A Bootstrap Test for the Probability of Ruin in the Compound Poisson Risk Process

In this article we propose a bootstrap test for the probability of ruin in the compound Poisson risk process. We adopt the P-value approach, which leads to a more complete assessment of the underlying risk than the probability of ruin alone. We provide second-order accurate P-values for this testing problem and consider both parametric and nonparametric estimators of the individual claim amount distribution. Simulation studies show that the suggested bootstrap P-values are very accurate and outperform their analogues based on the asymptotic normal approximation.

Toll-like receptor 2 is highly expressed in lesions of acne inversa and colocalizes with C-type lectin receptor

BACKGROUND: Acne inversa (hidradenitis suppurativa) is a chronic inflammatory and cicatricial disorder that affects skin areas rich in apocrine glands and terminal hairs, such as perineum and axillae. The exact pathogenesis of the disease is not well understood and the mechanisms by which bacterial superinfection contributes to the disease progression are not clear. Toll-like receptors (TLRs) expressed by inflammatory cells play a crucial role in the innate immune response to bacteria. OBJECTIVES: We sought to investigate the role of TLR2 in the pathogenesis of acne inversa. METHODS: We investigated the expression of TLR2 using real-time polymerase chain reaction analysis and immunohistochemical stainings of tissue samples from patients with acne inversa. Furthermore, we phenotypically characterized the infiltrating cells and their expression of TLR2. RESULTS: Compared with normal skin, a highly increased in situ expression of TLR2 in acne inversa skin lesions was found at both the mRNA and the protein level. The most abundant cells in the dermal infiltrate of acne inversa were CD68+ macrophages, CD209+ dendritic cells (DCs) and CD3+ T cells. CD19+ B cells and CD56+ natural killer cells were found only in small numbers. Double staining with fluorescence-labelled antibodies showed that TLR2 was expressed by infiltrating macrophages (CD68+) and DCs (CD209+). Flow cytometric analysis of isolated infiltrating cells further confirmed surface expression of TLR2 by macrophages and DCs. CONCLUSIONS: These data indicate that the enhanced expression of TLR2 by infiltrating macrophages and DCs may contribute to the pathogenesis of inflammatory lesions of acne inversa.

Human beta-defensin-2 and psoriasin are overexpressed in lesions of acne inversa

BACKGROUND: Acne inversa is a chronic inflammatory disorder of apocrine gland-bearing skin. The role of the innate immune system in the pathogenesis of the disease is controversial. OBJECTIVES: We investigated the expression of antimicrobial peptide/proteins in acne inversa. METHODS: Tissue samples were obtained from patients with acne inversa and compared with normal-appearing skin. The expression of psoriasin and human beta-defensin (hBD)-2 on messenger RNA and protein level was analyzed. RESULTS: Both messenger RNA and protein levels of psoriasin and hBD-2 were significantly increased in acne inversa. Macrophages expressing hBD-2 were found in the dermis. LIMITATIONS: Small sample size is a limitation. CONCLUSIONS: Antimicrobial peptide/proteins are overexpressed in acne inversa lesions as compared with normal-appearing skin. The site of the major expression depends on the particular antimicrobial peptide/protein. Psoriasin is overexpressed in epidermal keratinocytes whereas hBD-2 is produced mainly by dermal macrophages, leaving a relative deficiency of hBD-2 in the epidermis of acne inversa lesions.

Non-exponential return time distributions for vorticity extremes explained by fractional Poisson processes

Serial correlation of extreme midlatitude cyclones observed at the storm track exits is explained by deviations from a Poisson process. To model these deviations, we apply fractional Poisson processes (FPPs) to extreme midlatitude cyclones, which are defined by the 850 hPa relative vorticity of the ERA interim reanalysis during boreal winter (DJF) and summer (JJA) seasons. Extremes are defined by a 99% quantile threshold in the grid-point time series. In general, FPPs are based on long-term memory and lead to non-exponential return time distributions. The return times are described by a Weibull distribution to approximate the Mittag–Leffler function in the FPPs. The Weibull shape parameter yields a dispersion parameter that agrees with results found for midlatitude cyclones. The memory of the FPP, which is determined by detrended fluctuation analysis, provides an independent estimate for the shape parameter. Thus, the analysis exhibits a concise framework of the deviation from Poisson statistics (by a dispersion parameter), non-exponential return times and memory (correlation) on the basis of a single parameter. The results have potential implications for the predictability of extreme cyclones.

Multifractional Poisson process, multistable subordinator and related limit theorems

We introduce a multistable subordinator, which generalizes the stable subordinator to the case of time-varying stability index. This enables us to define a multifractional Poisson process. We study properties of these processes and establish the convergence of a continuous-time random walk to the multifractional Poisson process.