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.

scholarly journals Bayesian and E-Bayesian Estimations of Bathtub-Shaped Distribution under Generalized Type-I Hybrid Censoring

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 934
Author(s):  
Yuxuan Zhang ◽  
Kaiwei Liu ◽  
Wenhao Gui
Keyword(s):  
Bayesian Method ◽  
Real Data ◽  
Loss Functions ◽  
Type I ◽  
Statistical Efficiency ◽  
Unknown Parameters ◽  
Data Set ◽  
Hybrid Censoring ◽  
Bayesian Estimations ◽  
Generalized Type

For the purpose of improving the statistical efficiency of estimators in life-testing experiments, generalized Type-I hybrid censoring has lately been implemented by guaranteeing that experiments only terminate after a certain number of failures appear. With the wide applications of bathtub-shaped distribution in engineering areas and the recently introduced generalized Type-I hybrid censoring scheme, considering that there is no work coalescing this certain type of censoring model with a bathtub-shaped distribution, we consider the parameter inference under generalized Type-I hybrid censoring. First, estimations of the unknown scale parameter and the reliability function are obtained under the Bayesian method based on LINEX and squared error loss functions with a conjugate gamma prior. The comparison of estimations under the E-Bayesian method for different prior distributions and loss functions is analyzed. Additionally, Bayesian and E-Bayesian estimations with two unknown parameters are introduced. Furthermore, to verify the robustness of the estimations above, the Monte Carlo method is introduced for the simulation study. Finally, the application of the discussed inference in practice is illustrated by analyzing a real data set.

scholarly journals Modelling Mortgage Insurance Claims Experience: A Case Study

1994 ◽  
Vol 24 (1) ◽  
pp. 97-129 ◽  
Author(s):  
Greg Taylor
Keyword(s):  
Geographic Location ◽  
Real Data ◽  
Internal Variables ◽  
Functional Dependencies ◽  
Data Set ◽  
Mortgage Insurance ◽  
Section 8 ◽  
Sequence Of Events ◽  
Claim Frequency ◽  
Credit Worthiness

AbstractMortgage insurance indemnifies a mortage lender against loss on default by the borrower. The sequence of events leading to a claim under this type of insurance is relatively complex, depending not only on the credit worthiness of the borrower but also on a number of external economic factors.Prominent among these external factors are the loan to valuation ratio of the insured loan, the disposable income of the borrower, and movements in property values. A broad theoretical model of the functional dependencies of claim frequency and average claim size on these variables is established in Sections 6 and 7. Section 8 fits these models, extended by other “internal” variables such as the geographic location of the mortgaged property, to a real data set.Section 9 compares the fitted model with the data, and finds an acceptable fit despite extreme fluctuations in the claims experience recorded in the data set.

scholarly journals A novel gene-set association test based on variance-gamma distribution

2018 ◽  
Vol 28 (9) ◽  
pp. 2868-2875
Author(s):  
Zhongxue Chen ◽  
Qingzhong Liu ◽  
Kai Wang
Keyword(s):  
Gamma Distribution ◽  
Type I Error ◽  
Null Distribution ◽  
Real Data ◽  
Association Test ◽  
P Value ◽  
Type I ◽  
Test Statistic ◽  
Data Set ◽  
Variance Gamma

Several gene- or set-based association tests have been proposed recently in the literature. Powerful statistical approaches are still highly desirable in this area. In this paper we propose a novel statistical association test, which uses information of the burden component and its complement from the genotypes. This new test statistic has a simple null distribution, which is a special and simplified variance-gamma distribution, and its p-value can be easily calculated. Through a comprehensive simulation study, we show that the new test can control type I error rate and has superior detecting power compared with some popular existing methods. We also apply the new approach to a real data set; the results demonstrate that this test is promising.

scholarly journals Study on Lindley Distribution Accelerated Life Tests: Application and Numerical Simulation

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2080
Author(s):  
E. H. Hafez ◽  
Fathy H. Riad ◽  
Sh. A. M. Mubarak ◽  
M. S. Mohamed
Keyword(s):  
Real Data ◽  
Upper And Lower Bounds ◽  
Type Ii ◽  
Research Project ◽  
Data Set ◽  
Lindley Distribution ◽  
Accelerated Life Tests ◽  
Accelerated Life ◽  
Life Tests ◽  
Censored Sample

Saving money and time are very important in any research project, so we must find a way to decrease the time of the experiment. This method is called the accelerated life tests (ALT) under censored samples, which is a very efficient method to reduce time, which leads to a decrease in the cost of the experiment. This research project includes inference on Lindley distribution in a simple step-stress ALT for the Type II progressive censored sample. The paper contains two major sections, which are a simulation study and a real-data application on the experimental design of an industry experiment on lamps. These sections are used to conduct results on the study of the distribution. The simulation was done using Mathematica 11 program. To use real data in the censored sample, we fitted them to be compatible with the Lindley distribution using the modified Kolmogorov–Smirnov (KS) goodness of fit test for progressive Type II censored data. We used the tampered random variable (TRV) acceleration model to generate early failures of items under stress. We also found the values of the distribution parameter and the accelerating factor using the maximum likelihood estimation of (MLEs) and Bayes estimates (BEs) using symmetric loss function for both simulated data and real data. Next, we estimated the upper and lower bounds of the parameters using three methods, namely approximate confidence intervals (CIs), Bootstrap CIs, and credible CIs, for both parameters of the distribution, ψ and ζ. Finally, we found the value of the parameter for the real data set under normal use conditions and stress conditions and graphed the reliability functions under normal and accelerated use.

scholarly journals The Weighted Power Lindley Distribution with Applications on the Life Time Data

2020 ◽  
pp. 225-237
Author(s):  
Aafaq A. Rather ◽  
Gamze Özel
Keyword(s):  
Information Matrix ◽  
Life Time ◽  
Real Data ◽  
Data Sets ◽  
Lifetime Data ◽  
Time Data ◽  
Data Set ◽  
Lindley Distribution ◽  
Power Lindley Distribution ◽  
New Distribution

In this paper, we have proposed a new version of power lindley distribution known as weighted power lindley distribution. The different structural properties of the newly model have been studied. The maximum likelihood estimators of the parameters and the Fishers information matrix have been discussed. It also provides more flexibility to analyze complex real data sets.  An application of the model to a real data set is analyzed using the new distribution, which shows that the weighted power Lindley distribution can be used quite effectively in analyzing real lifetime data.

scholarly journals On a new generalized lindley distribution: Properties, estimation and applications

PLoS ONE ◽  
2021 ◽  
Vol 16 (2) ◽  
pp. e0244328
Author(s):  
Ali Algarni
Keyword(s):  
Asymptotic Variance ◽  
Real Data ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Data Set ◽  
Lindley Distribution ◽  
New Family ◽  
Proposed Model ◽  
The Subject ◽  
Mean Square Error Criterion

In this study, an extension of the generalized Lindley distribution using the Marshall-Olkin method and its own sub-models is presented. This new model for modelling survival and lifetime data is flexible. Several statistical properties and characterizations of the subject distribution along with its reliability analysis are presented. Statistical inference for the new family such as the Maximum likelihood estimators and the asymptotic variance covariance matrix of the unknown parameters are discussed. A simulation study is considered to compare the efficiency of the different estimators based on mean square error criterion. Finally, a real data set is analyzed to show the flexibility of our proposed model compared with the fit attained by some other competitive distributions.

Negative binomial improved second degree lindley distribution and its application

2020 ◽  
pp. 569-581
Author(s):  
R. Ashly ◽  
C. S. Rajitha
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Data Set ◽  
Factorial Moments ◽  
Lindley Distribution ◽  
Second Degree

The objective of this paper is to introduce a new two parameter mixed negative binomial distribution, namely negative binomial-improved second degree Lindley(NB-ISL) distribution. This distribution is obtained by mixing the negative binomial distribution with the improved second degree Lindley distribution. Many mixed distributions have been used in the literature for modeling the over dispersed count data, which provide a better fit compared to the Poisson and negative binomial distribution. In addition, we present the basic statistical properties of the new distribution such as factorial moments, mean and variance and the behavior of mean, variance and coefficient of variation are also discussed. Parameter estimation is implemented by using maximum likelihood estimation method. The performance of the NB-ISL distribution is shown in practice by applying it on real data set and compare it with some well-known count distributions. The result shows that the negative binomial-improved second degree Lindley distribution provides a better fit compared to Poisson, negative binomial and negative binomial-Lindley distributions.

scholarly journals Some Size Biased Probability Models for Adult out Migration Pattern

2020 ◽  
pp. 78-91
Author(s):  
Brijesh P. Singh ◽  
Sandeep Singh ◽  
Utpal Dhar Das ◽  
Gunjan Singh
Keyword(s):  
Maximum Likelihood ◽  
Poisson Distribution ◽  
Gamma Distribution ◽  
Real Data ◽  
Migration Pattern ◽  
Probability Models ◽  
Data Set ◽  
Proposed Model ◽  
Method Of Maximum Likelihood

In this paper an attempt has been made to inspect the distribution of the number of adult migrants from household through size biased probability models based on certain assumptions. Size Biased Poisson distribution compounded with various forms of Gamma distribution i.e. Gamma (1,θ) , Gamma (2,θ) and mixture of Gamma (1,θ) and Gamma (2,θ)  has been examined for some real data set of adult migration. The parameters of the proposed model have been estimated by method of maximum likelihood.  test indicates that the distributions proposed here are quite satisfactory to explain the pattern of adult out migration.

scholarly journals Statistical Analysis for Generalized Progressive Hybrid Censored Data from Lindley Distribution under Step-Stress Partially Accelerated Life Test Model

2021 ◽  
Vol 50 (1) ◽  
pp. 105-120
Author(s):  
Aakriti Pandey ◽  
Arun Kaushik ◽  
Sanjay K. Singh ◽  
Umesh Singh
Keyword(s):  
Mean Squared Error ◽  
Real Data ◽  
Estimation Procedure ◽  
Accelerated Life Test ◽  
Test Model ◽  
Life Test ◽  
Data Set ◽  
Lindley Distribution ◽  
Accelerated Life ◽  
Censoring Scheme

The aim of this paper is to present the estimation procedure for the step-stress partially accelerated life test model under the generalized progressive hybrid censoring scheme. The uncertainties are assumed to be governed by Lindley distribution. The problem with point and interval estimation of the parameters as well as the acceleration factor using maximum likelihood approach for the step-stress partially accelerated life test model has been considered. A simulation study is conducted to monitor the performance of the estimators on the basis of the mean squared error under the considered censoring scheme. The expected total time of the test under an accelerated condition is computed to examine the effects of the parameters on the duration of the test. In addition, a graph of the expected total time of the test under accelerated and un-accelerated conditions is provided to highlight the effect due to acceleration. One real data set has been analyzed for illustrative purposes.

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.

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