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

The effect of skewness and kurtosis on the Kenward-Roger approximation when group distributions differ

This study examined the independent effect of skewness and kurtosis on the robustness of the linear mixed model (LMM), with the Kenward-Roger (KR) procedure, when group distributions are different, sample sizes are small, and sphericity cannot be assumed. Methods: A Monte Carlo simulation study considering a split-plot design involving three groups and four repeated measures was performed. Results: The results showed that when group distributions are different, the effect of skewness on KR robustness is greater than that of kurtosis for the corresponding values. Furthermore, the pairings of skewness and kurtosis with group size were found to be relevant variables when applying this procedure. Conclusions: With sample sizes of 45 and 60, KR is a suitable option for analyzing data when the distributions are: (a) mesokurtic and not highly or extremely skewed, and (b) symmetric with different degrees of kurtosis. With total sample sizes of 30, it is adequate when group sizes are equal and the distributions are: (a) mesokurtic and slightly or moderately skewed, and sphericity is assumed; and (b) symmetric with a moderate or high/extreme violation of kurtosis. Alternative analyses should be considered when the distributions are highly or extremely skewed and samples sizes are small.

Independent and combined associations of risky single-occasion drinking and drinking volume with alcohol use disorder: Evidence from a sample of young Swiss men.

BACKGROUND: Risky single-occasion drinking (RSOD) is a prevalent and potentially harmful alcohol use pattern associated with increased alcohol use disorder (AUD). However, RSOD is commonly associated with a higher level of alcohol intake, and most studies have not controlled for drinking volume (DV). Thus, it is unclear whether the findings provide information about RSOD or DV. This study sought to investigate the independent and combined effects of RSOD and DV on AUD. METHODS: Data were collected in the longitudinal Cohort Study on Substance Use Risk Factors (C-SURF) among 5598 young Swiss male alcohol users in their early twenties. Assessment included DV, RSOD, and AUD at two time points. Generalized linear models for binomial distributions provided evidence regarding associations of DV, RSOD, and their interaction. RESULTS: DV, RSOD, and their interaction were significantly related to the number of AUD criteria. The slope of the interaction was steeper for non/rare RSOD than for frequent RSOD. CONCLUSIONS: RSOD appears to be a harmful pattern of drinking, associated with increased AUD and it moderated the relationship between DV and AUD. This study highlighted the importance of taking drinking patterns into account, for both research and public health planning, since RSO drinkers constitute a vulnerable subgroup for AUD.

A priori estimation of accuracy and of the number of wells to be employed in limiting dilution assays

The use of limiting dilution assay (LDA) for assessing the frequency of responders in a cell population is a method extensively used by immunologists. A series of studies addressing the statistical method of choice in an LDA have been published. However, none of these studies has addressed the point of how many wells should be employed in a given assay. The objective of this study was to demonstrate how a researcher can predict the number of wells that should be employed in order to obtain results with a given accuracy, and, therefore, to help in choosing a better experimental design to fulfill one's expectations. We present the rationale underlying the expected relative error computation based on simple binomial distributions. A series of simulated in machina experiments were performed to test the validity of the a priori computation of expected errors, thus confirming the predictions. The step-by-step procedure of the relative error estimation is given. We also discuss the constraints under which an LDA must be performed.

Measurement of the electroweak production of dijets in association with a Z-boson and distributions sensitive to vector boson fusion in proton-proton collisions at √s = 8 TeV using the ATLAS detector

Measurements of fiducial cross sections for the electroweak production of two jets in association with a Z-boson are presented. The measurements are performed using 20.3 fb−1 of proton-proton collision data collected at a centre-of-mass energy of p s = 8TeV by the ATLAS experiment at the Large Hadron Collider. The electroweak component is extracted by a fit to the dijet invariant mass distribution in a fiducial region chosen to enhance the electroweak contribution over the dominant background in which the jets are produced via the strong interaction. The electroweak cross sections measured in two fiducial regions are in good agreement with the Standard Model expectations and the background-only hypothesis is rejected with significance above the 5ơ level. The electroweak process includes the vector boson fusion production of a Z-boson and the data are used to place limits on anomalous triple gauge boson couplings. In addition, measurements of cross sections and differential distributions for inclusive Z-boson-plus-dijet production are performed in five fiducial regions, each with different sensitivity to the electroweak contribution. The results are corrected for detector effects and compared to predictions from the Sherpa and Powheg event generators.

Orthogonal combinatorial mutagenesis: a codon-level combinatorial mutagenesis method useful for low multiplicity and amino acid-scanning protocols

We describe here a method to generate combinatorial libraries of oligonucleotides mutated at the codon-level, with control of the mutagenesis rate so as to create predictable binomial distributions of mutants. The method allows enrichment of the libraries with single, double or larger multiplicity of amino acid replacements by appropriate choice of the mutagenesis rate, depending on the concentration of synthetic precursors. The method makes use of two sets of deoxynucleoside-phosphoramidites bearing orthogonal protecting groups [4,4′-dimethoxytrityl (DMT) and 9-fluorenylmethoxycarbonyl (Fmoc)] in the 5′ hydroxyl. These phosphoramidites are divergently combined during automated synthesis in such a way that wild-type codons are assembled with commercial DMT-deoxynucleoside-methyl-phosphoramidites while mutant codons are assembled with Fmoc-deoxynucleoside-methyl-phosphoramidites in an NNG/C fashion in a single synthesis column. This method is easily automated and suitable for low mutagenesis rates and large windows, such as those required for directed evolution and alanine scanning. Through the assembly of three oligonucleotide libraries at different mutagenesis rates, followed by cloning at the polylinker region of plasmid pUC18 and sequencing of 129 clones, we concluded that the method performs essentially as intended.

Size frequency distributions of abnormal protein deposits in Alzheimer’s disease and variant Creutzfeldt-Jakob disease

TThe size frequency distributions of ß-amyloid (Aß) and prion protein (PrPsc) deposits were studied in Alzheimer’s disease (AD) and the variant form of Creutzfeldt-Jakob disease (vCJD) respectively. All size distributions were unimodal and positively skewed. Aß deposits reached a greater maximum size and their distributions were significantly less skewed than the PrPsc deposits. All distributions were approximately log-normal in shape but only the diffuse PrPsc deposits did not deviate significantly from a log-normal model. There were fewer larger classic Aß deposits than predicted and the florid PrPsc deposits occupied a more restricted size range than predicted by a log-normal model. Hence, Aß deposits exhibit greater growth than the corresponding PrPsc deposits. Surface diffusion may be particularly important in determining the growth of the diffuse PrPsc deposits. In addition, there are factors limiting the maximum size of the Aß and florid PrPsc deposits.

Reference Values For High-density Lipoprotein Particle Size And Volume By Dynamic Light Scattering In A Brazilian Population Sample And Their Relationships With Metabolic Parameters.

Current data indicate that the size of high-density lipoprotein (HDL) may be considered an important marker for cardiovascular disease risk. We established reference values of mean HDL size and volume in an asymptomatic representative Brazilian population sample (n=590) and their associations with metabolic parameters by gender. Size and volume were determined in HDL isolated from plasma by polyethyleneglycol precipitation of apoB-containing lipoproteins and measured using the dynamic light scattering (DLS) technique. Although the gender and age distributions agreed with other studies, the mean HDL size reference value was slightly lower than in some other populations. Both HDL size and volume were influenced by gender and varied according to age. HDL size was associated with age and HDL-C (total population); non- white ethnicity and CETP inversely (females); HDL-C and PLTP mass (males). On the other hand, HDL volume was determined only by HDL-C (total population and in both genders) and by PLTP mass (males). The reference values for mean HDL size and volume using the DLS technique were established in an asymptomatic and representative Brazilian population sample, as well as their related metabolic factors. HDL-C was a major determinant of HDL size and volume, which were differently modulated in females and in males.

Precision of distances and ordering of microsatellite markers in consensus linkage maps of chromosomes 1, 3 and 4 from two reciprocal chicken populations using bootstrap sampling

Some factors complicate comparisons between linkage maps from different studies. This problem can be resolved if measures of precision, such as confidence intervals and frequency distributions, are associated with markers. We examined the precision of distances and ordering of microsatellite markers in the consensus linkage maps of chromosomes 1, 3 and 4 from two F 2 reciprocal Brazilian chicken populations, using bootstrap sampling. Single and consensus maps were constructed. The consensus map was compared with the International Consensus Linkage Map and with the whole genome sequence. Some loci showed segregation distortion and missing data, but this did not affect the analyses negatively. Several inversions and position shifts were detected, based on 95% confidence intervals and frequency distributions of loci. Some discrepancies in distances between loci and in ordering were due to chance, whereas others could be attributed to other effects, including reciprocal crosses, sampling error of the founder animals from the two populations, F(2) population structure, number of and distance between microsatellite markers, number of informative meioses, loci segregation patterns, and sex. In the Brazilian consensus GGA1, locus LEI1038 was in a position closer to the true genome sequence than in the International Consensus Map, whereas for GGA3 and GGA4, no such differences were found. Extending these analyses to the remaining chromosomes should facilitate comparisons and the integration of several available genetic maps, allowing meta-analyses for map construction and quantitative trait loci (QTL) mapping. The precision of the estimates of QTL positions and their effects would be increased with such information.

Endothelial Nitric Oxide Genotypes and Haplotypes Are Not Associated with End-Stage Renal Disease

The identification of genetic markers associated with chronic kidney disease (CKD) may help to predict its development. Because reduced nitric oxide (NO) bioavailability and endothelial dysfunction are involved in CKD, genetic polymorphisms in the gene encoding the enzyme involved in NO synthesis (endothelial NO synthase [eNos]) may affect the susceptibility to CKD and the development of end-stage renal disease (ESRD). We compared genotype and haplotype distributions of three relevant eNOS polymorphisms (T(-786) C in the promoter region, Glu298Asp in exon 7, and 4b/4a in intron 4) in 110 healthy control subjects and 127 ESRD patients. Genotypes for the T(-786) C and Glu298Asp polymorphisms were determined by TaqMan (R) Allele Discrimination assay and real-time polymerase chain reaction. Genotypes for the intron 4 polymorphism were determined by polymerase chain reaction and fragment separation by electrophoresis. The software program PHASE 2.1 was used to estimate the haplotypes frequencies. We considered significant a probability value of p < 0.05/number of haplotypes (p < 0.05/8 = 0.0063). We found no significant differences between groups with respect to age, ethnicity, and gender. CKD patients had higher blood pressure, total cholesterol, and creatinine levels than healthy control subjects (all p < 0.05). Genotype and allele distributions for the three eNOS polymorphisms were similar in both groups (p > 0.05). We found no significant differences in haplotype distribution between groups (p > 0.05). The lack of significant associations between eNOS polymorphisms and ESRD suggests that eNOS polymorphisms may not be relevant to the genetic component of CKD that leads to ESRD.

Haplotype distribution of five nuclear genes based on network genealogies and Bayesian inference indicates that Trypanosoma cruzi hybrid strains are polyphyletic

Chagas disease is still a major public health problem in Latin America. Its causative agent, Trypanosoma cruzi, can be typed into three major groups, T. cruzi I, T. cruzi II and hybrids. These groups each have specific genetic characteristics and epidemiological distributions. Several highly virulent strains are found in the hybrid group; their origin is still a matter of debate. The null hypothesis is that the hybrids are of polyphyletic origin, evolving independently from various hybridization events. The alternative hypothesis is that all extant hybrid strains originated from a single hybridization event. We sequenced both alleles of genes encoding EF-1 alpha, actin and SSU rDNA of 26 T. cruzi strains and DHFR-TS and TR of 12 strains. This information was used for network genealogy analysis and Bayesian phylogenies. We found T. cruzi I and T. cruzi II to be monophyletic and that all hybrids had different combinations of T. cruzi I and T. cruzi II haplotypes plus hybrid-specific haplotypes. Bootstrap values (networks) and posterior probabilities (Bayesian phylogenies) of clades supporting the monophyly of hybrids were far below the 95% confidence interval, indicating that the hybrid group is polyphyletic. We hypothesize that T. cruzi I and T. cruzi II are two different species and that the hybrids are extant representatives of independent events of genome hybridization, which sporadically have sufficient fitness to impact on the epidemiology of Chagas disease.

Fractionation of Zn, Cd and Pb in a Tropical Soil After Nine-Year Sewage Sludge Applications

A long-term field experiment was carried out in the experiment farm of the Sao Paulo State University, Brazil, to evaluate the phytoavailability of Zn, Cd and Pb in a Typic Eutrorthox soil treated with sewage sludge for nine consecutive years, using the sequential extraction and organic matter fractionation methods. During 2005-2006, maize (Zea mays L.) was used as test plants and the experimental design was in randomized complete blocks with four treatments and five replicates. The treatments consisted of four sewage sludge rates (in a dry basis): 0.0 (control, with mineral fertilization), 45.0, 90.0 and 127.5 t ha(-1), annually for nine years. Before maize sowing, the sewage sludge was manually applied to the soil and incorporated at 10 cm depth. Soil samples (0-20 cm layer) for Zn, Cd and Pb analysis were collected 60 days after sowing. The successive applications of sewage sludge to the soil did not affect heavy metal (Cd and Pb) fractions in the soil, with exception of Zn fractions. The Zn, Cd and Pb distributions in the soil were strongly associated with humin and residual fractions, which are characterized by stable chemical bonds. Zinc, Cd and Pb in the soil showed low phytoavailability after nine-year successive applications of sewage sludge to the soil.

Dimensionless spray flux in wet granulation: Monte-Carlo simulations and experimental validation

Dimensionless spray flux Ψa is a dimensionless group that characterises the three most important variables in liquid dispersion: flowrate, drop size and powder flux through the spray zone. In this paper, the Poisson distribution was used to generate analytical solutions for the proportion of nuclei formed from single drops (fsingle) and the fraction of the powder surface covered by drops (fcovered) as a function of Ψa. Monte-Carlo simulations were performed to simulate the spray zone and investigate how Ψa, fsingle and fcovered are related. The Monte-Carlo data was an excellent match with analytical solutions of fcovered and fsingle as a function of Ψa. At low Ψa, the proportion of the surface covered by drops (fcovered) was equal to Ψa. As Ψa increases, drop overlap becomes more dominant and the powder surface coverage levels off. The proportion of nuclei formed from single drops (fsingle) falls exponentially with increasing Ψa. In the ranges covered, these results were independent of drop size, number of drops, drop size distribution (mono-sized, bimodal and trimodal distributions), and the uniformity of the spray. Experimental data of nuclei size distributions as a function of spray flux were fitted to the analytical solution for fsingle by defining a cutsize for single drop nuclei. The fitted cutsizes followed the spray drop sizes suggesting that the method is robust and that the cutsize does indicate the transition size between single drop and agglomerate nuclei. This demonstrates that the nuclei distribution is determined by the dimensionless spray flux and the fraction of drop controlled nuclei can be calculated analytically in advance.

Comparison of experimental and numerical studies of ionizing flow over a cylinder

Comparisons are made between experimental measurements and numerical simulations of ionizing flows generated in a superorbital facility. Nitrogen, with a freestream velocity of around 10 km/s, was passed over a cylindrical model, and images were recorded using two-wavelength holographic interferometry. The resulting density, electron concentration, and temperature maps were compared with numerical simulations from the Langley Research Center aerothermodynamic upwind relaxation algorithm. The results showed generally good agreement in shock location and density distributions. Some discrepancies were observed for the electron concentration, possibly, because simulations were of a two-dimensional flow, whereas the experiments were likely to have small three-dimensional effects.

Surface Waves and Roughness in Self-Aerated Supercritical Flow

In high-velocity open channel flows, free-surface aeration is commonly observed. The effects of surface waves on the air-water flow properties are tested herein. The study simulates the air-water flow past a fixed-location phase-detection probe by introducing random fluctuations of the flow depth. The present model yields results that are close to experimental observations in terms of void fraction, bubble count rate and bubble/droplet chord size distributions. The results show that the surface waves have relatively little impact on the void fraction profiles, but that the bubble count rate profiles and the distributions of bubble and chord sizes are affected by the presence of surface waves.