variables to Accompanying Distributions
- On a Multidimensional Version of the Kolmogorov Uniform Limit Theorem
- Calculation of the Wasserstein Distance Between Probability Distributions on the Line
- Estimates in Total Variation for Convolutions of Compound Distributions
- Poisson perturbations
- Compound Poisson limit theorems for Markov chains
- Asymptotic Expansions in the Exponent: a Compound Poisson Approach
- Compound Poisson approximations for sums of discrete nonlattice variables
- Estimate of the Accuracy of the Compound Poisson Approximation for the Distribution of the Number of Matching Patterns
- Kerstan's Method in the Multivariate Poisson Approximation: An Expansion in the Exponent
- On the Minimal Condition of Weak Dependency in the Central Limit Theorem for Stationary Sequences
- Infinitely divisible approximations for discrete nonlattice variables
- Convergence theorems for the lengths of consecutive successes of Markov Bernoulli sequences
- On Compound Poisson Approximations Under Moment Restrictions
- Compound Poisson approximation for the distribution of extremes
- Poisson approximation for (k1, k2)-events via the Stein-Chen method
- Estimates for the Convergence Rate to the Poisson Distribution for Random Sums of Independent Indicators
- Compound Poisson Approximation for Dissociated Random Variables via Stein's Method
- Second-Order Approximation of Random Polygonal Lines in the Donsker-Prokhorov Invariance Principle
- Multidimensional Version of the Second Uniform Limit Theorem of Kolmogorov
- A Note on Dobrushin's Theorem and Couplings in Poisson Approximation in Abelian Groups
- Poisson Approximation via the Convolution with Kornya--Presman Signed Measures
- On Choosing and Bounding Probability Metrics
- Compound Poisson approximations for word patterns under Markovian hypotheses
- On improvements of the order of approximation in the Poisson limit theorem
- On Alternative Approximating Distributions in the Multivariate Version of Kolmogorov's Second Uniform Limit Theorem
- On large deviations for sums of discrete m-dependent random variables
- Lower bound estimates for discrete approximations to sums of weakly dependent random variables
- On moderate deviations in Poisson approximation
- COMPOUND POISSON APPROXIMATION OF THE NUMBER DISTRIBUTION FOR MONOTONE STRINGS OF FIXED LENGTH IN A RANDOM SEQUENCE
- On Negative Binomial Approximation
- Refined total variation bounds in the multivariate and compound Poisson approximation
- Variationsabstand zwischen der Verteilung einer Summe unabhängiger nichtnegativer ganzzahliger Zufallsgrößen und Poissonschen Verteilungen
- An Approximation to the Distribution of Sums by Infinitely Divisible Laws
- Prescribing a System of Random Variables by Conditional Distributions
- Univariate Discrete Distributions
- A Generalization of Poisson's Distribution for Markoff Chains
- Introduction to nonparametric estimation
- On the limiting distribution of extrema
- Sharp constants in the Poisson approximation
- Approximation methods in probability theory
- Approximation of symmetric three-state Markov chain by compound Poisson law
- Approximating dependent rare events
- Compound Poisson approximations for symmetric vectors
- Compound Poisson approximations for sums of 1-dependent random variables. II
- A new method for obtaining sharp compound Poisson approximation error estimates for sums of locally dependent random variables
- On a saddlepoint approximation to the Markov binomial distribution
- Approximation for counts of head runs
- On approximation of Markov binomial distributions
- On limiting cluster size distributions for processes of exceedances for stationary sequences
- Compound Poisson approximations for sums of 1-dependent random variables. I
- A Charlier-Parseval approach to Poisson approximation and its applications
- Compound Poisson and signed compound Poisson approximations to the Markov binomial law
- Compound Poisson approximation via information functionals
- On exceedances of high levels
- Pseudo-binomial approximation to \((k_1, k_2)\)-runs
- Compound Poisson approximation with association or negative association via Stein's method
- Two limit theorems for Markov binomial distribution
- Estimating the parameters of rare events
- Error bounds for the compound Poisson approximation
- Translated Poisson approximation for Markov chains
- On variational bounds in the compound Poisson approximation of the individual risk model
- Approximation with accompanying distributions and asymptotic expansions. I
- Approximation with accompanying laws
- A note on the approximation of the uniform empirical process
- An expansion in the exponent for compound binomial approximations
- Poisson type approximations for the Markov binomial distribution
- Inference for the limiting cluster size distribution of extreme values
- Extremes and related properties of random sequences and processes
- Approximation of aggregate claims distributions by compound Poisson distributions
- Asymptotic expansions in the Poisson limit theorem
- Approximation of distributions of sums of Banach-valued random elements with infinitely divisible laws. I.
- Precision of approximation of the generalized binomial distribution by convolutions of Poisson measures
- Estimates for the closeness of successive convolutions of multidimensional symmetric distributions
- Approximations of distributions of sums of lattice random variables. I
- On the extreme order statistics for a stationary sequence
- Approximation of distributions of sums of Banach-valued random elements by infinitely divisible laws. II
- A compound Poisson convergence theorem
- Approximation of mixture of distributions
- Certain class of nonuniform estimates in multidimensional limit theorems
- Compound Poisson approximation for nonnegative random variables via Stein's method
- Approximation of convolutions of probability distributions by infinitely divisible laws under weakened moment restrictions
- Limit theorems for extreme values of chain-dependent processes
- Weak convergence results for extremal processes generated by dependent random variables
- On signed normal-Poisson approximations
- Asymptotic expansions for generalized Poisson measures
- Approximation of convolutions by accompanying laws under the existence of moments of low orders
- On the approximation by convolution of the generalized Poisson measure and the Gaussian distribution. I
- On some estimates based on sample behavior near high level excursions
- Stein's method for compound Poisson approximation: The local approach
- Generalized Poisson distributions as limits of sums for arrays of dependent random vectors
- Poisson approximation of the partial sum process in Banach spaces
- Approximation of the generalized Poisson binomial distribution: Asymptotic expansions
- Compound Poisson approximations for individual models with dependent risks.
- Moment inequalities connected with accompanying Poisson laws in Abelian groups
- On Ch. Jordan's series for probability
- Signed Poisson approximation: A possible alternative to normal and Poisson laws
- Concentration functions and the accuracy of approximation by infinitely divisible laws in a Hilbert space
- On the number of overflown urns and excess balls in an allocation model with limited urn capacity
- Compound Poisson approximation in total variation
- Signed Poisson approximations for Markov chains
- On closeness of two discrete weighted sums
- Infinitely divisible approximations for sums of \(m\)-dependent random variables
- Approximation of distributions of integral additive functions by discrete charges. I
- Compound Poisson approximation for multiple runs in a Markov chain
- Stein's method and birth-death processes
- Total variation asymptotics for sums of independent integer random variables
- Poisson approximation for expectations of unbounded functions of independent random variables
- Compound Poisson approximation: A user's guide
- Local theorems for the Markov binomial distribution
- Compound Poisson approximation for counts of rare patterns in Markov chains and extreme sojourns in birth-death chains.
- Non-uniform theorems for discrete measures
- Compound Poisson approximation for unbounded functions on a group, with application to large deviations
- On asymptotic expansions in the first uniform Kolmogorov theorem
- On multivariate Le Cam theorem and compound Poisson measures
- Strong Poisson and mixed approximations of sums of independent random variables in Banach spaces
- Improved bounds for approximations to compound distributions
- Asymptotic expansions in the compound Poisson limit theorem
- Poisson approximation in terms of the Gini-Kantorovich distance
- Rare events and Poisson point processes
- Monotonicity properties of the Poisson approximation to the binomial distribution
- An improved multivariate version of Kolmogorov's second uniform limit theorem
- Compound Poisson approximation to weighted sums of symmetric discrete variables
- Smoothing effect of compound Poisson approximations to the distributions of weighted sums
- On the accuracy of Poisson approximation
- Poisson approximation
- Stein's method for conditional compound Poisson approximation
- Stein factors for negative binomial approximation in Wasserstein distance
- Improved lower bounds on the total variation distance for the Poisson approximation
- On Hipp's compound Poisson approximations via concentration functions
- On mass transportation
- Approximation of a sample by a Poisson point process
- An approximation theorem for the Poisson binomial distribution
- A shorter proof of Kanter's Bessel function concentration bound
- Sur la distribution limite du terme maximum d'une série aléatoire
- Compound Poisson approximation for long increasing sequences
- A New Markov Binomial Distribution
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