Estimation of parametric and nonparametric models for univariate claim severity distributions - an approach using R

This paper presents an analysis of motor vehicle insurance claims relating to vehicle damage and to associated medical expenses. We use univariate severity distributions estimated with parametric and non-parametric methods. The methods are implemented using the statistical package R. Parametric analysis is limited to estimation of normal and lognormal distributions for each of the two claim types. The nonparametric analysis presented involves kernel density estimation. We illustrate the benefits of applying transformations to data prior to employing kernel based methods. We use a log-transformation and an optimal transformation amongst a class of transformations that produces symmetry in the data. The central aim of this paper is to provide educators with material that can be used in the classroom to teach statistical estimation methods, goodness of fit analysis and importantly statistical computing in the context of insurance and risk management. To this end, we have included in the Appendix of this paper all the R code that has been used in the analysis so that readers, both students and educators, can fully explore the techniques described

Probability of achieving optimal molecular response to imatinib in chronic myeloid leukemia (CML) patients: Pharmacokinetic/Pharmacodynamic (PK/PD) relationships observed under field-conditions

Objectives: Imatinib has been increasingly proposed for therapeutic drug monitoring (TDM), as trough concentrations (Cmin) correlate with response rates in CML patients. This analysis aimed to evaluate the impact of imatinib exposure on optimal molecular response rates in a large European cohort of patients followed by centralized TDM.¦Methods: Sequential PK/PD analysis was performed in NONMEM 7 on 2230 plasma (PK) samples obtained along with molecular response (PD) data from 1299 CML patients. Model-based individual Bayesian estimates of exposure, parameterized as to initial dose adjusted and log-normalized Cmin (log-Cmin) or clearance (CL), were investigated as potential predictors of optimal molecular response, while accounting for time under treatment (stratified at 3 years), gender, CML phase, age, potentially interacting comedication, and TDM frequency. PK/PD analysis used mixed-effect logistic regression (iterative two-stage method) to account for intra-patient correlation.¦Results: In univariate analyses, CL, log-Cmin, time under treatment, TDM frequency, gender (all p<0.01) and CML phase (p=0.02) were significant predictors of the outcome. In multivariate analyses, all but log-Cmin remained significant (p<0.05). Our model estimates a 54.1% probability of optimal molecular response in a female patient with a median CL of 14.4 L/h, increasing by 4.7% with a 35% decrease in CL (percentile 10 of CL distribution), and decreasing by 6% with a 45% increased CL (percentile 90), respectively. Male patients were less likely than female to be in optimal response (odds ratio: 0.62, p<0.001), with an estimated probability of 42.3%.¦Conclusions: Beyond CML phase and time on treatment, expectedly correlated to the outcome, an effect of initial imatinib exposure on the probability of achieving optimal molecular response was confirmed in field-conditions by this multivariate analysis. Interestingly, male patients had a higher risk of suboptimal response, which might not exclusively derive from their 18.5% higher CL, but also from reported lower adherence to the treatment. A prospective longitudinal study would be desirable to confirm the clinical importance of identified covariates and to exclude biases possibly affecting this observational survey.

Universality of rain event size distributions

We compare rain event size distributions derived from measurements in climatically different regions, which we find to be well approximated by power laws of similar exponents over broad ranges. Differences can be seen in the large-scale cutoffs of the distributions. Event duration distributions suggest that the scale-free aspects are related to the absence of characteristic scales in the meteorological mesoscale.

A parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics

This paper discusses the use of probabilistic or randomized algorithms for solving combinatorial optimization problems. Our approach employs non-uniform probability distributions to add a biased random behavior to classical heuristics so a large set of alternative good solutions can be quickly obtained in a natural way and without complex conguration processes. This procedure is especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods, both of exact and approximate nature, may fail to reach their full potential. The results obtained are promising enough to suggest that randomizing classical heuristics is a powerful method that can be successfully applied in a variety of cases.

Population genetic structure and demography analysis in palinurus elephas populations from atlantic and mediterranean waters

Report for the scientific sojourn at the University of Reading, United Kingdom, from January until May 2008. The main objectives have been firstly to infer population structure and parameters in demographic models using a total of 13 microsatellite loci for genotyping approximately 30 individuals per population in 10 Palinurus elephas populations both from Mediterranean and Atlantic waters. Secondly, developing statistical methods to identify discrepant loci, possibly under selection and implement those methods using the R software environment. It is important to consider that the calculation of the probability distribution of the demographic and mutational parameters for a full genetic data set is numerically difficult for complex demographic history (Stephens 2003). The Approximate Bayesian Computation (ABC), based on summary statistics to infer posterior distributions of variable parameters without explicit likelihood calculations, can surmount this difficulty. This would allow to gather information on different demographic prior values (i.e. effective population sizes, migration rate, microsatellite mutation rate, mutational processes) and assay the sensitivity of inferences to demographic priors by assuming different priors.

Break zones in the distributions of alleles and species in alpine plants

Aim  We test for the congruence between allele-based range boundaries (break zones) in silicicolous alpine plants and species-based break zones in the silicicolous flora of the European Alps. We also ask whether such break zones coincide with areas of large elevational variation.Location  The European Alps.Methods  On a regular grid laid across the entire Alps, we determined areas of allele- and species-based break zones using respective clustering algorithms, identifying discontinuities in cluster distributions (breaks), and quantifying integrated break densities (break zones). Discontinuities were identified based on the intra-specific genetic variation of 12 species and on the floristic distribution data from 239 species, respectively. Coincidence between the two types of break zones was tested using Spearman's correlation. Break zone densities were also regressed on topographical complexity to test for the effect of elevational variation.Results  We found that two main break zones in the distribution of alleles and species were significantly correlated. Furthermore, we show that these break zones are in topographically complex regions, characterized by massive elevational ranges owing to high mountains and deep glacial valleys. We detected a third break zone in the distribution of species in the eastern Alps, which is not correlated with topographic complexity, and which is also not evident from allelic distribution patterns. Species with the potential for long-distance dispersal tended to show larger distribution ranges than short-distance dispersers.Main conclusions  We suggest that the history of Pleistocene glaciations is the main driver of the congruence between allele-based and species-based distribution patterns, because occurrences of both species and alleles were subject to the same processes (such as extinction, migration and drift) that shaped the distributions of species and genetic lineages. Large elevational ranges have had a profound effect as a dispersal barrier for alleles during post-glacial immigration. Because plant species, unlike alleles, cannot spread via pollen but only via seed, and thus disperse less effectively, we conclude that species break zones are maintained over longer time spans and reflect more ancient patterns than allele break zones.Conny Thiel-Egenter and Nadir Alvarez contributed equally to this paper and are considered joint first authors.

Activity in inferior parietal and medial prefrontal cortex signals the accumulation of evidence in a probability learning task.

In an uncertain environment, probabilities are key to predicting future events and making adaptive choices. However, little is known about how humans learn such probabilities and where and how they are encoded in the brain, especially when they concern more than two outcomes. During functional magnetic resonance imaging (fMRI), young adults learned the probabilities of uncertain stimuli through repetitive sampling. Stimuli represented payoffs and participants had to predict their occurrence to maximize their earnings. Choices indicated loss and risk aversion but unbiased estimation of probabilities. BOLD response in medial prefrontal cortex and angular gyri increased linearly with the probability of the currently observed stimulus, untainted by its value. Connectivity analyses during rest and task revealed that these regions belonged to the default mode network. The activation of past outcomes in memory is evoked as a possible mechanism to explain the engagement of the default mode network in probability learning. A BOLD response relating to value was detected only at decision time, mainly in striatum. It is concluded that activity in inferior parietal and medial prefrontal cortex reflects the amount of evidence accumulated in favor of competing and uncertain outcomes.

Predicting reptile distributions at the mesoscale: relation to climate and topography

Aim To explore the respective power of climate and topography to predict the distribution of reptiles in Switzerland, hence at a mesoscale level. A more detailed knowledge of these relationships, in combination with maps of the potential distribution derived from the models, is a valuable contribution to the design of conservation strategies. Location All of Switzerland. Methods Generalized linear models are used to derive predictive habitat distribution models from eco-geographical predictors in a geographical information system, using species data from a field survey conducted between 1980 and 1999. Results The maximum amount of deviance explained by climatic models is 65%, and 50% by topographical models. Low values were obtained with both sets of predictors for three species that are widely distributed in all parts of the country (Anguis fragilis , Coronella austriaca , and Natrix natrix), a result that suggests that including other important predictors, such as resources, should improve the models in further studies. With respect to topographical predictors, low values were also obtained for two species where we anticipated a strong response to aspect and slope, Podarcis muralis and Vipera aspis . Main conclusions Overall, both models and maps derived from climatic predictors more closely match the actual reptile distributions than those based on topography. These results suggest that the distributional limits of reptile species with a restricted range in Switzerland are largely set by climatic, predominantly temperature-related, factors.

Bats of Borneo: diversity, distributions and representation in protected areas

Protected areas are valuable in conserving tropical biodiversity, but an insufficient understanding of species diversity and distributions makes it difficult to evaluate their effectiveness. This is especially true on Borneo, a species rich island shared by three countries, and is particularly concerning for bats, a poorly known component of mammal diversity that may be highly susceptible to landscape changes. We reviewed the diversity, distributions and conservation status of 54 bat species to determine the representation of these taxa in Borneo's protected areas, and whether these reserves complement each other in terms of bat diversity. Lower and upper bound estimates of bat species composition were characterised in 23 protected areas and the proposed boundaries of the Heart of Borneo conservation area. We used lower and upper bound estimates of species composition. By using actual inventories, species representation was highly irregular, and even if some reserves were included in the Heart of Borneo, the protected area network would still exhibit low complementarity. By inferring species presence from distributions, composition between most reserves was similar, and complementarity was much higher. Predicting species richness using abundance information suggested that bat species representation in reserves may lie between these two extremes. We recommend that researchers better sample biodiversity over the island and address the conservation threats faced in Borneo both within and outside protected areas. While the Heart of Borneo Initiative is commendable, it should not divert attention from other conservation areas.

Lumbar spine texture enhances 10-year fracture probability assessment.

We found that lumbar spine texture analysis using trabecular bone score (TBS) is a risk factor for MOF and a risk factor for death in a retrospective cohort study from a large clinical registry for the province of Manitoba, Canada. INTRODUCTION: FRAX® estimates the 10-year probability of major osteoporotic fracture (MOF) using clinical risk factors and femoral neck bone mineral density (BMD). Trabecular bone score (TBS), derived from texture in the spine dual X-ray absorptiometry (DXA) image, is related to bone microarchitecture and fracture risk independently of BMD. Our objective was to determine whether TBS provides information on MOF probability beyond that provided by the FRAX variables. METHODS: We included 33,352 women aged 40-100 years (mean 63 years) with baseline DXA measurements of lumbar spine TBS and femoral neck BMD. The association between TBS, the FRAX variables, and the risk of MOF or death was examined using an extension of the Poisson regression model. RESULTS: During the mean of 4.7 years, 1,754 women died and 1,872 sustained one or more MOF. For each standard deviation reduction in TBS, there was a 36 % increase in MOF risk (HR 1.36, 95 % CI 1.30-1.42, p < 0.001) and a 32 % increase in death (HR 1.32, 95 % CI 1.26-1.39, p < 0.001). When adjusted for significant clinical risk factors and femoral neck BMD, lumbar spine TBS was still a significant predictor of MOF (HR 1.18, 95 % CI 1.12-1.23) and death (HR 1.20, 95 % CI 1.14-1.26). Models for estimating MOF probability, accounting for competing mortality, showed that low TBS (10th percentile) increased risk by 1.5-1.6-fold compared with high TBS (90th percentile) across a broad range of ages and femoral neck T-scores. CONCLUSIONS: Lumbar spine TBS is able to predict incident MOF independent of FRAX clinical risk factors and femoral neck BMD even after accounting for the increased death hazard.

Extremal properties of certain risk models

Cette thèse s'intéresse à étudier les propriétés extrémales de certains modèles de risque d'intérêt dans diverses applications de l'assurance, de la finance et des statistiques. Cette thèse se développe selon deux axes principaux, à savoir: Dans la première partie, nous nous concentrons sur deux modèles de risques univariés, c'est-à- dire, un modèle de risque de déflation et un modèle de risque de réassurance. Nous étudions le développement des queues de distribution sous certaines conditions des risques commun¬s. Les principaux résultats sont ainsi illustrés par des exemples typiques et des simulations numériques. Enfin, les résultats sont appliqués aux domaines des assurances, par exemple, les approximations de Value-at-Risk, d'espérance conditionnelle unilatérale etc. La deuxième partie de cette thèse est consacrée à trois modèles à deux variables: Le premier modèle concerne la censure à deux variables des événements extrême. Pour ce modèle, nous proposons tout d'abord une classe d'estimateurs pour les coefficients de dépendance et la probabilité des queues de distributions. Ces estimateurs sont flexibles en raison d'un paramètre de réglage. Leurs distributions asymptotiques sont obtenues sous certaines condi¬tions lentes bivariées de second ordre. Ensuite, nous donnons quelques exemples et présentons une petite étude de simulations de Monte Carlo, suivie par une application sur un ensemble de données réelles d'assurance. L'objectif de notre deuxième modèle de risque à deux variables est l'étude de coefficients de dépendance des queues de distributions obliques et asymétriques à deux variables. Ces distri¬butions obliques et asymétriques sont largement utiles dans les applications statistiques. Elles sont générées principalement par le mélange moyenne-variance de lois normales et le mélange de lois normales asymétriques d'échelles, qui distinguent la structure de dépendance de queue comme indiqué par nos principaux résultats. Le troisième modèle de risque à deux variables concerne le rapprochement des maxima de séries triangulaires elliptiques obliques. Les résultats théoriques sont fondés sur certaines hypothèses concernant le périmètre aléatoire sous-jacent des queues de distributions. -- This thesis aims to investigate the extremal properties of certain risk models of interest in vari¬ous applications from insurance, finance and statistics. This thesis develops along two principal lines, namely: In the first part, we focus on two univariate risk models, i.e., deflated risk and reinsurance risk models. Therein we investigate their tail expansions under certain tail conditions of the common risks. Our main results are illustrated by some typical examples and numerical simu¬lations as well. Finally, the findings are formulated into some applications in insurance fields, for instance, the approximations of Value-at-Risk, conditional tail expectations etc. The second part of this thesis is devoted to the following three bivariate models: The first model is concerned with bivariate censoring of extreme events. For this model, we first propose a class of estimators for both tail dependence coefficient and tail probability. These estimators are flexible due to a tuning parameter and their asymptotic distributions are obtained under some second order bivariate slowly varying conditions of the model. Then, we give some examples and present a small Monte Carlo simulation study followed by an application on a real-data set from insurance. The objective of our second bivariate risk model is the investigation of tail dependence coefficient of bivariate skew slash distributions. Such skew slash distributions are extensively useful in statistical applications and they are generated mainly by normal mean-variance mixture and scaled skew-normal mixture, which distinguish the tail dependence structure as shown by our principle results. The third bivariate risk model is concerned with the approximation of the component-wise maxima of skew elliptical triangular arrays. The theoretical results are based on certain tail assumptions on the underlying random radius.

A comparative study of dyslipidaemia in men and woman with androgenic alopecia

Several studies have analyzed the relationship between androgenetic alopecia and cardiovascular disease (mainly heart disease). However few studies have analyzed lipid values in men and women separately. This case-control study included 300 patients consecutively admitted to an outpatient clinic, 150 with early onset androgenetic alopecia (80 males and 70 females) and 150 controls (80 males and 70 females) with other skin diseases. Female patients with androgenic alopecia showed significant higher triglycerides values (123.8 vs 89.43 mg/dl, p = 0.006), total cholesterol values (196.1 vs 182.3 mg/dl, p = 0.014), LDL-C values (114.1 vs 98.8 mg/dl, p = 0.0006) and lower HDL-C values (56.8 vs 67.7 mg/dl, p <0.0001) versus controls respectively. Men with androgenic alopecia showed significant higher triglycerides values (159.7 vs 128.7 mg/dl, p = 0.04) total cholesterol values (198.3 vs 181.4 mg/dl, p = 0.006) and LDL-C values (124.3 vs 106.2, p = 0.0013) versus non-alopecic men. A higher prevalence of dyslipidemia in women and men with androgenic alopecia has been found. The elevated lipid values in these patients may contribute, alongside other mechanisms, to the development of cardiovascular disease in patient with androgenic alopecia.

Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible considerationof densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended theEuclidean structure of the simplex to a Hilbert space structure of the set of densitieswithin a bounded interval, and van den Boogaart (2005) generalized this to the setof densities bounded by an arbitrary reference density. From the many variations ofthe Hilbert structures available, we work with three cases. For bounded variables, abasis derived from Legendre polynomials is used. For variables with a lower bound, westandardize them with respect to an exponential distribution and express their densitiesas coordinates in a basis derived from Laguerre polynomials. Finally, for unboundedvariables, a normal distribution is used as reference, and coordinates are obtained withrespect to a Hermite-polynomials-based basis.To get the coordinates, several approaches can be considered. A numerical accuracyproblem occurs if one estimates the coordinates directly by using discretized scalarproducts. Thus we propose to use a weighted linear regression approach, where all k-order polynomials are used as predictand variables and weights are proportional to thereference density. Finally, for the case of 2-order Hermite polinomials (normal reference)and 1-order Laguerre polinomials (exponential), one can also derive the coordinatesfrom their relationships to the classical mean and variance.Apart of these theoretical issues, this contribution focuses on the application of thistheory to two main problems in sedimentary geology: the comparison of several grainsize distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock orsediment, like their composition