A CLASS OF MIXTURE OF EXPERTS MODELS FOR GENERAL INSURANCE: APPLICATION TO CORRELATED CLAIM FREQUENCIES

2019 ◽  
Vol 49 (03) ◽  
pp. 647-688 ◽  
Author(s):  
Tsz Chai Fung ◽  
Andrei L. Badescu ◽  
X. Sheldon Lin
Keyword(s):  
Risk Level ◽  
Automobile Insurance ◽  
Ecm Algorithm ◽  
Mixture Of Experts ◽  
Data Set ◽  
Proposed Model ◽  
Insurance Perspective ◽  
Claim Frequency ◽  
Complex Features ◽  
Insurance Data

AbstractThis paper focuses on the estimation and application aspects of the Erlang count logit-weighted reduced mixture of experts model (EC-LRMoE), which is a fully flexible multivariate insurance claim frequency regression model. We first prove the identifiability property of the proposed model to ensure that it is a suitable candidate for statistical inference. An expectation conditional maximization (ECM) algorithm is developed for efficient model calibrations. Three simulation studies are performed to examine the effectiveness of the proposed ECM algorithm and the versatility of the proposed model. The applicability of the EC-LRMoE is shown through fitting an European automobile insurance data set. Since the data set contains several complex features, we find it necessary to adopt such a flexible model. Apart from showing excellent fitting results, we are able to interpret the fitted model in an insurance perspective and to visualize the relationship between policyholders’ information and their risk level. Finally, we demonstrate how the fitted model may be useful for insurance ratemaking.

scholarly journals Bayesian Bonus-Malus Premium with Poisson-Lindley Distributed Claim Frequency and Lognormal-Gamma DistributedClaim Severity in Automobile Insurance

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Gamma Distribution ◽  
Bayesian Method ◽  
Real Data ◽  
Automobile Insurance ◽  
Data Set ◽  
Lindley Distribution ◽  
Insured Individual ◽  
Claim Frequency

The traditional automobile insurance bonus-malus system (BMS) merit-rating depends on thenumber of claims. An insured individual who makes a small severity claim is penalized unfairly compared to aninsured person who makes a large severity claim. A model for assigning the bonus-malus premium wasproposed. Consideration was based on both the number and size of the claims that were assumed to follow aPoisson-Lindley distribution and a Lognormal-Gamma distribution, respectively. The Bayesian method wasapplied to compute the bonus-malus premiums, integrated by both frequency and severity components based onthe posterior criteria. Practical examples using a real data set are provided. This approach offers a fairer methodof penalizing all policyholders in the portfolio.

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

2019 ◽  
Vol XVI (2) ◽  
pp. 1-11
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Muhammad Akbar Ali Shah ◽  
Emrah Altun
Keyword(s):  
Real Data ◽  
Continuous Model ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Probability Weighted Moment ◽  
Record Statistics ◽  
Maximum Likelihood Criterion

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

Human Activity Recognition using Fourier Transform Inspired Deep Learning Combination Model

2019 ◽  
Vol 9 (1) ◽  
pp. 16-31
Author(s):  
Kyungkoo Jun
Keyword(s):  
Fourier Transform ◽  
Deep Learning ◽  
Short Term Memory ◽  
Window Size ◽  
Sensor Data ◽  
Data Sets ◽  
Data Set ◽  
Proposed Model ◽  
Testing Data ◽  
Labeling Scheme

Background & Objective: This paper proposes a Fourier transform inspired method to classify human activities from time series sensor data. Methods: Our method begins by decomposing 1D input signal into 2D patterns, which is motivated by the Fourier conversion. The decomposition is helped by Long Short-Term Memory (LSTM) which captures the temporal dependency from the signal and then produces encoded sequences. The sequences, once arranged into the 2D array, can represent the fingerprints of the signals. The benefit of such transformation is that we can exploit the recent advances of the deep learning models for the image classification such as Convolutional Neural Network (CNN). Results: The proposed model, as a result, is the combination of LSTM and CNN. We evaluate the model over two data sets. For the first data set, which is more standardized than the other, our model outperforms previous works or at least equal. In the case of the second data set, we devise the schemes to generate training and testing data by changing the parameters of the window size, the sliding size, and the labeling scheme. Conclusion: The evaluation results show that the accuracy is over 95% for some cases. We also analyze the effect of the parameters on the performance.

AN EFFICIENT MACHINE LEARNING MODEL FOR PREDICTION OF ACUTE MYOCARDIAL INFARCTION

2020 ◽  
Vol 13 ◽  
Author(s):  
Dhilsath Fathima.M ◽  
S. Justin Samuel ◽  
R. Hari Haran
Keyword(s):  
Machine Learning ◽  
Myocardial Infarction ◽  
Acute Myocardial Infarction ◽  
Logistic Regression ◽  
Decision Tree ◽  
Learning Model ◽  
Training Dataset ◽  
Data Set ◽  
Machine Learning Model ◽  
Proposed Model

Aim: This proposed work is used to develop an improved and robust machine learning model for predicting Myocardial Infarction (MI) could have substantial clinical impact. Objectives: This paper explains how to build machine learning based computer-aided analysis system for an early and accurate prediction of Myocardial Infarction (MI) which utilizes framingham heart study dataset for validation and evaluation. This proposed computer-aided analysis model will support medical professionals to predict myocardial infarction proficiently. Methods: The proposed model utilize the mean imputation to remove the missing values from the data set, then applied principal component analysis to extract the optimal features from the data set to enhance the performance of the classifiers. After PCA, the reduced features are partitioned into training dataset and testing dataset where 70% of the training dataset are given as an input to the four well-liked classifiers as support vector machine, k-nearest neighbor, logistic regression and decision tree to train the classifiers and 30% of test dataset is used to evaluate an output of machine learning model using performance metrics as confusion matrix, classifier accuracy, precision, sensitivity, F1-score, AUC-ROC curve. Results: Output of the classifiers are evaluated using performance measures and we observed that logistic regression provides high accuracy than K-NN, SVM, decision tree classifiers and PCA performs sound as a good feature extraction method to enhance the performance of proposed model. From these analyses, we conclude that logistic regression having good mean accuracy level and standard deviation accuracy compared with the other three algorithms. AUC-ROC curve of the proposed classifiers is analyzed from the output figure.4, figure.5 that logistic regression exhibits good AUC-ROC score, i.e. around 70% compared to k-NN and decision tree algorithm. Conclusion: From the result analysis, we infer that this proposed machine learning model will act as an optimal decision making system to predict the acute myocardial infarction at an early stage than an existing machine learning based prediction models and it is capable to predict the presence of an acute myocardial Infarction with human using the heart disease risk factors, in order to decide when to start lifestyle modification and medical treatment to prevent the heart disease.

scholarly journals Tomato Leaf Disease Diagnosis Based on Improved Convolution Neural Network by Attention Module

Agriculture ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 651
Author(s):  
Shengyi Zhao ◽  
Yun Peng ◽  
Jizhan Liu ◽  
Shuo Wu
Keyword(s):  
Neural Network ◽  
High Performance ◽  
Model Comparison ◽  
Research Direction ◽  
Disease Diagnosis ◽  
Tomato Leaf ◽  
Identification Accuracy ◽  
Main Research ◽  
Proposed Model ◽  
Complex Features

Crop disease diagnosis is of great significance to crop yield and agricultural production. Deep learning methods have become the main research direction to solve the diagnosis of crop diseases. This paper proposed a deep convolutional neural network that integrates an attention mechanism, which can better adapt to the diagnosis of a variety of tomato leaf diseases. The network structure mainly includes residual blocks and attention extraction modules. The model can accurately extract complex features of various diseases. Extensive comparative experiment results show that the proposed model achieves the average identification accuracy of 96.81% on the tomato leaf diseases dataset. It proves that the model has significant advantages in terms of network complexity and real-time performance compared with other models. Moreover, through the model comparison experiment on the grape leaf diseases public dataset, the proposed model also achieves better results, and the average identification accuracy of 99.24%. It is certified that add the attention module can more accurately extract the complex features of a variety of diseases and has fewer parameters. The proposed model provides a high-performance solution for crop diagnosis under the real agricultural environment.

Predicting Physical Activity and Lifelong Health Through Personal Control and Educational Attainment

2021 ◽  
pp. 003151252110292
Author(s):  
Jinyi Zhou ◽  
Xuesong Ding ◽  
Yuefan Zhai ◽  
Qing Yi
Keyword(s):  
Physical Activity ◽  
Educational Level ◽  
Personal Development ◽  
Educational Achievement ◽  
Personal Control ◽  
Well Being ◽  
Mediating Effect ◽  
Data Set ◽  
Education And Health ◽  
Proposed Model

Prior studies have shown that physical activity (PA) is strongly associated with lifelong health and well-being. Thus, analyses of relationships among individual differences, PA, education, and health may provide important insights into the sustainability of PA-related personal development efforts. In this longitudinal study, we tested a proposed model in a data set of 12,686 participants from the National Longitudinal Survey of Youth 1979 (NLSY 79). We used hierarchical regressions and bootstrapping to test hypotheses concerning the main effect of personal control on lifetime health, the mediating effect of PA, and the moderating effect of educational achievement. We found that individuals’ self-reported PA was positively related to their health status. Additionally, there was a positive mediating effect of self-reported PA on the relationship between personal control and health when the individual’s educational level was high, and there was a negative mediating effect of self-reported PA when an individual’s educational level was low. Based on these results, we provide relevant government policy suggestions for increasing fitness participation, constructing sports facilities, and encouraging educational institutions to include health education in their efforts.

Messages of Oscillatory Correlograms: A Spike Train Model

2008 ◽  
Vol 20 (5) ◽  
pp. 1211-1238 ◽  
Author(s):  
Gaby Schneider
Keyword(s):  
Spike Train ◽  
Null Model ◽  
Simulated Data ◽  
Joint Analysis ◽  
Data Set ◽  
Proposed Model ◽  
Peak Asymmetry ◽  
Millisecond Range ◽  
Temporal Interactions ◽  
Underlying Processes

Oscillatory correlograms are widely used to study neuronal activity that shows a joint periodic rhythm. In most cases, the statistical analysis of cross-correlation histograms (CCH) features is based on the null model of independent processes, and the resulting conclusions about the underlying processes remain qualitative. Therefore, we propose a spike train model for synchronous oscillatory firing activity that directly links characteristics of the CCH to parameters of the underlying processes. The model focuses particularly on asymmetric central peaks, which differ in slope and width on the two sides. Asymmetric peaks can be associated with phase offsets in the (sub-) millisecond range. These spatiotemporal firing patterns can be highly consistent across units yet invisible in the underlying processes. The proposed model includes a single temporal parameter that accounts for this peak asymmetry. The model provides approaches for the analysis of oscillatory correlograms, taking into account dependencies and nonstationarities in the underlying processes. In particular, the auto- and the cross-correlogram can be investigated in a joint analysis because they depend on the same spike train parameters. Particular temporal interactions such as the degree to which different units synchronize in a common oscillatory rhythm can also be investigated. The analysis is demonstrated by application to a simulated data set.

scholarly journals Investigating the Broken-Heart Effect: a Model for Short-Term Dependence between the Remaining Lifetimes of Joint Lives

2012 ◽  
Vol 7 (2) ◽  
pp. 236-257 ◽  
Author(s):  
Jaap Spreeuw ◽  
Iqbal Owadally
Keyword(s):  
Mortality Rates ◽  
Short Term ◽  
Numerical Work ◽  
Data Set ◽  
Multiple State ◽  
Multiple State Model ◽  
Insurance Data ◽  
Over Time ◽  
Assurance Contracts

AbstractWe analyze the mortality of couples by fitting a multiple state model to a large insurance data set. We find evidence that mortality rates increase after the death of a partner and, in addition, that this phenomenon diminishes over time. This is popularly known as a “broken-heart” effect and we find that it affects widowers more than widows. Remaining lifetimes of joint lives therefore exhibit short-term dependence. We carry out numerical work involving the pricing and valuation of typical contingent assurance contracts and of a joint life and survivor annuity. If insurers ignore dependence, or mis-specify it as long-term dependence, then significant mis-pricing and inappropriate provisioning can result. Detailed numerical results are presented.

scholarly journals Mixture of Inverse Weibull and Lognormal Distributions: Properties, Estimation, and Illustration

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
K. S. Sultan ◽  
A. S. Al-Moisheer
Keyword(s):  
Information Matrix ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Component Mixture ◽  
Data Set ◽  
Hazard Functions ◽  
Lognormal Distributions ◽  
Proposed Model ◽  
Estimation Of Model Parameters

We discuss the two-component mixture of the inverse Weibull and lognormal distributions (MIWLND) as a lifetime model. First, we discuss the properties of the proposed model including the reliability and hazard functions. Next, we discuss the estimation of model parameters by using the maximum likelihood method (MLEs). We also derive expressions for the elements of the Fisher information matrix. Next, we demonstrate the usefulness of the proposed model by fitting it to a real data set. Finally, we draw some concluding remarks.

scholarly journals Boosted Mixture of Experts: An Ensemble Learning Scheme

1999 ◽  
Vol 11 (2) ◽  
pp. 483-497 ◽  
Author(s):  
Ran Avnimelech ◽  
Nathan Intrator
Keyword(s):  
Recognition Task ◽  
Mixture Of Experts ◽  
Data Set ◽  
Combination Model ◽  
Digit Recognition ◽  
Learning Procedure ◽  
Nist Database ◽  
Boosting Algorithm ◽  
Regression Problems ◽  
Classification And Regression

We present a new supervised learning procedure for ensemble machines, in which outputs of predictors, trained on different distributions, are combined by a dynamic classifier combination model. This procedure may be viewed as either a version of mixture of experts (Jacobs, Jordan, Nowlan, & Hinton, 1991), applied to classification, or a variant of the boosting algorithm (Schapire, 1990). As a variant of the mixture of experts, it can be made appropriate for general classification and regression problems by initializing the partition of the data set to different experts in a boostlike manner. If viewed as a variant of the boosting algorithm, its main gain is the use of a dynamic combination model for the outputs of the networks. Results are demonstrated on a synthetic example and a digit recognition task from the NIST database and compared with classical ensemble approaches.

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