Related papers: Mixed Poisson families with real-valued mixing dis…
We construct an example of a continuous centered random process with light tails of finite-dimensional distribution but with heavy tail of maximum distribution.
Understanding the shape of a distribution of data is of interest to people in a great variety of fields, as it may affect the types of algorithms used for that data. We study one such problem in the framework of distribution property…
This paper describes a compound Poisson-based random effects structure for modeling zero-inflated data. Data with large proportion of zeros are found in many fields of applied statistics, for example in ecology when trying to model and…
We propose in this paper a random intercept Poisson model in which the random effect distribution is assumed to follow a generalized log-gamma (GLG) distribution. We derive the first two moments for the marginal distribution as well as the…
A new two-parameter discrete distribution, namely the PoiG distribution is derived by the convolution of a Poisson variate and an independently distributed geometric random variable. This distribution generalizes both the Poisson and…
It has been shown that some macroeconomic time series, especially those where outliers could be present, can be well modelled using heavy tailed distributions for the noise components. Methods for deciding when and where heavy-tailed models…
It is generally known that counting statistics is not correctly described by a Gaussian approximation. Nevertheless, in neutron scattering, it is common practice to apply this approximation to the counting statistics; also at low counting…
A new family of tree-structured Markov random fields for a vector of discrete counting random variables is introduced. According to the characteristics of the family, the marginal distributions of the Markov random fields are all Poisson…
The term "moderate deviations" is often used in the literature to mean a class of large deviation principles that, in some sense, fill the gap between a convergence in probability to zero (governed by a large deviation principle) and a weak…
We consider moderately trimmed sums of non-negative i.i.d. random variables. We show that for every distribution function there exists a proper moderate trimming such that for the trimmed sum a non-trivial strong law of large numbers holds.…
We study the fundamental task of outlier-robust mean estimation for heavy-tailed distributions in the presence of sparsity. Specifically, given a small number of corrupted samples from a high-dimensional heavy-tailed distribution whose mean…
The solution of $ X=AX+1 $ is analyzed for a discrete variable $ A $ with $ \mathbb{P}\left[A=0\right]>0 $. Accordingly, a fast algorithm is presented to calculate the obtained heavy tail density. To exemplify, the compound product…
Probability distributions having power-law tails are observed in a broad range of social, economic, and biological systems. We describe here a potentially useful common framework. We derive distribution functions $\{p_k\}$ for situations in…
The exact expression for the probability density $p_{_N}(x)$ for sums of a finite number $N$ of random independent terms is obtained. It is shown that the very tail of $p_{_N}(x)$ has a Gaussian form if and only if all the random terms are…
The presence of non-Gaussian tails is a prevalent characteristic in many financial modeling scenarios, necessitating the use of complex non-Gaussian distributions such as the generalized beta of the second kind (GB2) and the skewed…
We propose new goodness-of-fit tests for the Poisson distribution. The testing procedure entails fitting a weighted Poisson distribution, which has the Poisson as a special case, to observed data. Based on sample data, we calculate an…
In every finite mixture of different normal distributions, there will always be exactly one of those distributions that not only is over-represented in the right tail of the mixture, but even completely overwhelms all other subpopulations…
This paper proposes a new method to combine several densities such that each density dominates a separate part of a joint distribution. The method is fully unsupervised, i.e. the parameters in the densities and the thresholds are…
Often, it is required to estimate the probability that a quantity such as toxicity level, plutonium, temperature, rainfall, damage, wind speed, wave size, earthquake magnitude, risk, etc., exceeds an unsafe high threshold. The probability…
For purposes of Value-at-Risk estimation, we consider several multivariate families of heavy-tailed distributions, which can be seen as multidimensional versions of Paretian stable and Student's t distributions allowing different marginals…