A note on residual allocation models

Residual allocation models (RAMs) arise in many subjects including Bayesian statistics, combinatorics, ecology, finance, information theory, machine learning, and population genetics. In this paper, we give a brief review of RAM and presents a few examples where the model arises. An extended discussion will focus a concrete model, the GEM distribution, and its ordered analogue, the Poisson-Dirichlet distribution. The paper concludes with a discussion of the GEM process.     

INFLUENCE OF THERMAL TREATMENTS ON THE POLYMORPHISM IN STEREOIRREGULAR ISOTACTIC POLYPROPYLENE: EFFECT OF STEREO-DEFECT DISTRIBUTION

The influence of cooling rate from the melt on the polymorphism and crystallinity is investigated as a function of isotacticity and stereo-defect distribution in polypropylenes. Detailed analysis of wide angle x-ray diffraction patterns shows that crystallinity in the materials used is nearly independent of the experimental cooling rates (0.5–40°C/min). At high cooling rates, the materials exist mainly in the α-phase, whereas the amount of the γ-phase increases at the lower cooling rates. With an increasing amount of stereo-defects, this cooling-rate dependence of the polymorphism is enhanced. The effect of different stereo-defect distributions, as observed in metallocene-(random) and Ziegler–Natta (blocklike) derived isotactic polypropylenes, was investigated. The formation of the γ-phase is more prevalent in materials with a random defect distribution compared to the materials in which the stereo-defects have a blocklike distribution. The crystallinity decreases more rapidly as a function of the tacticity in the random defect-distributed materials.     

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In this paper, for a kind of risk models with heavy-tailed and delayed claims, we derive the asymptotics of the infinite-time ruin probability and the uniform asymptotics of the finite-time ruin probability. The numerical simulation results are also presented. The results of theoretical analysis and numerical simulation show that the influence of the delay for the claim payment is nearly negligible to the ruin probability when the initial capital and running-time are all large.     

Kinetics of Ion Transport by Macrocyclic Carriers in Liquid Membrane Systems

Abstract

The relationship between the extractability of a metal ion (K⁺ or Pb²⁺) and the rate of its transfer by neutral macrocyclic carriers (dibenzo-18-crown-6, dicyclo-hexano-18-crown-6, 18-crown-6, and polynactin) was investigated in chloroform membrane systems. The experimentally determined apparent rate constants are compatible with the diffusion-limited process. Both the rate of ion uptake and the rate of ion transport depend crucially on the extractability of the metal ion rather than on the apparent rate constant.     

Intensity‐based estimation of extreme loss event probability and value at risk

We develop a methodology for the estimation of extreme loss event probability and the value at risk, which takes into account both the magnitudes and the intensity of the extreme losses. Specifically, the extreme loss magnitudes are modeled with a generalized Pareto distribution, whereas their intensity is captured by an autoregressive conditional duration model, a type of self‐exciting point process. This allows for an explicit interaction between the magnitude of the past losses and the intensity of future extreme losses. The intensity is further used in the estimation of extreme loss event probability. The method is illustrated and backtested on 10 assets and compared with the established and baseline methods. The results show that our method outperforms the baseline methods, competes with an established method, and provides additional insight and interpretation into the prediction of extreme loss event probability. Copyright © 2012 John Wiley & Sons, Ltd.     

Facile Fabrication of Nanorod‐Assembled Fluorine‐Substituted Hydroxyapatite (FHA) Microspheres

Nanorod‐assembled FHA microspheres with different F contents were for the first time prepared through a facile one‐step hydrothermal method. The effect of the reaction time and pH value of reaction solutions on the FHA morphology was investigated to elucidate the self‐assembly process of FHA microspheres. The results showed pH values had significant effect on the morphology of the formed FHA crystals, which were self‐assembled into sphere‐like sturctures at high pH conditions and rod‐like structures at low pH values. The results suggested that formation of FHA crystals with varied morphology may be directly related to Ca²⁺ release kinetics from EDTA‐Ca‐Na₂ at different pH conditions. Furthermore, it was found that the chemical stability of FHA microspheres was dependent on the F content in the materials, and high F contents in FHA microspheres lead to improved chemical stability. These results suggest that the prepared self‐assembled FHA microspheres may be used for teeth substitution materials due to their unique hierarchical structures and controllable chemical stability.     

Bayesian robustness under a skew-normal class of prior distribution

We develop a global sensitivity analysis to measure the robustness of the Bayesian estimators with respect to a class of prior distributions. This class arises when we consider multiplicative contamination of a base prior distribution. A similar structure was presented by van der Linde [12]. Some particular specifications for this multiplicative contamination class coincide with well known families of skewed distributions. In this paper, we explore the skew-normal multiplicative contamination class for the prior distribution of the location parameter of a normal model. Results of a Bayesian conjugation and expressions for some measures of distance between posterior means and posterior variance are obtained. We also elaborate on the behavior of the posterior means and of the posterior variances through a simulation study.     

Bayesian Estimation for the Order of INAR(q) Mo del

In this paper, we consider the problem of determining the order of INAR(q) model on the basis of the Bayesian estimation theory. The Bayesian es-timator for the order is given with respect to a squared-error loss function. The consistency of the estimator is discussed. The results of a simulation study for the estimation method are presented.     

What can statistical process control show us about ionization chamber stability?

PurposeStatistical process control (SPC) has been shown to be a suitable tool for medical physicists to monitor quality and keep variability low and within specifications. We report our findings regarding ionisation chamber stability in our department when using a radioactive stability check device (RSCD) and we compare them with similar previously published records, including calibration results.MethodsWe retrospectively studied the stability of a PPC 40 parallel-plate chamber, and two Farmer chambers (FC65-G and FC65-P) by checking them with dedicated RSCDs. We analysed the data following SPC methodology which includes plotting I-MR control charts, monitoring out-of-control observations, calculating process capability ratios (C_p), and estimating conformance to specifications. We also estimated the C_p and adherence to specifications of previously published data.ResultsThe PPC40 chamber hardly went out of the control limits over the whole six-year period assessed. However, Farmer chamber verifications drifted in opposite directions in phase II, and the deviations observed did not agree with their calibration records, which only increased by a maximum of 0.5%. In phase I the most unstable chamber was the FC65-P with a C_p equal to 0.9 at a specification level of ±1%. The PPC40 chamber was stable to within a maximum C_p of 1.3. Several sets of analysed data, including ours and those from other authors, fitted well within these limits: within ±1.9% and ±1.5% for a C_p of 1.5 and 1.33 respectively.ConclusionsSPC with constant long-term RSCD checking gave us a meaningful plot of the instability of our ionisation chambers. Although a period of two years between calibrations should not be surpassed, in the interim this check can conform to specifications of ±1.5%.     

A multivariate evolutionary credibility model for mortality improvement rates

The present paper proposes an evolutionary credibility model that describes the joint dynamics of mortality through time in several populations. Instead of modeling the mortality rate levels, the time series of population-specific mortality rate changes, or mortality improvement rates are considered and expressed in terms of correlated time factors, up to an error term. Dynamic random effects ensure the necessary smoothing across time, as well as the learning effect. They also serve to stabilize successive mortality projection outputs, avoiding dramatic changes from one year to the next. Statistical inference is based on maximum likelihood, properly recognizing the random, hidden nature of underlying time factors. Empirical illustrations demonstrate the practical interest of the approach proposed in the present paper.