scholarly journals Analysis of Relativity Premium in Bonus-Malus System Based on Optimal Linear Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Yu Chen ◽  
Long Li
Keyword(s):  
Bayesian Method ◽  
Linear Method ◽  
Bayesian Estimator ◽  
Linear Estimator ◽  
Quadratic Loss ◽  
Automobile Insurance ◽  
Actuarial Mathematics ◽  
Irregular Pattern ◽  
Optimal Linear ◽  
Optimal Linear Estimator

A bonus-malus system plays a very important role in actuarial mathematics through determining its relativity premium, which is extensively used in automobile insurance. There are many ways including Bayesian estimator and ordinary linear estimator to calculate the relativity premium. There is no doubt that Bayesian estimator is the most accurate estimator; however, it is undesirable for commercial purposes for its rather irregular pattern. This paper aims to introduce an optimal linear estimator for relativity premium, which has a simple pattern and is obtained under the quadratic loss function such that the result is close to Bayesian method. The Loimaranta efficiency of such an optimal linear estimator has been studied and compared with the two methods mentioned above.

scholarly journals Quasi-E-Bayesian criteria versus quasi-Bayesian, quasi-hierarchical Bayesian and quasi-empirical Bayesian methods for estimating the scale parameter of the Erlang distribution

2016 ◽  
Vol 4 (1) ◽  
pp. 62 ◽  
Author(s):  
Hesham Reyad ◽  
Adil Younis ◽  
Amal Alkhedir
Keyword(s):  
Loss Function ◽  
Bayesian Method ◽  
Scale Parameter ◽  
Likelihood Function ◽  
Hierarchical Bayes ◽  
Erlang Distribution ◽  
Quadratic Loss ◽  
Hierarchical Bayesian ◽  
Empirical Bayesian ◽  
Symmetric Loss

This paper proposes a new modification for the E-Bayesian method of estimation to introduce a new technique namely Quasi E-Bayesian method (or briefly QE-Bayesian). The suggested criteria built in replacing the likelihood function by the quasi likelihood function in the E-Bayesian technique. This study is devoted to evaluate the performance of the new method versus the quasi-Bayesian, quasi-hierarchical Bayesian and quasi-empirical Bayesian approaches in estimating the scale parameter of the Erlang distribution. All estimators are obtained under symmetric loss function [squared error loss (SELF))] and four different asymmetric loss functions [Precautionary loss function (PLF), entropy loss function (ELF), Degroot loss function (DLF) and quadratic loss function (QLF)]. The properties of the QE-Bayesian estimates are introduced and the relations between the QE-Bayes and quasi-hierarchical Bayes estimates are discussed. Comparisons among all estimators are performed in terms of mean square error (MSE) via Monte Carlo simulation.

scholarly journals Insights from a Simple Expression for Linear Fisher Information in a Recurrently Connected Population of Spiking Neurons

2011 ◽  
Vol 23 (6) ◽  
pp. 1484-1502 ◽  
Author(s):  
Jeffrey Beck ◽  
Vikranth R. Bejjanki ◽  
Alexandre Pouget
Keyword(s):  
Lower Bound ◽  
Fisher Information ◽  
Covariance Structure ◽  
Simple Expression ◽  
Spiking Neurons ◽  
Linear Estimator ◽  
Sources Of Information ◽  
Tuning Curves ◽  
Input Noise ◽  
Optimal Linear

A simple expression for a lower bound of Fisher information is derived for a network of recurrently connected spiking neurons that have been driven to a noise-perturbed steady state. We call this lower bound linear Fisher information, as it corresponds to the Fisher information that can be recovered by a locally optimal linear estimator. Unlike recent similar calculations, the approach used here includes the effects of nonlinear gain functions and correlated input noise and yields a surprisingly simple and intuitive expression that offers substantial insight into the sources of information degradation across successive layers of a neural network. Here, this expression is used to (1) compute the optimal (i.e., information-maximizing) firing rate of a neuron, (2) demonstrate why sharpening tuning curves by either thresholding or the action of recurrent connectivity is generally a bad idea, (3) show how a single cortical expansion is sufficient to instantiate a redundant population code that can propagate across multiple cortical layers with minimal information loss, and (4) show that optimal recurrent connectivity strongly depends on the covariance structure of the inputs to the network.

Indicated Mean Effective Pressure Estimator Order Determination and Reduction When Using Estimated Engine Statistics

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
J. S. Arbuckle ◽  
J. B. Burl
Keyword(s):  
Estimation Error ◽  
Correlated Data ◽  
Training Data ◽  
Linear Estimator ◽  
Strongly Correlated ◽  
Effective Pressure ◽  
Cylinder Pressure ◽  
Indicated Mean Effective Pressure ◽  
Optimal Linear ◽  
Data Points

The indicated mean effective pressure (IMEP) is typically used as an engine running quality metric. IMEP depends on cylinder pressure, which is costly to measure, therefore it is useful to estimate IMEP from currently measured crankshaft encoder data. In this paper, the difficulties in developing an optimal linear estimator from acceleration computed from crankshaft rotational speed and cylinder pressure data are discussed, and strategies are presented to reduce these difficulties. Estimating IMEP from crankshaft data requires the determination of which data to use in the estimator. Without this step, the estimator can become unnecessarily complex due the inclusion of strongly correlated data points in the estimator. A strategy to determine the angular location of the acceleration points to use is presented and is shown to greatly reduce the estimator complexity without significantly affecting estimation error. Additionally, while increasing the estimator order usually decreases the estimation error, it will be shown that increasing the estimator order can actually increase the estimation error. This effect is due to uncertainties in the gains of the estimator. These uncertainties in the gains can result from using limited training data to estimate the statistics necessary to compute the gains or when dealing with a nonstationary system. A method of reducing the effect of these uncertainties by optimizing the estimator order based on the number of available training data cycles is developed and demonstrated.

scholarly journals A Simulation Study of Bayesian Estimator for Seemingly Unrelated Regression under Different Distributional Assumptions

2021 ◽  
pp. 1-8
Author(s):  
Ojo O. Oluwadare ◽  
Owonipa R. Oluremi ◽  
Enesi O. Lateifat
Keyword(s):  
Normal Distribution ◽  
Simulation Study ◽  
Bayesian Method ◽  
Mean Squared Error ◽  
Classical Method ◽  
Seemingly Unrelated Regression ◽  
Bayesian Estimator ◽  
Squared Error ◽  
Unrelated Regression ◽  
Distributional Assumptions

This paper presents Bayesian analysis of Seemingly Unrelated Regression (SUR) model. An independent prior for parameters was used. The Bayesian method was compared with classical method of estimation to know the most efficient estimator under different distributional assumptions through a simulation study. In order to facilitate comparison among these estimators, Mean Squared Error (MSE) was considered as a criterion. Furthermore, based on the simulation, it was deduced that MSE of the Bayesian estimator is smaller than all the classical methods of estimation for SUR model while Normal distribution was considered as an ideal distribution  in generation of disturbances in any simulation study.

scholarly journals Pricing of Premium for Automobile Insurance using Bayesian Method

2019 ◽  
Vol 8 (3) ◽  
pp. 6226-6229
Keyword(s):  
Parameter Estimation ◽  
Bayesian Method ◽  
Random Variables ◽  
Independent Random Variables ◽  
Automobile Insurance ◽  
Insurance Company ◽  
Bayes Method ◽  
Aggregate Claim ◽  
Distribution Parameter Estimation ◽  
Mutually Independent

The aggregate claim model can be used to determine the amount of premium charged to the insured by the insurance company. This model consists of two mutually independent random variables, namely the number of claims that occur per period and the amount of claim for each event. In this study, the number of claims is Poisson distributed, and the amount of claim is distributed by generalized extreme value (GEV). The Bayes method is used to estimate the parameters of each distribution. Parameter estimation results are used to calculate the expectations and variances of the aggregate claim model which are then used to calculate insurance premiums. Based on the estimation results, the amount of premium charged to the insured ranges from IDR 3,831,480 to IDR 6,443,860.

Predicting robust complete and full band gaps in three-dimensional frame structures

2021 ◽  
Vol 263 (5) ◽  
pp. 1442-1454
Author(s):  
Luiz Henrique Marra da Silva Ribeiro ◽  
Vinícius Fonseca Dal Poggetto ◽  
Danilo Beli ◽  
Adriano Todorovic Fabro ◽  
José Roberto de França Arruda
Keyword(s):  
Band Gap ◽  
Structural Damage ◽  
Periodic Structures ◽  
Three Dimensional ◽  
Band Gaps ◽  
Frame Structure ◽  
Dimensional Structure ◽  
Linear Estimator ◽  
Frame Element ◽  
Optimal Linear

Vibration can cause structural damage in dynamic systems when not designed properly. Recently, several approaches are emerging in structural dynamics as possible alternatives for passive vibration and noise control, such as phononic crystals and metamaterials. In this work, a three-dimensional frame that presents intersection of longitudinal, flexural and torsional band gaps is investigated. For periodic structures, the Irreducible Brillion Zone (IBZ) gives information for any possible angle of propagation of a wave. The manufacturing process induces variability along each three-dimensional frame element. The present study verifies the robustness of the band gaps of the three-dimensional structure against spatially varying geometry and mechanical properties. The spatial random fields are modeled using the expansion optimal linear estimator (EOLE). Bayesian statistics is used to infer on the stochastic response simulated using the Monte Carlo method combined with the EOLE. The three-dimensional frame is modeled via Euler-Bernoulli beam and ordinary shaft theories as well as with Timoshenko and Saint-Venant theories. It is shown that the three-dimensional frame structure exhibits a complete (for all waves) and full (throughout the IBZ) robust band gap against the proposed variability. Both models are able to predict this robust band gap.

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