Applying Generalized Linear Models to Insurance Data: Frequency/Severity versus Pure Premium Modeling

2016 ◽  
pp. 39-59
Author(s):  
Dan Tevet
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Pure Premium ◽  
Data Frequency ◽  
Insurance Data

scholarly journals Fitting Tweedie's Compound Poisson Model to Insurance Claims Data: Dispersion Modelling

2002 ◽  
Vol 32 (1) ◽  
pp. 143-157 ◽  
Author(s):  
Gordon K. Smyth ◽  
Bent Jørgensen
Keyword(s):  
Generalized Linear Models ◽  
Exponential Family ◽  
Linear Models ◽  
Likelihood Function ◽  
Poisson Model ◽  
Insurance Claims ◽  
Poisson Arrival ◽  
Insurance Claims Data ◽  
The Cost ◽  
Insurance Data

AbstractWe reconsider the problem of producing fair and accurate tariffs based on aggregated insurance data giving numbers of claims and total costs for the claims. Jørgensen and de Souza (Scand Actuarial J., 1994) assumed Poisson arrival of claims and gamma distributed costs for individual claims. Jørgensen and de Souza (1994) directly modelled the risk or expected cost of claims per insured unit, μ say. They observed that the dependence of the likelihood function on μ is as for a linear exponential family, so that modelling similar to that of generalized linear models is possible. In this paper we observe that, when modelling the cost of insurance claims, it is generally necessary to model the dispersion of the costs as well as their mean. In order to model the dispersion we use the framework of double generalized linear models. Modelling the dispersion increases the precision of the estimated tariffs. The use of double generalized linear models also allows us to handle the case where only the total cost of claims and not the number of claims has been recorded.

scholarly journals Penghitungan Premi Asuransi Kendaraan Bermotor Menggunakan Generalized Linear Models dengan Distribusi Tweedie

2021 ◽  
Vol 3 (2) ◽  
pp. 115-127
Author(s):  
Tri Andika Julia Putra ◽  
Donny Citra Lesmana ◽  
I Gusti Putu Purnaba
Keyword(s):  
Generalized Linear Models ◽  
Exponential Family ◽  
Linear Models ◽  
Insurance Company ◽  
Number Of Children ◽  
Multiple Data ◽  
Pure Premium ◽  
Premium Price ◽  
Tweedie Distribution ◽  
The Cost

ABSTRAKSeorang aktuaris mempunyai tugas penting dalam menentukan harga premi yang sesuai untuk setiap nasabah dengan risiko dan karakteristik yang berbeda. Banyak variabel yang dapat mempengaruhi harga premi. Oleh karena itu, aktuaris harus mengetahui variabel-variabel yang berpengaruh signifikan terhadap premi. Tujuan dari penelitian ini adalah untuk menentukan variabel yang dapat mempengaruhi besaran premi murni menggunakan distribusi campuran dalam menentukan besarnya premi melalui Generalized Linear Models (GLM) serta menentukan model harga premi yang sesuai berdasarkan variabel-variabel yang mempengaruhinya. Salah satu analisis statistik yang dapat digunakan untuk memodelkan premi asuransi adalah Generalized Linear Models. GLM merupakan perluasan dari model regresi klasik yang dapat mengakomodasi fleksibilitas untuk menggunakan beberapa distribusi data tetapi terbatas pada distribusi keluarga eksponensial. Dalam model GLM, premi diperoleh dengan mengalikan nilai ekspektasi bersyarat dari frekuensi klaim dan biaya klaim. Berdasarkan penelitian yang telah dilakukan diketahui bahwa frekuensi klaim dan besarnya klaim mengikuti distribusi Tweedie. Dari kedua model tersebut diketahui bahwa variabel yang mempengaruhi premi murni adalah jumlah anak, pendapatan per bulan, status pernikahan, pendidikan, pekerjaan, penggunaan kendaraan, besarnya bluebook yang dibayarkan, dan jenis kendaraan nasabah. Hal ini menunjukkan bahwa model GLM merupakan model yang representatif dan berguna bagi perusahaan asuransi. ABSTRACTIt is an important task for an actuary in determining the appropriate premium price for each customer with different risks and characteristics. Many variables can affect the premium price. Therefore, actuaries must determine the variables that significantly affect the premium. The purpose of this study is to determine the variables that can affect the amount of pure premium using a mixed distribution in determining the amount of premium through Generalized Linear Models (GLM) and determine the appropriate premium price model based on the variables that influence it. One of the statistical analyzes that can be used to model insurance premiums is the Generalized Linear Models. GLM is an extension of the classic regression model that can accommodate the flexibility of its users to use multiple data distributions but is limited to the exponential family distribution. In the GLM model, the premium is obtained by multiplying the conditional expected value of the frequency of claims and the cost of claims. Based on the research that has been done, it is known that the frequency of claims and the size of claims follow the Tweedie distribution. From the two models, it is known that the variables affecting the pure premium are the number of children, monthly income, marital status, education, occupation, vehicle use, the number of bluebooks paid, and the type of vehicle from the customer. This shows that the GLM model is a representative and useful model for the insurance company business.

Effect of Different Dentifrices, Bleaching with 35% Hydrogen Peroxide, and Red Wine on Surface Color and Roughness of Bovine Enamel

2020 ◽  
Vol 02 ◽  
Author(s):  
RM Garcia ◽  
WF Vieira-Junior ◽  
JD Theobaldo ◽  
NIP Pini ◽  
GM Ambrosano ◽  
...  
Keyword(s):  
Hydrogen Peroxide ◽  
Generalized Linear Models ◽  
Repeated Measures ◽  
Red Wine ◽  
Linear Models ◽  
Artificial Saliva ◽  
Surface Color ◽  
Dental Bleaching ◽  
Surface Alteration ◽  
Bovine Enamel

Objective: To evaluate color and roughness of bovine enamel exposed to dentifrices, dental bleaching with 35% hydrogen peroxide (HP), and erosion/staining by red wine. Methods: Bovine enamel blocks were exposed to: artificial saliva (control), Oral-B Pro-Health (stannous fluoride with sodium fluoride, SF), Sensodyne Repair & Protect (bioactive glass, BG), Colgate Pro-Relief (arginine and calcium carbonate, AR), or Chitodent (chitosan, CHI). After toothpaste exposure, half (n=12) of the samples were bleached (35% HP), and the other half were not (n=12). The color (CIE L*a* b*, ΔE), surface roughness (Ra), and scanning electron microscopy were evaluated. Color and roughness were assessed at baseline, post-dentifrice and/or -dental bleaching, and after red wine. The data were subjected to analysis of variance (ANOVA) (ΔE) for repeated measures (Ra), followed by Tukey ́s test. The L*, a*, and b* values were analyzed by generalized linear models (a=0.05). Results: The HP promoted an increase in Ra values; however, the SF, BG, and AR did not enable this alteration. After red wine, all groups apart from SF (unbleached) showed increases in Ra values; SF and AR promoted decreases in L* values; AR demonstrated higher ΔE values, differing from the control; and CHI decreased the L* variation in the unbleached group. Conclusion: Dentifrices did not interfere with bleaching efficacy of 35% HP. However, dentifrices acted as a preventive agent against surface alteration from dental bleaching (BG, SF, and AR) or red wine (SF). Dentifrices can decrease (CHI) or increase (AR and SF) staining by red wine.

Economic burden of readmission due to postoperative cerebrospinal fluid leak in Chinese patients

2020 ◽  
Vol 9 (16) ◽  
pp. 1105-1115
Author(s):  
Shuqing Wu ◽  
Xin Cui ◽  
Shaoyu Zhang ◽  
Wenqi Tian ◽  
Jiazhen Liu ◽  
...  
Keyword(s):  
Cerebrospinal Fluid ◽  
Generalized Linear Models ◽  
Economic Burden ◽  
Linear Models ◽  
Chinese Patients ◽  
Cerebrospinal Fluid Leakage ◽  
Index Hospitalization ◽  
Real World Data ◽  
Factors Associated ◽  
Hospitalization Cost

Aim: This real-world data study investigated the economic burden and associated factors of readmissions for cerebrospinal fluid leakage (CSFL) post-cranial, transsphenoidal, or spinal index surgeries. Methods: Costs of CSFL readmissions and index hospitalizations during 2014–2018 were collected. Readmission cost was measured as absolute cost and as percentage of index hospitalization cost. Factors associated with readmission cost were explored using generalized linear models. Results: Readmission cost averaged US$2407–6106, 35–94% of index hospitalization cost. Pharmacy costs were the leading contributor. Generalized linear models showed transsphenoidal index surgery and surgical treatment for CSFL were associated with higher readmission costs. Conclusion: CSFL readmissions are a significant economic burden in China. Factors associated with higher readmission cost should be monitored.

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