scholarly journals Bivariate Mixed Poisson and Normal Generalised Linear Models with Sarmanov Dependence—An Application to Model Claim Frequency and Optimal Transformed Average Severity

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 73
Author(s):  
Ramon Alemany ◽  
Catalina Bolancé ◽  
Roberto Rodrigo ◽  
Raluca Vernic
Keyword(s):  
Linear Models ◽  
Negative Binomial ◽  
Bivariate Distribution ◽  
Generalised Linear Models ◽  
Natural Logarithm ◽  
Insurance Portfolio ◽  
Different Types ◽  
Claim Frequency ◽  
Mixed Poisson Distribution ◽  
Box Cox Transformation

The aim of this paper is to introduce dependence between the claim frequency and the average severity of a policyholder or of an insurance portfolio using a bivariate Sarmanov distribution, that allows to join variables of different types and with different distributions, thus being a good candidate for modeling the dependence between the two previously mentioned random variables. To model the claim frequency, a generalized linear model based on a mixed Poisson distribution -like for example, the Negative Binomial (NB), usually works. However, finding a distribution for the claim severity is not that easy. In practice, the Lognormal distribution fits well in many cases. Since the natural logarithm of a Lognormal variable is Normal distributed, this relation is generalised using the Box-Cox transformation to model the average claim severity. Therefore, we propose a bivariate Sarmanov model having as marginals a Negative Binomial and a Normal Generalized Linear Models (GLMs), also depending on the parameters of the Box-Cox transformation. We apply this model to the analysis of the frequency-severity bivariate distribution associated to a pay-as-you-drive motor insurance portfolio with explanatory telematic variables.

scholarly journals Modelling Claim Frequency in Vehicle Insurance

2016 ◽  
Vol 64 (2) ◽  
pp. 683-689
Author(s):  
Jiří Valecký
Keyword(s):  
Linear Models ◽  
Negative Binomial ◽  
Poisson Model ◽  
Binomial Model ◽  
Insurance Company ◽  
Linear Effect ◽  
New Findings ◽  
Insurance Portfolio ◽  
Systematic Component ◽  
Claim Frequency

The paper is focused on modelling claim frequency and extends the work of Kafková and Křivánková, 2014 (Kafková, S., Křivánková, L. 2014. Generalized linear models in vehicle insurance. Acta universitatis agriculturae et silviculturae mendelianae brunensis, 62(2): 383–388). We showed that overdispersion, non-linear systematic component and interacted rating factors should be considered when the claim frequency is modelled. We detected overdispersion in the Poisson model and employed the negative-binomial model to show that considering heterogeneity over insurance policies yields better fit of the model. We also analysed the linear effect of continuous rating factors and their mutual influences. We showed that non-linearity and interactions between rating factors yield the better fit of the model, as well as new findings related to the analysis of claim frequency. All empirical models were estimated on the insurance portfolio of Czech insurance company collected during the years 2004–2008.

scholarly journals Effect of month of birth on the risk of suicide

2006 ◽  
Vol 188 (5) ◽  
pp. 416-422 ◽  
Author(s):  
Emad Salib ◽  
Mario Cortina-Borja
Keyword(s):  
Suicide Risk ◽  
Linear Models ◽  
Negative Binomial ◽  
Early Summer ◽  
The Other ◽  
Month Of Birth ◽  
Generalised Linear Models ◽  
England And Wales ◽  
Risk Increase ◽  
New Strategies

BackgroundMonth of birth as a suicide risk factor has not been adequately explored. The findings of published studies are contradictory and inconclusive.AimsTo examine the association between suicide and month of birth using suicide data for a 22-year period in England and Wales. The sample size of 26915 suicides greatly exceeds all previous studies.MethodWe analysed all suicides (ICD-9 codes E950-959) and deaths from undetermined injury (E980-989) reported between 1979 and 2001 in England and Wales for persons born between 1955 and 1966, using Poisson and negative binomial generalised linear models with seasonal components.ResultsBirthrates of people who later kill themselves show disproportionate excess for April, May and June compared with the other months. Overall, we found an increase of 17% in the risk of suicide for people born in the peak month (spring -early summer) compared with those born in the trough month (autumn-early winter); this risk increase was larger for women (29.6%) than for men (13.7%).ConclusionsThe ‘month of birth’ factor in suicide can be interpreted in terms of the foetal origins hypothesis. Our findings might have implications for our understanding of the multifaceted aetiology of suicide and may eventually offer new strategies for research and prevention.

scholarly journals On Outliers and Interventions in Count Time Series following GLMs

2014 ◽  
Vol 43 (3) ◽  
pp. 181-193 ◽  
Author(s):  
Roland Fried ◽  
Tobias Liboschik ◽  
Hanan Elsaied ◽  
Stella Kitromilidou ◽  
Konstantinos Fokianos
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Robust Estimation ◽  
Linear Models ◽  
Sequential Testing ◽  
Generalised Linear Models ◽  
Count Time Series ◽  
Different Types ◽  
Robust Parameter ◽  
Robust Parameter Estimation

We discuss the analysis of count time series following generalised linear models in the presence of outliers and intervention effects. Different modifications of such models are formulated which allow to incorporate, detect and to a certain degree distinguish extraordinary events (interventions) of different types in count time series retrospectively. An outlook on extensions to the problem of robust parameter estimation, identification of the model orders by robust estimation of autocorrelations and partial autocorrelations, and online surveillance by sequential testing for outlyingness is provided. 

scholarly journals Effects of location of Norway spruce (Picea abies) stumps on their colonisation by insects in the mountains

2019 ◽  
Vol 61 (1) ◽  
pp. 64-77
Author(s):  
Iwona Skrzecz ◽  
Maria Bulka ◽  
Joanna Ukalska
Keyword(s):  
Picea Abies ◽  
Sea Level ◽  
Linear Models ◽  
Negative Binomial ◽  
Sun Exposure ◽  
Limited Information ◽  
Generalised Linear Models ◽  
The Family ◽  
Microclimatic Conditions ◽  
Physical And Chemical

Abstract Tree stumps provide habitat for insect assemblages, which are influenced by various factors. Among these factors, physical and chemical changes of the stumps, fungi developing in the dead wood and stump size are most often reported. However there is limited information about the abundance of insects in stumps that are located on mountains where there are different microclimatic conditions. The studies pointed at the determination whether the location of Picea abies stumps in mountains at different altitudes above sea level and on mountainsides with different sun exposure has an impact on the frequency of insects colonising them. The study was carried out in the Eastern Sudety Mountains situated in south-western Poland. The stumps were in clearcuts located at the altitudes 600–700 m and 900–1000 m above sea level and on southern and northern mountainsides. The insects were collected from 0.05 m2 of bark from each stump and identified to the family, order or species level. The numbers of insects in the stumps were modelled with the use of the Poisson distribution or the negative binomial distribution and the generalised linear models. Picea abies stumps were colonised by insects from 16 families in 3 orders (Coleoptera, Diptera, Hymenoptera) in which the Coleoptera was most frequently represented by the families Cerambycidae, Curculionidae (with the sub-family Scolytinae). In the stumps located at the elevation of 900–1000 m there were 28% more insects than in the stumps at 600–700 m. The stumps located on mountainsides with northern exposure were colonised more abundantly by Cerambycidae. Numbers of Curculionidae in the stumps were affected by altitude. Most Curculionidae were found in the stumps located at the elevation 900–1000 m above sea level. The interaction of altitude and mountainside exposure showed more insects in the stumps at higher altitude, regardless of the mountainside exposure. The results showed that the total number of insects in the stumps was influenced by their location in mountains.

scholarly journals Comparison of Approaches to Testing Equality of Expectations Among Samples from Poisson and Negative Binomial Distribution

2018 ◽  
Vol 66 (4) ◽  
pp. 1025-1034
Author(s):  
Martin Tejkal ◽  
Zuzana Hübnerová
Keyword(s):  
Maximum Likelihood ◽  
Sample Size ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Linear Models ◽  
Negative Binomial ◽  
Test Statistics ◽  
Power Functions ◽  
Generalised Linear Models ◽  
The Relationship

The paper deals with testing of the hypothesis of equality of expectations among p samples from Poisson or negative binomial distribution. a comparison of two main approaches is carried out. The first approach is based on transforming the samples from either Poisson or negative binomial distribution in order to achieve normality or variance stability, and then testing the hypothesis of equality of expectations via the F‑test. In the second approach, test statistics coming from the theory of maximum likelihood appearing in generalised linear models framework, specially designed for testing the hypothesis among samples from the respective distributions (Poisson or negative binomial), are used. The comparison is done graphically, by plotting the simulated power functions of the test of the hypothesis of equality of expectations, when first or second approach was used. Additionally, the relationship between the power functions obtained via the respective approaches and sample sizes is studied by evaluating the respective power functions as functions of a sample size numerically.

Nonnull asymptotic distributions of three classic criteria in generalised linear models

Biometrika ◽  
1994 ◽  
Vol 81 (4) ◽  
pp. 709-720 ◽  
Author(s):  
GAUSS M. CORDEIRO ◽  
DENISE A. BOTTER ◽  
SILVIA L. DE PAULA FERRARI
Keyword(s):  
Linear Models ◽  
Asymptotic Distributions ◽  
Generalised Linear Models

Quantitative Models of Motor Responses Subject to Longitudinal, Lateral, and Preview Constraints

1978 ◽  
Vol 20 (1) ◽  
pp. 35-39 ◽  
Author(s):  
Tarald O. Kvålseth
Keyword(s):  
Experimental Data ◽  
Motor Control ◽  
Linear Models ◽  
Movement Time ◽  
Arm Movements ◽  
Second Order ◽  
Motor Responses ◽  
First Order ◽  
Different Types ◽  
Index Of Difficulty

First- and second-order linear models of mean movement time for serial arm movements aimed at a target and subject to preview constraints and lateral constraints were formulated as extensions of the so-called Fitts's law of motor control. These models were validated on the basis of experimental data from five subjects and found to explain from 80% to 85% of the variation in movement time in the case of the first-order models and from 93% to 95% of such variation for the second-order models. Fitts's index of difficulty (ID) was generally found to contribute more to the movement time than did either the preview ID or the lateral ID defined. Of the different types of errors, target overshoots occurred far more frequently than undershoots.

Assessing covariability among populations in the presence of intraseries correlation: Columbia River spring-summer chinook salmon (Oncorhynchus tshawytscha) stocks

2000 ◽  
Vol 57 (3) ◽  
pp. 616-627 ◽  
Author(s):  
Louis W Botsford ◽  
Charles M Paulsen
Keyword(s):  
Chinook Salmon ◽  
Degrees Of Freedom ◽  
Oncorhynchus Tshawytscha ◽  
Columbia River ◽  
Data Types ◽  
Natural Logarithm ◽  
Different Types ◽  
John Day River ◽  
One Year ◽  
John Day

We assessed covariability among a number of spawning populations of spring-summer run chinook salmon (Oncorhynchus tshawytscha) in the Columbia River basin by computing correlations among several different types of spawner and recruit data. We accounted for intraseries correlation explicitly in judging the significance of correlations. To reduce the errors involved in computing effective degrees of freedom, we computed a generic effective degrees of freedom for each data type. In spite of the fact that several of these stocks have declined, covariability among locations using several different combinations of spawner and recruitment data indicated no basinwide covariability. There was, however, significant covariability among index populations within the three main subbasins: the Snake River, the mid-Columbia River, and the John Day River. This covariability was much stronger and more consistent in data types reflecting survival (e.g., the natural logarithm of recruits per spawner) than in data reflecting abundance (e.g., spawning escapement). We also tested a measure of survival that did not require knowing the age structure of spawners, the ratio of spawners in one year to spawners 4 years earlier. It displayed a similar spatial pattern.

scholarly journals Temporal analysis of the relationship between dengue and meteorological variables in the city of Rio de Janeiro, Brazil, 2001-2009

2012 ◽  
Vol 28 (11) ◽  
pp. 2189-2197 ◽  
Author(s):  
Adriana Fagundes Gomes ◽  
Aline Araújo Nobre ◽  
Oswaldo Gonçalves Cruz
Keyword(s):  
Minimum Temperature ◽  
Rio De Janeiro ◽  
Linear Models ◽  
Negative Binomial ◽  
Critical Factor ◽  
Temporal Analysis ◽  
Temporal And Spatial Distribution ◽  
Temperature And Precipitation ◽  
The Relationship ◽  
The City

Dengue, a reemerging disease, is one of the most important viral diseases transmitted by mosquitoes. Climate is considered an important factor in the temporal and spatial distribution of vector-transmitted diseases. This study examined the effect of seasonal factors and the relationship between climatic variables and dengue risk in the city of Rio de Janeiro, Brazil, from 2001 to 2009. Generalized linear models were used, with Poisson and negative binomial distributions. The best fitted model was the one with "minimum temperature" and "precipitation", both lagged by one month, controlled for "year". In that model, a 1°C increase in a month's minimum temperature led to a 45% increase in dengue cases in the following month, while a 10-millimeter rise in precipitation led to a 6% increase in dengue cases in the following month. Dengue transmission involves many factors: although still not fully understood, climate is a critical factor, since it facilitates analysis of the risk of epidemics.

scholarly journals An Ethology of Adaptation: Dolphins Stop Feeding but Continue Socializing in Construction-Degraded Habitat

2021 ◽  
Vol 8 ◽  
Author(s):  
Ann Weaver
Keyword(s):  
Linear Models ◽  
Negative Binomial ◽  
Environmental Changes ◽  
Bottlenose Dolphins ◽  
Observation Time ◽  
Mixed States ◽  
The West ◽  
Behavioral Adaptations ◽  
Construction Zone ◽  
Free Ranging

Adaptation is a biological mechanism by which organisms adjust physically or behaviorally to changes in their environment to become more suited to it. This is a report of free-ranging bottlenose dolphins’ behavioral adaptations to environmental changes from coastal construction in prime habitat. Construction was a 5-year bridge removal and replacement project in a tidal inlet along west central Florida’s Gulf of Mexico coastline. It occurred in two consecutive 2.5-year phases to replace the west and east lanes, respectively. Lane phases involved demolition/removal of above-water cement structures, below-water cement structures, and reinstallation of below + above water cement structures (N = 2,098 photos). Data were longitudinal (11 years: 2005–2016, N = 1,219 surveys 2–4 times/week/11 years, N = 4,753 dolphins, 591.95 h of observation in the construction zone, 126 before-construction surveys, 568 during-construction surveys, 525 after-construction surveys). The dependent variable was numbers of dolphins (count) in the immediate construction zone. Three analyses examined presence/absence, total numbers of dolphins, and numbers of dolphins engaged in five behavior states (forage-feeding, socializing, direct travel, meandering travel, and mixed states) across construction. Analyses were GLIMMIX generalized linear models for logistic and negative binomial regressions to account for observation time differences as an exposure (offset) variable. Results showed a higher probability of dolphin presence than absence before construction began, more total dolphins before construction, and significant decreases in the numbers of feeding but not socializing dolphins. Significant changes in temporal rhythms also revealed finer-grained adaptations. Conclusions were that the dolphins adapted to construction in two ways, by establishing feeding locations beyond the disturbed construction zone and shifting temporal rhythms of behaviors that they continued to exhibit in the construction zone to later in the day when construction activities were minimized. This is the first study to suggest that the dolphins learned to cope with coastal construction with variable adjustments.

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