Shaul K. Bar‐Lev
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View article: Boundedness of Variance Functions of Natural Exponential Families with Unbounded Support
Boundedness of Variance Functions of Natural Exponential Families with Unbounded Support Open
The variance function (VF) is central to natural exponential family (NEF) theory. Prompted by an online query about whether, beyond the classical normal NEF, other real-line NEFs with bounded VFs exist, we establish three complementary set…
View article: Generalized Linear Model (GLM) Applications for the Exponential Dispersion Model Generated by the Landau Distribution
Generalized Linear Model (GLM) Applications for the Exponential Dispersion Model Generated by the Landau Distribution Open
The exponential dispersion model (EDM) generated by the Landau distribution, denoted by EDM-EVF (exponential variance function), belongs to the Tweedie scale with power infinity. Its density function does not have an explicit form and, as …
View article: Optimal E-Values for Exponential Families: the Simple Case
Optimal E-Values for Exponential Families: the Simple Case Open
We provide a general condition under which e-variables in the form of a simple-vs.-simple likelihood ratio exist when the null hypothesis is a composite, multivariate exponential family. Such `simple' e-variables are easy to compute and ex…
View article: The Exponential Dispersion Model Generated by the Landau Distribution—A Comprehensive Review and Further Developments
The Exponential Dispersion Model Generated by the Landau Distribution—A Comprehensive Review and Further Developments Open
The paper comprehensively studies the natural exponential family and its associated exponential dispersion model generated by the Landau distribution. These families exhibit probabilistic and statistical properties and are suitable for mod…
View article: Cumulant-Based Goodness-of-Fit Tests for the Tweedie, Bar-Lev and Enis Class of Distributions
Cumulant-Based Goodness-of-Fit Tests for the Tweedie, Bar-Lev and Enis Class of Distributions Open
The class of natural exponential families (NEFs) of distributions having power variance functions (NEF-PVFs) is huge (uncountable), with enormous applications in various fields. Based on a characterization property that holds for the cumul…
View article: The Large Arcsine Exponential Dispersion Model—Properties and Applications to Count Data and Insurance Risk
The Large Arcsine Exponential Dispersion Model—Properties and Applications to Count Data and Insurance Risk Open
The large arcsine exponential dispersion model (LAEDM) is a class of three-parameter distributions on the non-negative integers. These distributions show the specific characteristics of being leptokurtic, zero-inflated, overdispersed, and …
View article: A New Class of Counting Distributions Embedded in the Lee–Carter Model for Mortality Projections: A Bayesian Approach
A New Class of Counting Distributions Embedded in the Lee–Carter Model for Mortality Projections: A Bayesian Approach Open
The Lee–Carter model, the dominant mortality projection modeling in the literature, was criticized for its homoscedastic error assumption. This was corrected in extensions to the model based on the assumption that the number of deaths foll…
View article: A Comparative Study of Goodness-of-Fit Tests for the Laplace Distribution
A Comparative Study of Goodness-of-Fit Tests for the Laplace Distribution Open
The Laplace distribution is one of the earliest distributions in probability theory and is a frequently used distribution in many fields. Consequently, various goodness-of-fit tests for the Laplace distribution have been thoroughly derived…
View article: On the Notion of Reproducibility and Its Full Implementation to Natural Exponential Families
On the Notion of Reproducibility and Its Full Implementation to Natural Exponential Families Open
Let F=Fθ:θ∈Θ⊂R be a family of probability distributions indexed by a parameter θ and let X1,⋯,Xn be i.i.d. r.v.’s with L(X1)=Fθ∈F. Then, F is said to be reproducible if for all θ∈Θ and n∈N, there exists a sequence (αn)n≥1 and a mapping gn:…
View article: Exponential dispersion models for overdispersed zero-inflated count data
Exponential dispersion models for overdispersed zero-inflated count data Open
We consider three new classes of exponential dispersion models of discrete probability distributions which are defined by specifying their variance functions in their mean value parameterization. In a previous paper (Bar-Lev and Ridder, 20…
View article: New exponential dispersion models for count data: the ABM and LM classes
New exponential dispersion models for count data: the ABM and LM classes Open
In their fundamental paper on cubic variance functions (VFs), Letac and Mora ( The Annals of Statistics , 1990) presented a systematic, rigorous and comprehensive study of natural exponential families (NEFs) on the real line, their charact…
View article: New exponential dispersion models for count data -- the ABM and LM classes
New exponential dispersion models for count data -- the ABM and LM classes Open
In their fundamental paper on cubic variance functions, Letac and Mora (The Annals of Statistics,1990) presented a systematic, rigorous and comprehensive study of natural exponential families on the real line, their characterization throug…
View article: New exponential dispersion models for count data -- properties and applications
New exponential dispersion models for count data -- properties and applications Open
In their fundamental paper on cubic variance functions (VFs), Letac and Mora (The Annals of Statistics,1990) presented a systematic, rigorous and comprehensive study of natural exponential families (NEFs) on the real line, their characteri…
View article: Independent, Tough Identical Results: The Class of Tweedie on Power Variance Functions and the Class of Bar-Lev and Enis on Reproducible Natural Exponential Families
Independent, Tough Identical Results: The Class of Tweedie on Power Variance Functions and the Class of Bar-Lev and Enis on Reproducible Natural Exponential Families Open
The Rao-Blackwell theorem has had a fundamental role in statistical theory. However, as opposed to what seems natural, Rao and Blackwell did not investigate and write the theorem jointly. In fact, they both published the same result indepe…
View article: Monte Carlo Methods for Insurance Risk Computation
Monte Carlo Methods for Insurance Risk Computation Open
In this paper we consider the problem of computing tail probabilities of the distribution of a random sum of positive random variables. We assume that the individual claim variables follow a reproducible natural exponential family (NEF) di…
View article: Monte Carlo Methods for Insurance Risk Computation
Monte Carlo Methods for Insurance Risk Computation Open
In this paper we consider the problem of computing tail probabilities of the distribution of a random sum of positive random variables. We assume that the individual variables follow a reproducible natural exponential family (NEF) distribu…
View article: A Blood Bank Model with Perishable Blood and Demand Impatience
A Blood Bank Model with Perishable Blood and Demand Impatience Open
We consider a stochastic model for a blood bank, in which amounts of blood are offered and demanded according to independent compound Poisson processes. Blood is perishable, i.e., blood can only be kept in storage for a limited amount of t…
View article: ANALYSIS AND OPTIMIZATION OF BLOOD-TESTING PROCEDURES
ANALYSIS AND OPTIMIZATION OF BLOOD-TESTING PROCEDURES Open
This paper is devoted to the performance analysis and optimization of blood testing procedures. We present a queueing model of two queues in series, representing the two stages of a blood-testing procedure. Service (testing) in stage 1 is …
View article: A Stochastic Approach to Blood Supply, Demand and Screening in Central Blood Banks - A Review
A Stochastic Approach to Blood Supply, Demand and Screening in Central Blood Banks - A Review Open
One of the major issues in securing blood supply to patients worldwide is to provide blood of the best achievable quality, in the needed quantities. Central Blood Services (CBS’s) worldwide are daily faced with the problem how to sat…
View article: The Kendal- Ressel Exponential Dispersion Model: Some Statistical Aspects and Estimation
The Kendal- Ressel Exponential Dispersion Model: Some Statistical Aspects and Estimation Open
In this paper we revisit the NEF class of distributions generated by the Kendall-Ressel density. We study some of the statistical properties of this class (KR-NEF), as well as those of an associated class of Exponential Dispersion Model (K…
View article: A Numerical Study of Small Parameter Behavior of Some Families of Distributions
A Numerical Study of Small Parameter Behavior of Some Families of Distributions Open
Limiting distributions play an important role in approximating the exact distributions, especially when they have a rather cumbersome analytic form, or simply when they do not have a closed from. The question that naturally arises is how g…
View article: When does the minimum of a sample of an exponential family belong to an exponential family?
When does the minimum of a sample of an exponential family belong to an exponential family? Open
It is well known that if $({X}_{1},...,{X}_{n})$ are i.i.d. r.v.'s taken from either the exponential distribution or the geometric one, then the distribution of $\\min({X}_{1},...,{X}_{n})$ is, with a change of parameter, is also exponenti…