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

Estimation of Genetic Divergence and Gene Flow between Culex pipiens and Culex quinquefasciatus (Diptera: Culicidae) in Argentina

Allele frequencies at seven polymorphic loci controlling the synthesis of enzymes were analyzed in six populations of Culex pipiens L. and Cx. quinquefasciatus Say. Sampling sites were situated along a north-south line of about 2,000 km in Argentina. The predominant alleles at Mdh, Idh, Gpdh and Gpi loci presented similar frequencies in all the samples. Frequencies at the Pgm locus were similar for populations pairs sharing the same geographic area. The loci Cat and Hk-1 presented significant geographic variation. The latter showed a marked latitudinal cline, with a frequency for allele b ranging from 0.99 in the northernmost point to 0.04 in the southernmost one, a pattern that may be explained by natural selection (FST = 0.46; p < 0.0001) on heat sensitive alleles. The average value of FST (0.088) and Nm (61.12) indicated a high gene flow between adjacent populations. A high correlation was found between genetic and geographic distance (r = 0.83; p < 0.001). The highest genetic identity (IN = 0.988) corresponded to the geographically closest samples from the central area. In one of these localities Cx. quinquefasciatus was predominant and hybrid individuals were detected, while in the other, almost all the specimens were identified as Cx. pipiens. To verify the fertility between Cx. pipiens and Cx. quinquefasciatus from the northern- and southernmost populations, experimental crosses were performed. Viable egg rafts were obtained from both reciprocal crosses. Hatching ranged from 76.5 to 100%. The hybrid progenies were fertile through two subsequent generations

Restriction site-associated DNA sequencing, genotyping error estimation and de novo assembly optimization for population genetic inference.

Restriction site-associated DNA sequencing (RADseq) provides researchers with the ability to record genetic polymorphism across thousands of loci for nonmodel organisms, potentially revolutionizing the field of molecular ecology. However, as with other genotyping methods, RADseq is prone to a number of sources of error that may have consequential effects for population genetic inferences, and these have received only limited attention in terms of the estimation and reporting of genotyping error rates. Here we use individual sample replicates, under the expectation of identical genotypes, to quantify genotyping error in the absence of a reference genome. We then use sample replicates to (i) optimize de novo assembly parameters within the program Stacks, by minimizing error and maximizing the retrieval of informative loci; and (ii) quantify error rates for loci, alleles and single-nucleotide polymorphisms. As an empirical example, we use a double-digest RAD data set of a nonmodel plant species, Berberis alpina, collected from high-altitude mountains in Mexico.

A correlation sensitivity analysis of non-life underwriting risk in solvency capital requirement estimation

This paper analyses the impact of using different correlation assumptions between lines of business when estimating the risk-based capital reserve, the Solvency Capital Requirement (SCR), under Solvency II regulations. A case study is presented and the SCR is calculated according to the Standard Model approach. Alternatively, the requirement is then calculated using an Internal Model based on a Monte Carlo simulation of the net underwriting result at a one-year horizon, with copulas being used to model the dependence between lines of business. To address the impact of these model assumptions on the SCR we conduct a sensitivity analysis. We examine changes in the correlation matrix between lines of business and address the choice of copulas. Drawing on aggregate historical data from the Spanish non-life insurance market between 2000 and 2009, we conclude that modifications of the correlation and dependence assumptions have a significant impact on SCR estimation.

The nature of the Cr-C bond: direct estimation of aromaticity in Fischer carbenes

Report for the scientific sojourn at the the Philipps-Universität Marburg, Germany, from september to december 2007. For the first, we employed the Energy-Decomposition Analysis (EDA) to investigate aromaticity on Fischer carbenes as it is related through all the reaction mechanisms studied in my PhD thesis. This powerful tool, compared with other well-known aromaticity indices in the literature like NICS, is useful not only for quantitative results but also to measure the degree of conjugation or hyperconjugation in molecules. Our results showed for the annelated benzenoid systems studied here, that electron density is more concentrated on the outer rings than in the central one. The strain-induced bond localization plays a major role as a driven force to keep the more substituted ring as the less aromatic. The discussion presented in this work was contrasted at different levels of theory to calibrate the method and ensure the consistency of our results. We think these conclusions can also be extended to arene chemistry for explaining aromaticity and regioselectivity reactions found in those systems.In the second work, we have employed the Turbomole program package and density-functionals of the best performance in the state of art, to explore reaction mechanisms in the noble gas chemistry. Particularly, we were interested in compounds of the form H--Ng--Ng--F (where Ng (Noble Gas) = Ar, Kr and Xe) and we investigated the relative stability of these species. Our quantum chemical calculations predict that the dixenon compound HXeXeF has an activation barrier for decomposition of 11 kcal/mol which should be large enough to identify the molecule in a low-temperature matrix. The other noble gases present lower activation barriers and therefore are more labile and difficult to be observable systems experimentally.

Estimation of glomerular filtration rate in hospitalised patients: are we overestimating renal function?

QUESTIONS UNDER STUDY AND PRINCIPLES: Estimating glomerular filtration rate (GFR) in hospitalised patients with chronic kidney disease (CKD) is important for drug prescription but it remains a difficult task. The purpose of this study was to investigate the reliability of selected algorithms based on serum creatinine, cystatin C and beta-trace protein to estimate GFR and the potential added advantage of measuring muscle mass by bioimpedance. In a prospective unselected group of patients hospitalised in a general internal medicine ward with CKD, GFR was evaluated using inulin clearance as the gold standard and the algorithms of Cockcroft, MDRD, Larsson (cystatin C), White (beta-trace) and MacDonald (creatinine and muscle mass by bioimpedance). 69 patients were included in the study. Median age (interquartile range) was 80 years (73-83); weight 74.7 kg (67.0-85.6), appendicular lean mass 19.1 kg (14.9-22.3), serum creatinine 126 μmol/l (100-149), cystatin C 1.45 mg/l (1.19-1.90), beta-trace protein 1.17 mg/l (0.99-1.53) and GFR measured by inulin 30.9 ml/min (22.0-43.3). The errors in the estimation of GFR and the area under the ROC curves (95% confidence interval) relative to inulin were respectively: Cockcroft 14.3 ml/min (5.55-23.2) and 0.68 (0.55-0.81), MDRD 16.3 ml/min (6.4-27.5) and 0.76 (0.64-0.87), Larsson 12.8 ml/min (4.50-25.3) and 0.82 (0.72-0.92), White 17.6 ml/min (11.5-31.5) and 0.75 (0.63-0.87), MacDonald 32.2 ml/min (13.9-45.4) and 0.65 (0.52-0.78). Currently used algorithms overestimate GFR in hospitalised patients with CKD. As a consequence eGFR targeted prescriptions of renal-cleared drugs, might expose patients to overdosing. The best results were obtained with the Larsson algorithm. The determination of muscle mass by bioimpedance did not provide significant contributions.

Solvency Capital estimation and Risk Measures

This paper examines why a financial entity’s solvency capital estimation might be underestimated if the total amount required is obtained directly from a risk measurement. Using Monte Carlo simulation we show that, in some instances, a common risk measure such as Value-at-Risk is not subadditive when certain dependence structures are considered. Higher risk evaluations are obtained for independence between random variables than those obtained in the case of comonotonicity. The paper stresses, therefore, the relationship between dependence structures and capital estimation.

Assessment of adult formulas for glomerular filtration rate estimation in children.

BACKGROUND: Estimated glomerular filtration rate (eGFR) is an important diagnostic instrument in clinical practice. The National Kidney Foundation-Kidney Disease Quality Initiative (NKF-KDOQI) guidelines do not recommend using formulas developed for adults to estimate GFR in children; however, studies confirming these recommendations are scarce. The aim of our study was to evaluate the accuracy of the new Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) formula, the Modification of Diet in Renal Disease (MDRD) formula, and the Cockcroft-Gault formula in children with various stages of chronic kidney disease (CKD). METHODS: A total of 550 inulin clearance (iGFR) measurements for 391 children were analyzed. The cohort was divided into three groups: group 1, with iGFR >90 ml/min/1.73 m(2); group 2, with iGFR between 60 and 90 ml/min/1.73 m(2); group 3, with iGFR of <60 ml/min/1.73 m(2). RESULTS: All formulas overestimate iGFR with a significant bias (p < 0.001), present poor accuracies, and have poor Spearman correlations. For an accuracy of 10 %, only 11, 6, and 27 % of the eGFRs are accurate when using the MDRD, CKD-EPI, and Cockcroft-Gault formulas, respectively. For an accuracy of 30 %, these formulas do not reach the NKF-KDOQI guidelines for validation, with only 25, 20, and 70 % of the eGFRs, respectively, being accurate. CONCLUSIONS: Based on our results, the performances of all of these formulas are unreliable for eGFR in children across all CKD stages and cannot therefore be applied in the pediatric population group.

Bone mineral density (BMD), micro-architecture estimation (TBS) and vertebral fracture assessment (VFA) extracted from a single DXA device in combination with clinical risk factors improve significantly the identification of women at high risk of fracture

Introduction: Osteoporosis (OP) is a systemic skeletal disease characterized by a low bone mineral density (BMD) and a micro-architectural (MA) deterioration. Clinical risk factors (CRF) are often used as a MA approximation. MA is yet evaluable in daily practice by the Trabecular Bone Score (TBS) measure. TBS is a novel grey-level texture measurement reflecting bone micro-architecture based on the use of experimental variograms of 2D projection images. TBS is very simple to obtain, by reanalyzing a lumbar DXA-scan. TBS has proven to have diagnosis and prognosis value, partially independent of CRF and BMD. The aim of the OsteoLaus cohort is to combine in daily practice the CRF and the information given by DXA (BMD, TBS and vertebral fracture assessment (VFA)) to better identify women at high fracture risk. Method: The OsteoLaus cohort (1400 women 50 to 80 years living in Lausanne, Switzerland) started in 2010. This study is derived from the cohort COLAUS who started in Lausanne in 2003. The main goals of COLAUS is to obtain information on the epidemiology and genetic determinants of cardiovascular risk in 6700 men and women. CRF for OP, bone ultrasound of the heel, lumbar spine and hip BMD, VFA by DXA and MA evaluation by TBS are recorded in OsteoLaus. Preliminary results are reported. Results: We included 631 women: mean age 67.4±6.7 y, BMI 26.1±4.6, mean lumbar spine BMD 0.943±0.168 (T-score -1.4 SD), TBS 1.271±0.103. As expected, correlation between BMD and site matched TBS is low (r2=0.16). Prevalence of VFx grade 2/3, major OP Fx and all OP Fx is 8.4%, 17.0% and 26.0% respectively. Age- and BMI-adjusted ORs (per SD decrease) are 1.8 (1.2- 2.5), 1.6 (1.2-2.1), 1.3 (1.1-1.6) for BMD for the different categories of fractures and 2.0 (1.4-3.0), 1.9 (1.4-2.5), 1.4 (1.1-1.7) for TBS respectively. Only 32 to 37% of women with OP Fx have a BMD < -2.5 SD or a TBS < 1.200. If we combine a BMD < -2.5 SD or a TBS < 1.200, 54 to 60% of women with an osteoporotic Fx are identified. Conclusion: As in the already published studies, these preliminary results confirm the partial independence between BMD and TBS. More importantly, a combination of TBS subsequent to BMD increases significantly the identification of women with prevalent OP Fx which would have been miss-classified by BMD alone. For the first time we are able to have complementary information about fracture (VFA), density (BMD), micro- and macro architecture (TBS & HAS) from a simple, low ionizing radiation and cheap device: DXA. Such complementary information is very useful for the patient in the daily practice and moreover will likely have an impact on cost effectiveness analysis.

Interpretation of partial fingermarks using an automated fingerprint identification system

Abstract : In the subject of fingerprints, the rise of computers tools made it possible to create powerful automated search algorithms. These algorithms allow, inter alia, to compare a fingermark to a fingerprint database and therefore to establish a link between the mark and a known source. With the growth of the capacities of these systems and of data storage, as well as increasing collaboration between police services on the international level, the size of these databases increases. The current challenge for the field of fingerprint identification consists of the growth of these databases, which makes it possible to find impressions that are very similar but coming from distinct fingers. However and simultaneously, this data and these systems allow a description of the variability between different impressions from a same finger and between impressions from different fingers. This statistical description of the withinand between-finger variabilities computed on the basis of minutiae and their relative positions can then be utilized in a statistical approach to interpretation. The computation of a likelihood ratio, employing simultaneously the comparison between the mark and the print of the case, the within-variability of the suspects' finger and the between-variability of the mark with respect to a database, can then be based on representative data. Thus, these data allow an evaluation which may be more detailed than that obtained by the application of rules established long before the advent of these large databases or by the specialists experience. The goal of the present thesis is to evaluate likelihood ratios, computed based on the scores of an automated fingerprint identification system when the source of the tested and compared marks is known. These ratios must support the hypothesis which it is known to be true. Moreover, they should support this hypothesis more and more strongly with the addition of information in the form of additional minutiae. For the modeling of within- and between-variability, the necessary data were defined, and acquired for one finger of a first donor, and two fingers of a second donor. The database used for between-variability includes approximately 600000 inked prints. The minimal number of observations necessary for a robust estimation was determined for the two distributions used. Factors which influence these distributions were also analyzed: the number of minutiae included in the configuration and the configuration as such for both distributions, as well as the finger number and the general pattern for between-variability, and the orientation of the minutiae for within-variability. In the present study, the only factor for which no influence has been shown is the orientation of minutiae The results show that the likelihood ratios resulting from the use of the scores of an AFIS can be used for evaluation. Relatively low rates of likelihood ratios supporting the hypothesis known to be false have been obtained. The maximum rate of likelihood ratios supporting the hypothesis that the two impressions were left by the same finger when the impressions came from different fingers obtained is of 5.2 %, for a configuration of 6 minutiae. When a 7th then an 8th minutia are added, this rate lowers to 3.2 %, then to 0.8 %. In parallel, for these same configurations, the likelihood ratios obtained are on average of the order of 100,1000, and 10000 for 6,7 and 8 minutiae when the two impressions come from the same finger. These likelihood ratios can therefore be an important aid for decision making. Both positive evolutions linked to the addition of minutiae (a drop in the rates of likelihood ratios which can lead to an erroneous decision and an increase in the value of the likelihood ratio) were observed in a systematic way within the framework of the study. Approximations based on 3 scores for within-variability and on 10 scores for between-variability were found, and showed satisfactory results. Résumé : Dans le domaine des empreintes digitales, l'essor des outils informatisés a permis de créer de puissants algorithmes de recherche automatique. Ces algorithmes permettent, entre autres, de comparer une trace à une banque de données d'empreintes digitales de source connue. Ainsi, le lien entre la trace et l'une de ces sources peut être établi. Avec la croissance des capacités de ces systèmes, des potentiels de stockage de données, ainsi qu'avec une collaboration accrue au niveau international entre les services de police, la taille des banques de données augmente. Le défi actuel pour le domaine de l'identification par empreintes digitales consiste en la croissance de ces banques de données, qui peut permettre de trouver des impressions très similaires mais provenant de doigts distincts. Toutefois et simultanément, ces données et ces systèmes permettent une description des variabilités entre différentes appositions d'un même doigt, et entre les appositions de différents doigts, basées sur des larges quantités de données. Cette description statistique de l'intra- et de l'intervariabilité calculée à partir des minuties et de leurs positions relatives va s'insérer dans une approche d'interprétation probabiliste. Le calcul d'un rapport de vraisemblance, qui fait intervenir simultanément la comparaison entre la trace et l'empreinte du cas, ainsi que l'intravariabilité du doigt du suspect et l'intervariabilité de la trace par rapport à une banque de données, peut alors se baser sur des jeux de données représentatifs. Ainsi, ces données permettent d'aboutir à une évaluation beaucoup plus fine que celle obtenue par l'application de règles établies bien avant l'avènement de ces grandes banques ou par la seule expérience du spécialiste. L'objectif de la présente thèse est d'évaluer des rapports de vraisemblance calcul és à partir des scores d'un système automatique lorsqu'on connaît la source des traces testées et comparées. Ces rapports doivent soutenir l'hypothèse dont il est connu qu'elle est vraie. De plus, ils devraient soutenir de plus en plus fortement cette hypothèse avec l'ajout d'information sous la forme de minuties additionnelles. Pour la modélisation de l'intra- et l'intervariabilité, les données nécessaires ont été définies, et acquises pour un doigt d'un premier donneur, et deux doigts d'un second donneur. La banque de données utilisée pour l'intervariabilité inclut environ 600000 empreintes encrées. Le nombre minimal d'observations nécessaire pour une estimation robuste a été déterminé pour les deux distributions utilisées. Des facteurs qui influencent ces distributions ont, par la suite, été analysés: le nombre de minuties inclus dans la configuration et la configuration en tant que telle pour les deux distributions, ainsi que le numéro du doigt et le dessin général pour l'intervariabilité, et la orientation des minuties pour l'intravariabilité. Parmi tous ces facteurs, l'orientation des minuties est le seul dont une influence n'a pas été démontrée dans la présente étude. Les résultats montrent que les rapports de vraisemblance issus de l'utilisation des scores de l'AFIS peuvent être utilisés à des fins évaluatifs. Des taux de rapports de vraisemblance relativement bas soutiennent l'hypothèse que l'on sait fausse. Le taux maximal de rapports de vraisemblance soutenant l'hypothèse que les deux impressions aient été laissées par le même doigt alors qu'en réalité les impressions viennent de doigts différents obtenu est de 5.2%, pour une configuration de 6 minuties. Lorsqu'une 7ème puis une 8ème minutie sont ajoutées, ce taux baisse d'abord à 3.2%, puis à 0.8%. Parallèlement, pour ces mêmes configurations, les rapports de vraisemblance sont en moyenne de l'ordre de 100, 1000, et 10000 pour 6, 7 et 8 minuties lorsque les deux impressions proviennent du même doigt. Ces rapports de vraisemblance peuvent donc apporter un soutien important à la prise de décision. Les deux évolutions positives liées à l'ajout de minuties (baisse des taux qui peuvent amener à une décision erronée et augmentation de la valeur du rapport de vraisemblance) ont été observées de façon systématique dans le cadre de l'étude. Des approximations basées sur 3 scores pour l'intravariabilité et sur 10 scores pour l'intervariabilité ont été trouvées, et ont montré des résultats satisfaisants.

Wing geometry as a tool for studying the Lutzomyia longipalpis (Diptera: Psychodidae) complex

Toro Toro (T) and Yungas (Y) have been described as genetically well differentiated populations of the Lutzomyia longipalpis (Lutz & Neiva, 1912) complex in Bolivia. Here we use geometric morphometrics to compare samples from these populations and new populations (Bolivia and Nicaragua), representing distant geographical origins, qualitative morphological variation ("one-spot" or "two-spots" phenotypes), ecologically distinct traits (peridomestic and silvatic populations), and possibly different epidemiological roles (transmitting or nor transmitting Leishmania chagasi). The Nicaragua (N) (Somotillo) sample was "one-spot" phenotype and a possible peridomestic vector. The Bolivian sample of the Y was also "one-spot" phenotype and a demonstrated peridomestic vector of visceral leishmaniasis (VL). The three remaining samples were silvatic, "two-spots" phenotypes. Two of them (Uyuni and T) were collected in the highlands of Bolivian where VL never has been reported. The last one (Robore, R) came from the lowlands of Bolivia, where human cases of VL are sporadically reported. The decomposition of metric variation into size and shape by geometric morphometric techniques suggests the existence of two groups (N/Y/R, and U/T). Several arguments indicate that such subdivision of Lu. longipalpis could correspond to different evolutionary units.

Geometry and physics of catenanes applied to the study of DNA replication.

The concept of ideal geometric configurations was recently applied to the classification and characterization of various knots. Different knots in their ideal form (i.e., the one requiring the shortest length of a constant-diameter tube to form a given knot) were shown to have an overall compactness proportional to the time-averaged compactness of thermally agitated knotted polymers forming corresponding knots. This was useful for predicting the relative speed of electrophoretic migration of different DNA knots. Here we characterize the ideal geometric configurations of catenanes (called links by mathematicians), i.e., closed curves in space that are topologically linked to each other. We demonstrate that the ideal configurations of different catenanes show interrelations very similar to those observed in the ideal configurations of knots. By analyzing literature data on electrophoretic separations of the torus-type of DNA catenanes with increasing complexity, we observed that their electrophoretic migration is roughly proportional to the overall compactness of ideal representations of the corresponding catenanes. This correlation does not apply, however, to electrophoretic migration of certain replication intermediates, believed up to now to represent the simplest torus-type catenanes. We propose, therefore, that freshly replicated circular DNA molecules, in addition to forming regular catenanes, may also form hemicatenanes.

Laboratory estimation of the effects of increasing temperatures on the duration of gonotrophic cycle of Anopheles albimanus (Diptera: Culicidae)

The increase of malaria transmission in the Pacific Coast of Colombia during the occurrence of El Niño warm event has been found not to be linked to increases in the density of the vector Anopheles albimanus, but to other temperature-sensitive variables such as longevity, duration of the gonotrophic cycle or the sporogonic period of Plasmodium. The present study estimated the effects of temperature on duration of the gonotrophic cycle and on maturation of the ovaries of An. albimanus. Blood fed adult mosquitoes were exposed to temperatures of 24, 27, and 30°C, held individually in oviposition cages and assessed at 12 h intervals. At 24, 27, and 30°C the mean development time of the oocytes was 91.2 h (95% C.I.: 86.5-96), 66.2 h (61.5-70.8), and 73.1 h (64-82.3), respectively. The mean duration of the gonotrophic cycle for these three temperatures was 88.4 h (81.88-94.9), 75 h (71.4-78.7), and 69.1 h (64.6-73.6) respectively. These findings indicate that both parameters in An. albimanus are reduced when temperatures rose from 24 to 30°C, in a nonlinear manner. According to these results the increase in malaria transmission during El Niño in Colombia could be associated with a shortening of the gonotrophic cycle in malaria vectors, which could enhance the frequency of man-vector contact, affecting the incidence of the disease.