On the small-time behavior of subordinators

We prove several results on the behavior near t=0 of $Y_t^{-t}$ for certain $(0,\infty)$-valued stochastic processes $(Y_t)_{t>0}$. In particular, we show for L\'{e}vy subordinators that the Pareto law on $[1,\infty)$ is the only possible weak limit and provide necessary and sufficient conditions for the convergence. More generally, we also consider the weak convergence of $tL(Y_t)$ as $t\to0$ for a decreasing function $L$ that is slowly varying at zero. Various examples demonstrating the applicability of the results are presented.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ363 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

New exponential dispersion models for count data -- the ABM and LM classes

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 through their variance functions and mean value parameterization. They presented a section that for some reason has been left unnoticed. This section deals with the construction of variance functions associated with natural exponential families of counting distributions on the set of nonnegative integers and allows to find the corresponding generating measures. As exponential dispersion models are based on natural exponential families, we introduce in this paper two new classes of exponential dispersion models based on their results. For these classes, which are associated with simple variance functions, we derive their mean value parameterization and their associated generating measures. We also prove that they have some desirable properties. Both classes are shown to be overdispersed and zero-inflated in ascending order, making them as competitive statistical models for those in use in both, statistical and actuarial modeling. To our best knowledge, the classes of counting distributions we present in this paper, have not been introduced or discussed before in the literature. To show that our classes can serve as competitive statistical models for those in use (e.g., Poisson, Negative binomial), we include a numerical example of real data. In this example, we compare the performance of our classes with relevant competitive models.Comment: 27 pages, 4 tables, 3 figure

Cumulant-Based Goodness-of-Fit Tests for the Tweedie, Bar-Lev and Enis Class of Distributions

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 cumulants of the members of this class, we developed a novel goodness-of-fit (gof) test for testing whether a given random sample fits fixed members of this class. We derived the asymptotic null distribution of the test statistic and developed an appropriate bootstrap scheme. As the content of the paper is mainly theoretical, we exemplify its applicability to only a few elements of the NEF-PVF class, specifically, the gamma and modified Bessel-type NEFs. A Monte Carlo study was executed for examining the performance of both—the asymptotic test and the bootstrap counterpart—in controlling the type I error rate and evaluating their power performance in the special case of gamma, while real data examples demonstrate the applicability of the gof test to the modified Bessel distribution

MTADV 5-MER peptide suppresses chronic inflammations as well as autoimmune pathologies and unveils a new potential target-Serum Amyloid A.

Despite the existence of potent anti-inflammatory biological drugs e.g., anti-TNF and anti IL-6 receptor antibodies, for treating chronic inflammatory and autoimmune diseases, these are costly and not specific. Cheaper oral available drugs remain an unmet need. Expression of the acute phase protein Serum Amyloid A (SAA) is dependent on release of pro-inflammatory cytokines IL-1, IL-6 and TNF-α during inflammation. Conversely, SAA induces pro-inflammatory cytokine secretion, including Th17, leading to a pathogenic vicious cycle and chronic inflammation. 5- MER peptide (5-MP) MTADV (methionine-threonine-alanine-aspartic acid-valine), also called Amilo-5MER, was originally derived from a sequence of a pro-inflammatory CD44 variant isolated from synovial fluid of a Rheumatoid Arthritis (RA) patient. This human peptide displays an efficient anti-inflammatory effects to ameliorate pathology and clinical symptoms in mouse models of RA, Inflammatory Bowel Disease (IBD) and Multiple Sclerosis (MS). Bioinformatics and qRT-PCR revealed that 5-MP, administrated to encephalomyelytic mice, up-regulates genes contributing to chronic inflammation resistance. Mass spectrometry of proteins that were pulled down from an RA synovial cell extract with biotinylated 5-MP, showed that it binds SAA. 5-MP disrupted SAA assembly, which is correlated with its pro-inflammatory activity. The peptide MTADV (but not scrambled TMVAD) significantly inhibited the release of pro-inflammatory cytokines IL-6 and IL-1β from SAA-activated human fibroblasts, THP-1 monocytes and peripheral blood mononuclear cells. 5-MP suppresses the pro-inflammatory IL-6 release from SAA-activated cells, but not from non-activated cells. 5-MP could not display therapeutic activity in rats, which are SAA deficient, but does inhibit inflammations in animal models of IBD and MS, both are SAA-dependent, as shown by others in SAA knockout mice. In conclusion, 5-MP suppresses chronic inflammation in animal models of RA, IBD and MS, which are SAA-dependent, but not in animal models, which are SAA-independent

The Large Arcsine Exponential Dispersion Model - Properties and Applications to Count Data and Insurance Risk

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 skewed to the right. Therefore, these distributions are well suited to fit count data with these properties. Furthermore, recent studies in actuarial sciences argue for the consideration of such distributions in the computation of risk factors. In this paper, we provide a thorough analysis of the LAEDM by deriving (a) the mean value parameterization of the LAEDM; (b) exact expressions for its probability mass function at n=0,1,…; (c) a simple bound for these probabilities that is sharp for large n; (d) a simulation algorithm for sampling from LAEDM. We have implemented the LAEDM for statistical modeling of various real count data sets. We assess its fitting performance by comparing it with the performances of traditional counting models. We use a simulation algorithm for computing tail probabilities of the aggregated claim size in an insurance risk model

New exponential dispersion models for count data: the ABM and LM classes

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 characterization through their VFs and mean value parameterization. They presented a section that for some reason has been left unnoticed. This section deals with the construction of VFs associated with NEFs of counting distributions on the set of nonnegative integers and allows to find the corresponding generating measures. As EDMs are based on NEFs, we introduce in this paper two new classes of EDMs based on their results. For these classes, which are associated with simple VFs, we derive their mean value parameterization and their associated generating measures. We also prove that they have some desirable properties. Both classes are shown to be overdispersed and zero inflated in ascending order, making them as competitive statistical models for those in use in both, statistical and actuarial modeling. To our best knowledge, the classes of counting distributions we present in this paper, have not been introduced or discussed before in the literature. To show that our classes can serve as competitive statistical models for those in use (e.g., Poisson, Negative binomial), we include a numerical example of real data. In this example, we compare the performance of our classes with relevant competitive models