Convergence and inference for mixed Poisson random sums

@article{Oliveira2020ConvergenceAI,
  title={Convergence and inference for mixed Poisson random sums},
  author={Gabriela Oliveira and Wagner Barreto‐Souza and Roger W. C. Silva},
  journal={arXiv: Probability},
  year={2020}
}
In this paper we obtain the limit distribution for partial sums with a random number of terms following a class of mixed Poisson distributions. The resulting weak limit is a mixing between a normal distribution and an exponential family, which we call by normal exponential family (NEF) laws. A new stability concept is introduced and a relationship between {\alpha}-stable distributions and NEF laws is established. We propose estimation of the parameters of the NEF models through the method of… Expand
1 Citations

Figures and Tables from this paper

Fractional Poisson random sum and its associated normal variance mixture
In this work, we study the partial sums of independent and identically distributed random variables with the number of terms following a fractional Poisson (FP) distribution. The FP sum contains theExpand

References

SHOWING 1-10 OF 47 REFERENCES
Convergence Rate Estimates in the Global CLT for Compound Mixed Poisson Distributions
Using the estimates of the accuracy of the normal approximation to distributions of Poisson-binomial random sums from [I. G. Shevtsova, Theory Probab. Appl., 62 (2018), pp. 278--294], we obtainExpand
General mixed Poisson regression models with varying dispersion
A general class of mixed Poisson regression models is introduced. This class is based on a mixing between the Poisson distribution and a distribution belonging to the exponential family. With this,Expand
Generalized negative binomial distributions as mixed geometric laws and related limit theorems*
In this paper we study a wide and flexible family of discrete distributions, the so-called generalized negative binomial (GNB) distributions that are mixed Poisson distributions in which the mixingExpand
Bounds of the accuracy of the normal approximation to the distributions of random sums under relaxed moment conditions∗
We improve bounds of accuracy of the normal approximation to the distribution of a sum of independent random variables under relaxed moment conditions, in particular, under the absence of moments ofExpand
Weak convergence to the Student and Laplace distributions
TLDR
A limit law for normalized random means is proposed that exhibits such heavy tails irrespective of the distribution of the underlying sampling units: the limit is a t-distribution if the random variables have finite variances. Expand
On convergence of the distributions of random sequences with independent random indexes to variance–mean mixtures
ABSTRACT We prove a transfer theorem for random sequences with independent random indexes in the double array limit setting under relaxed conditions. We also prove its partial inverse providing theExpand
On Convergence of the Distributions of Random Sequences with Independent Random Indexes to Variance-Mean Mixtures
We prove a version of a general transfer theorem for random sequences with independent random indexes in the double array limit setting under relaxed conditions. We also prove its partial inverseExpand
On normal variance–mean mixtures as limit laws for statistics with random sample sizes
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 necessaryExpand
Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling
The normal inverse Gaussian distribution is defined as a variance-mean mixture of a normal distribution with the inverse Gaussian as the mixing distribution. The distribution determines anExpand
The theory of geometric stable distributions and its use in modeling financial data
Abstract It is commonly accepted that stable distributions do provide useful models for asset returns. To accomodate the possibility of market crashes, we preserve the stability of stock priceExpand
...
1
2
3
4
5
...