RATEMAKING OF DEPENDENT RISKS

2017 ◽  
Vol 47 (3) ◽  
pp. 875-894
Author(s):  
J. M. Andrade e Silva ◽  
M. de Lourdes Centeno
Keyword(s):  
Power Function ◽  
Generalized Linear Models ◽  
Regression Models ◽  
Linear Models ◽  
Negative Binomial ◽  
Laguerre Polynomial ◽  
Random Variable ◽  
Insurance Company ◽  
Dependent Risks ◽  
The Mean

AbstractWe start by describing how, in some cases, we can use variance-related premium principles in ratemaking, when the claim numbers and individual claim amounts are independent. We use quasi-likelihood generalized linear models, under the assumption that the variance function is a power function of the mean of the underlying random variable. We extend this approach to the cases where the claim numbers are correlated. Some alternatives to deal with dependent risks are presented, taking explicitly into account overdispersion. We present regression models covering the bivariate Poisson, the generalized bivariate negative binomial and the bivariate Poisson–Laguerre polynomial, which nest the bivariate negative binomial. We apply these models to a portfolio of the Portuguese insurance company Tranquilidade and compare the results obtained.

scholarly journals On the Trends of Registered Birth and Death Rates in Nigeria: Evidence from Generalized Linear Models

2019 ◽  
Author(s):  
Monday Osagie Adenomon ◽  
Emmanuel Chukwuma Anikweze
Keyword(s):  
Generalized Linear Models ◽  
Regression Models ◽  
Linear Models ◽  
Negative Binomial ◽  
Negative Binomial Regression ◽  
Natural Increase ◽  
Negative Binomial Regression Model ◽  
Annual Data ◽  
Death Rates ◽  
Binomial Regression

This study investigated the trends of registered Death and Birth in Nigeria using Generalized Linear Models. Annual data on Death and Birth was collected from National Population Commission for the period of 2004 to 2017. The Natural increase calculated revealed a positive trend in the natural increase in Nigeria from 2004 to 2017. Evidence from summary statistics revealed some level of over dispersion (variance > mean). This study explored Poisson Regression Models and Negative Binomial Regression Models using two links (identity and log). The results revealed a positive increase in registration of birth and death rates in Nigeria and among the competing the models, Negative Binomial regression model with identity link emerged as the best model for modeling birth and death rates registration in Nigeria. Data on numbers of deaths and causes of death are essential if countries are to determine priorities, formulate and monitor policies for public health care as well as other government policies that may be based on such data

scholarly journals Robust Statistical Inference in Generalized Linear Models Based on Minimum Renyi’s Pseudodistance Estimators

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 123
Author(s):  
María Jaenada ◽  
Leandro Pardo
Keyword(s):  
Generalized Linear Models ◽  
Influence Function ◽  
Regression Models ◽  
Linear Models ◽  
Asymptotic Properties ◽  
Significant Loss ◽  
Superior Performance ◽  
Test Statistics ◽  
Linear Regression Models ◽  
Type Test

Minimum Renyi’s pseudodistance estimators (MRPEs) enjoy good robustness properties without a significant loss of efficiency in general statistical models, and, in particular, for linear regression models (LRMs). In this line, Castilla et al. considered robust Wald-type test statistics in LRMs based on these MRPEs. In this paper, we extend the theory of MRPEs to Generalized Linear Models (GLMs) using independent and nonidentically distributed observations (INIDO). We derive asymptotic properties of the proposed estimators and analyze their influence function to asses their robustness properties. Additionally, we define robust Wald-type test statistics for testing linear hypothesis and theoretically study their asymptotic distribution, as well as their influence function. The performance of the proposed MRPEs and Wald-type test statistics are empirically examined for the Poisson Regression models through a simulation study, focusing on their robustness properties. We finally test the proposed methods in a real dataset related to the treatment of epilepsy, illustrating the superior performance of the robust MRPEs as well as Wald-type tests.

scholarly journals Association Between Pulsatile Components of Blood Pressure and Severe Tooth Loss in Rural Ecuador: The Three Villages Study

2020 ◽  
Vol 11 ◽  
pp. 215013272092867 ◽  
Author(s):  
Oscar H. Del Brutto ◽  
Robertino M. Mera ◽  
Bettsy Y. Recalde ◽  
Andrew P. Torpey ◽  
John P. Hill ◽  
...  
Keyword(s):  
Blood Pressure ◽  
Arterial Hypertension ◽  
Generalized Linear Models ◽  
Tooth Loss ◽  
Linear Models ◽  
Community Dwelling ◽  
Multivariate Models ◽  
Mediation Analyses ◽  
The Mean ◽  
Relevant Covariates

Background: Arterial hypertension has been associated with severe tooth loss, but differential associations with individual components of blood pressure (BP) have scarcely been investigated. We assessed the independent associations between pulsatile/steady components of BP and severe tooth loss in community-dwelling adults residing in 3 rural Ecuadorian villages. Methods: Individuals aged ≥40 years living in Atahualpa, El Tambo, and Prosperidad were identified during door-to-door surveys. Data collection focused on the number of remaining teeth and measurements of pulsatile/steady components of BP. Multivariate models were fitted to assess independent associations between pulsatile/steady BP components and severe tooth loss, after adjusting for relevant covariates. Results: A total of 1543 individuals were included. Oral exams identified 426 (28%) individuals with severe tooth loss. BP levels ≥140/90 mm Hg were determined in 481 (31%) individuals. The mean pulse pressure (PP) level was 55.3 ± 19 mm Hg. For systolic BP (SBP), the mean level was 133.1 ± 23.5 mm Hg, and for diastolic BP (DBP) it was 77.8 ± 11.5 mm Hg. Univariate models showed significant associations between severe tooth loss and SBP and PP, but not with DBP. However, the significance was taken away in fully adjusted generalized linear models. Age remained as an independent significant covariate in models using SBP and PP. Causal mediation analyses disclosed that percentages of the effect of severe tooth loss mediated by age were 99.5% for SBP and 98.9% for PP. Conclusion: This study shows that age captures most of the effect of the association between pulsatile components of BP and severe tooth loss.

scholarly journals The opposite effects of routine metabolic rate and metabolic rate during startle responses on variation in the predictability of behaviour in hermit crabs

Behaviour ◽  
2016 ◽  
Vol 153 (13-14) ◽  
pp. 1545-1566 ◽  
Author(s):  
Mariana Velasque ◽  
Mark Briffa
Keyword(s):  
Metabolic Rate ◽  
Generalized Linear Models ◽  
Startle Response ◽  
Linear Models ◽  
Elevated Temperatures ◽  
Hermit Crabs ◽  
Routine Metabolic Rate ◽  
Intraindividual Variation ◽  
The Mean ◽  
Pagurus Bernhardus

Studies on animal behaviour have suggested a link between personality and energy expenditure. However, most models assume constant variation within individuals, even though individuals vary between observations. Such variation is called intraindividual variation in behaviour (IIV). We investigate if IIV in the duration of the startle response is associated with metabolic rates (MR) in the hermit crabPagurus bernhardus. We repeatedly measured startle response durations and MR during each observation. We used double hierarchical generalized linear models to ask whether among and IIV in behaviour was underpinned by MR. We found no association between the mean duration of the startle responses and either routine MR or MR during startle response. Nevertheless, we found that IIV increased with MR during startle responses and decreased with routine MR. These results indicate that crabs with higher MR during startle responses behave less predictably, and that predictability is reduced during exposure to elevated temperatures.

Modeling of the spatial distribution of Pacific spiny dogfish (Squalus suckleyi) in the Gulf of Alaska using generalized additive and generalized linear models

2013 ◽  
Vol 70 (9) ◽  
pp. 1372-1385 ◽  
Author(s):  
Jason R. Gasper ◽  
Gordon H. Kruse
Keyword(s):  
Spatial Distribution ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Negative Binomial ◽  
Fish Habitat ◽  
Additive Model ◽  
Gulf Of Alaska ◽  
Spiny Dogfish ◽  
Essential Fish Habitat ◽  
Mortality Estimation

The Pacific spiny dogfish (Squalus suckleyi) is a common bycatch species in the Gulf of Alaska. Their spatial distribution is poorly understood, as most catch is discarded at sea. We analyzed spiny dogfish spatial distribution from fishery-dependent and -independent observations of longline gear between 1996 and 2008 using generalized additive and generalized linear models. Poisson, negative binomial, and quasi-Poisson error structures were investigated; the quasi-Poisson generalized additive model fit best. Models showed that spiny dogfish catches were concentrated east of Kodiak Island in waters ≤100 m deep. Results facilitate design of future spiny dogfish assessment surveys and identification of areas in which to focus at-sea observations for fishing mortality estimation, and provide the basis for first-ever designation of spiny dogfish essential fish habitat, despite US legal requirements for essential fish habitat designations since 1996. Identified areas of high bycatch may expedite spatial management by indicating areas in which directed spiny dogfish fisheries could be focused or, conversely, areas in which heightened conservation and catch accounting efforts would be most effective to prevent overfishing of this long-lived, late-maturing species.

scholarly journals Chilling to the bone: Lower temperatures increase vertebrate predation by Tonatia bidens (Chiroptera: Phyllostomidae)

2020 ◽  
Vol 37 ◽  
pp. 1-5
Author(s):  
Fernando Carvalho ◽  
Daniela A.S. Bôlla ◽  
Viviane Mottin ◽  
Suelen Zonta Kiem ◽  
Jairo J. Zocche ◽  
...  
Keyword(s):  
Environmental Factors ◽  
Generalized Linear Models ◽  
Negative Binomial Distribution ◽  
Diet Composition ◽  
Linear Models ◽  
Negative Binomial ◽  
Meteorological Station ◽  
Foraging Patterns ◽  
Influence Of Temperature ◽  
The North

The greater round-eared bat, Tonatia bidens (Spix, 1823), is a medium-sized phyllostomid bat distributed in the north of Argentina, Paraguay and Brazil. The diet and foraging patterns of this species are poorly known. We analyzed the composition of the diet of a population of T. bidens and how the temperature influences the consumption of vertebrates and invertebrates. To describe diet composition, we conducted weekly collections of food scrap from two monospecific night-perches. Data of temperature for the study period were taken from the meteorological station installed 300 m from the collection perches. The influence of temperature was evaluated using generalized linear models (GLMs) with negative binomial distribution. Tonatia bidens consumed 28 taxons (204 records), being at least 17 Artropods and 11 Passeriformes birds. Temperature explained a greater proportion of vertebrate abundance (R2 = 0.23) than invertebrate (R2 = 0.16) or to both pooled (R2 = 0.11). The relation with temperature was positive with invertebrates and negative with the vertebrates. The diet of the population of T. bidens comprised mainly invertebrates, which were the most frequent and diverse taxa. Data suggests that T. bidens has a diverse diet, with proportion of the item’s consumption varying temporally. Environmental factors, such as the temperature presented on this work, seems to be good proxies for the dietary traits of this species.

scholarly journals Sunburns among beachgoers in the northern coast of Peru: frequency and factors associated

PeerJ ◽  
2021 ◽  
Vol 9 ◽  
pp. e11473
Author(s):  
Eliana L. Fernandez-Quiroz ◽  
Lizeth Gonzales-Chachapoyas ◽  
Ana L. Alcantara-Diaz ◽  
Binz Bulnes-Villalta ◽  
Zulmy Ayala-Porras ◽  
...  
Keyword(s):  
Generalized Linear Models ◽  
Regression Models ◽  
Linear Models ◽  
Secondary Data ◽  
Sun Exposure ◽  
Prevalence Ratio ◽  
Northern Coast ◽  
Factors Associated ◽  
Northern Peru ◽  
Skin Phototype

Background Overexposure to ultraviolet (UV) radiation has increased skin cancer incidence and the risk of sunburns, especially during the summer months. Objective Identify the frequency and factors associated with sunburns in a sample of beachgoers in the northern coast of Peru. Methods We conducted a secondary data analysis of a previous study that assessed the awareness, behavior and attitudes concerning sun exposure among beachgoers. We included adults between 18 and 59 years who went to a beach in northern Peru during summer (March 2018). Three generalized linear models of the Poisson family were constructed to evaluate the factors associated with having had at least one sunburn last summer. All regression models reported the adjusted prevalence ratio (aPR) with their respective 95% confidence interval (95% CI). Results Of a total of 402 participants, 225 (56.0%) had one to five sunburns and 25 (6.2%) had six or more. Beachgoers who were 1–15 days (aPR: 1.16, 95% CI [1.05–1.27]) or more than 15 days (aPR: 1.22, 95% CI [1.09–1.36]) exposed to the sun on the beach had a higher frequency of at least one sunburn. The non-regular wearing of a hat or cap also increased the frequency of sunburns (aPR: 1.06, 95% CI [1.01–1.12]). In contrast, those who had Skin Phototype III (aPR: 0.94, 95% CI [0.88–0.99]) or IV (aPR: 0.69, 95% CI [0.63–0.75]) had a lower frequency of sunburns. Conclusion Three out of five beachgoers had one or more sunburns in the last summer. The factors associated with a higher frequency were the time of sun exposure at the beach and the non-regular use of a hat or cap. Type III–IV skin phototypes were associated with a lower sunburn frequency.

Sign in / Sign up

Export Citation Format

Share Document