Generalized Log-Normal Chain-Ladder

We propose an asymptotic theory for distribution forecasting from the log normal chain-ladder model. The theory overcomes the difficulty of convoluting log normal variables and takes estimation error into account. The results differ from that of the over-dispersed Poisson model and from the chain-ladder based bootstrap. We embed the log normal chain-ladder model in a class of infinitely divisible distributions called the generalized log normal chain-ladder model. The asymptotic theory uses small $\sigma$ asymptotics where the dimension of the reserving triangle is kept fixed while the standard deviation is assumed to decrease. The resulting asymptotic forecast distributions follow t distributions. The theory is supported by simulations and an empirical application

Geometrically Designed Variable Knot Splines in Generalized (Non-)Linear Models

In this paper we extend the GeDS methodology, recently developed by Kaishev et al. (2016) for the Normal univariate spline regression case, to the more general GNM (GLM) context. Our approach is to view the (non-)linear predictor as a spline with free knots which are estimated, along with the regression coefficients and the degree of the spline, using a two stage algorithm. In stage A, a linear (degree one) free-knot spline is fitted to the data applying iteratively re-weighted least squares. In stage B, a Schoenberg variation diminishing spline approximation to the fit from stage A is constructed, thus simultaneously producing spline fits of second, third and higher degrees. We demonstrate, based on a thorough numerical investigation that the nice properties of the Normal GeDS methodology carry over to its GNM extension and GeDS favourably compares with other existing spline methods. The proposed GeDS GNM(GLM) methodology is extended to the multivariate case of more than one independent variable by utilizing tensor product splines and their related shape preserving variation diminishing property

Double Chain Ladder and Bornhuetter-Ferguson

In this article we propose a method close to Double Chain Ladder (DCL) introduced by Martínez-Miranda, Nielsen, and Verrall (2012a). The proposed method is motivated by the potential lack of stability of the DCL method (and of the classical Chain ladder method [CLM] itself). We consider the implicit estimation of the underwriting year inflation in the CLM method and the explicit estimation of it in DCL. This may represent a weak point for DCL and CLM because the underwriting year inflation might be estimated with significant uncertainty. A key feature of the new method is that the underwriting year inflation can be estimated from the less volatile incurred data and then transferred into the DCL model. We include an empirical illustration that illustrates the differences between the estimates of the IBNR and RBNS cash flows from DCL and the new method. We also apply bootstrap estimation to approximate the predictive distributions

Estimation of Mortalities

If a linear regression is fit to log-transformed mortalities and the estimate is back-transformed according to the formula Ee^Y = e^{\mu + \sigma^2/2} a systematic bias occurs unless the error distribution is normal and the scale estimate is gauged to normal variance. This result is a consequence of the uniqueness theorem for the Laplace transform. We determine the systematic bias of minimum-L_2 and minimum-L_1 estimation with sample variance and interquartile range of the residuals as scale estimates under a uniform and four contaminated normal error distributions. Already under innocent looking contaminations the true mortalities may be underestimated by 50% in the long run. Moreover, the logarithmic transformation introduces an instability into the model that results in a large discrepancy between rg_Huber estimates as the tuning constant regulating the degree of robustness varies. Contrary to the logarithm the square root stabilizes variance, diminishes the influence of outliers, automatically copes with observed zeros, allows the `nonparametric' back-transformation formula E Y^2 = \mue^2 + \sigma^2, and in the homoskedastic case avoids a systematic bias of minimum-L_2 estimation with sample variance. For the company-specific table 3 of [Loeb94], in the age range of 20-65 years, we fit a parabola to root mortalities by minimum-L_2 , minimum-L_1, and robust rg_Huber regression estimates, and a cubic and exponential by least squares. The fits thus obtained in the original model are excellent and practically indistinguishable by a \chi^2 goodness-of-fit test. Finally , dispensing with the transformation of observations, we employ a Poisson generalized linear model and fit an exponential and a cubic by maximum likelihood

Analysis of the three most prevalent injuries in Australian football demonstrates a season to season association between groin/hip/ osteitis pubis injuries with ACL knee injuries

BACKGROUND: Injuries are common in contact sports like Australian football. The Australian Football League (AFL) has developed an extensive injury surveillance database that can be used for epidemiological studies. OBJECTIVES: The purpose of this study is to identify any association between the three most prevalent injuries in the AFL. PATIENTS AND METHODS: From the AFL injury surveillance data 1997-2012 the injury incidence (new injuries per club per season) and the injury prevalence data (missed games per club per season) were analysed to detect the three most common injuries that would cause a player to miss a match in the AFL. The three most prevalent injuries in the AFL are hamstring strains, groin/hip/osteitis pubis injuries and Anterior Cruciate Ligament (ACL) knee injuries. Following this, further study was undertaken to detect the presence of any statistical relationship between injury incidences of the three most prevalent injuries over this sixteen year study period. RESULTS: Statistical analysis demonstrates for any given year that there was an association between having a groin/hip/osteitis pubis injuriy and having a knee ACL injury (P < 0.05) over the entire sixteen years. In other words if the number of groin/hip/osteitis pubis injuries in any given season were higher than average (alternatively lower) then the number of knee ACL injuries were also higher than average (alternatively lower) for that same season. Hamstring injuries had the highest variance of incidence of the three most prevalent injuries. CONCLUSIONS: Analysis of the AFL injury data demonstrates an association between incidence of groin/hip/osteitis pubis injuries and incidence of knee ACL injuries for any given playing season. This finding is difficult to explain with further research being required.Geoffrey M. Verral, Adrian Esterman, Timothy E. Hewet

In-sample forecasting: A brief review and new algorithms

Statistical methods often distinguish between in-sample and out-of-sample approaches. In particular this is the case when time is involved. Then often time series methods are proposed that extrapolate past patterns into the future via complicated recursion formulas. Standard statistical inference is on the other hand concerned with estimating parameters within the given sample. This review paper is about a statistical methodology, where all parameters are estimated in-sample while producing a forecast out-of-sample without recursion or extrapolation. A new super-simulation algorithm ensures a faster implementation of the simplest and perhaps most important version of in-sample forecasting

Distribution of Metals in the Termite Tumulitermes tumuli (Froggatt): Two Types of Malpighian Tubule Concretion Host Zn and Ca Mutually Exclusively

The aim of this study was to determine specific distribution of metals in the termite Tumulitermes tumuli (Froggatt) and identify specific organs within the termite that host elevated metals and therefore play an important role in the regulation and transfer of these back into the environment. Like other insects, termites bio-accumulate essential metals to reinforce cuticular structures and utilize storage detoxification for other metals including Ca, P, Mg and K. Previously, Mn and Zn have been found concentrated in mandible tips and are associated with increased hardness whereas Ca, P, Mg and K are accumulated in Malpighian tubules. Using high resolution Particle Induced X-Ray Emission (PIXE) mapping of whole termites and Scanning Electron Microscope (SEM) Energy Dispersive X-ray (EDX) spot analysis, localised accumulations of metals in the termite T. tumuli were identified. Tumulitermes tumuli was found to have proportionally high Mn concentrations in mandible tips. Malpighian tubules had significant enrichment of Zn (1.6%), Mg (4.9%), P (6.8%), Ca (2.7%) and K (2.4%). Synchrotron scanning X-ray Fluorescence Microprobe (XFM) mapping demonstrated two different concretion types defined by the mutually exclusive presence of Ca and Zn. In-situ SEM EDX realisation of these concretions is problematic due to the excitation volume caused by operating conditions required to detect minor amounts of Zn in the presence of significant amounts of Na. For this reason, previous researchers have not demonstrated this surprising finding

Pyritic stromatolites from the Paleoarchean Dresser Formation, Pilbara Craton: Resolving biogenicity and hydrothermally influenced ecosystem dynamics

This study investigates the paleobiological significance of pyritic stromatolites from the 3.48 billion‐year‐old Dresser Formation, Pilbara Craton. By combining paleoenvironmental analyses with observations from well‐preserved stromatolites in newly obtained drill cores, the research reveals stratiform and columnar to domal pyritic structures with wavy to wrinkly laminations and crest thickening, hosted within facies variably influenced by syn‐depositional hydrothermal activity. The columnar and domal stromatolites occur in strata with clearly distinguishable primary depositional textures. Mineralogical variability and fine‐scale interference textures between the microbialites and the enclosing sediment highlight interplays between microbial and depositional processes. The stromatolites consist of organomineralization – nanoporous pyrite and microspherulitic barite – hosting significant thermally mature organic matter (OM). This includes filamentous organic microstructures encased within nanoporous pyrite, resembling the extracellular polymeric substance (EPS) of microbes. These findings imply biogenicity and support the activity of microbial life in a volcano‐sedimentary environment with hydrothermal activity and evaporative cycles. Coupled changes in stromatolite morphology and host facies suggest growth in diverse niches, from dynamic, hydrothermally influenced shallow‐water environments to restricted brine pools strongly enriched in from seawater and hydrothermal activity. These observations, along with S stable isotope data indicating influence by S metabolisms, and accumulations of biologically significant metals and metalloids (Ni and As) within the microbialites, help constrain microbial processes. Columnar to domal stromatolites in dynamic, hydrothermally influenced shallow water deposits likely formed by microbial communities dominated by phototrophs. Stratiform pyritic structures within barite‐rich strata may reflect the prevalence of chemotrophs near hydrothermal venting, where hydrothermal activity and microbial processes influenced barite precipitation. Rapid pyrite precipitation, a putative taphonomic process for preserving microbial remnants, is attributed to microbial sulfate reduction and reduced S sourced from hydrothermal activity. In conclusion, this research underscores the biogenicity of the Dresser stromatolites and advances our understanding of microbial ecosystems in Earth's early history