scholarly journals GENERALIZING THE LOG-MOYAL DISTRIBUTION AND REGRESSION MODELS FOR HEAVY-TAILED LOSS DATA

2020 ◽  
pp. 1-43
Author(s):  
Zhengxiao Li ◽  
Jan Beirlant ◽  
Shengwang Meng
Keyword(s):  
Claim Data ◽  
Regression Modeling ◽  
Data Set ◽  
New Class ◽  
Data Regression ◽  
Loss Data ◽  
Catastrophic Loss ◽  
Earthquake Loss ◽  
Competing Models ◽  
Heavy Tailed

Abstract Catastrophic loss data are known to be heavy-tailed. Practitioners then need models that are able to capture both tail and modal parts of claim data. To this purpose, a new parametric family of loss distributions is proposed as a gamma mixture of the generalized log-Moyal distribution from Bhati and Ravi (2018), termed the generalized log-Moyal gamma (GLMGA) distribution. While the GLMGA distribution is a special case of the GB2 distribution, we show that this simpler model is effective in regression modeling of large and modal loss data. Regression modeling and applications to risk measurement are illustrated using a detailed analysis of a Chinese earthquake loss data set, comparing with the results of competing models from the literature. To this end, we discuss the probabilistic characteristics of the GLMGA and statistical estimation of the parameters through maximum likelihood. Further illustrations of the applicability of the new class of distributions are provided with the fire claim data set reported in Cummins et al. (1990) and a Norwegian fire losses data set discussed recently in Bhati and Ravi (2018).

scholarly journals A Family of Loss Distributions with an Application to the Vehicle Insurance Loss Data

2019 ◽  
pp. 731-744 ◽  
Author(s):  
Zubair Ahmad Ahmad ◽  
Eisa Mahmoudi Mahmoudi ◽  
G. G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Financial Risk ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Set ◽  
Loss Model ◽  
New Class ◽  
Proposed Model ◽  
Loss Distributions ◽  
Loss Data

Actuaries are often in search of nding an adequate loss model in the scenario of actuarial and financial risk management problems. In this work, we propose a new approach to obtain a new class of loss distributions. A special sub-model of the proposed family, called the Weibull-loss model isconsidered in detail. Some mathematical properties are derived and maximum likelihood estimates of the model parameters are obtained. Certain characterizations of the proposed family are also provided. A simulation study is done to evaluate the performance of the maximum likelihood estimators. Finally, an application of the proposed model to the vehicle insurance loss data set is presented.

scholarly journals On Heavy-tailed Crack Distribution for Loss Severity Modeling

2017 ◽  
Vol 6 (6) ◽  
pp. 92 ◽  
Author(s):  
Taehan Bae ◽  
Jingjiao Chen
Keyword(s):  
Regular Variation ◽  
Extreme Values ◽  
Model Fitting ◽  
Parametric Models ◽  
Data Sets ◽  
Crack Distribution ◽  
Loss Data ◽  
Catastrophic Loss ◽  
Heavy Tailed ◽  
Loss Severity

Heavy-tailedness and right-skewness are two typical features of loss data resulting from catastrophic events such as storms or earthquakes. In this paper we study the tail properties of the generalized crack distribution which has recently been introduced as an extension of the Birnbaum-Saunders distribution and the three-parameter Gaussian crack distribution. The theoretical tail relationships between the auxiliary (or baseline) distribution and the resulting generalized crack distribution are studied relying on the classical theories of extreme values and regular variation. A few concrete examples of heavy-tailed crack distribution are constructed and used for model fitting exercises on both simulated and real catastrophic loss data sets. The fitting results show that the heavy-tailed crack distribution with an appropriate choice of baseline density function outperforms some other commonly used parametric models.

scholarly journals Multivariate fractional phase–type distributions

2020 ◽  
Vol 23 (5) ◽  
pp. 1431-1451 ◽  
Author(s):  
Hansjörg Albrecher ◽  
Martin Bladt ◽  
Mogens Bladt
Keyword(s):  
Tail Dependence ◽  
Jump Process ◽  
Multivariate Distributions ◽  
New Class ◽  
Natural Time ◽  
Special Cases ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Markovian Jump Process ◽  
Heavy Tailed

Abstract We extend the Kulkarni class of multivariate phase–type distributions in a natural time–fractional way to construct a new class of multivariate distributions with heavy-tailed Mittag-Leffler(ML)-distributed marginals. The approach relies on assigning rewards to a non–Markovian jump process with ML sojourn times. This new class complements an earlier multivariate ML construction [2] and in contrast to the former also allows for tail dependence. We derive properties and characterizations of this class, and work out some special cases that lead to explicit density representations.

Univariate and bivariate extensions of the generalized exponential distributions

2021 ◽  
Vol 71 (6) ◽  
pp. 1581-1598
Author(s):  
Vahid Nekoukhou ◽  
Ashkan Khalifeh ◽  
Hamid Bidram
Keyword(s):  
Em Algorithm ◽  
Exponential Distribution ◽  
Bivariate Distribution ◽  
Generalized Exponential Distribution ◽  
Exponential Distributions ◽  
Unknown Parameters ◽  
Data Set ◽  
New Class ◽  
Special Cases ◽  
Univariate Distribution

Abstract The main aim of this paper is to introduce a new class of continuous generalized exponential distributions, both for the univariate and bivariate cases. This new class of distributions contains some newly developed distributions as special cases, such as the univariate and also bivariate geometric generalized exponential distribution and the exponential-discrete generalized exponential distribution. Several properties of the proposed univariate and bivariate distributions, and their physical interpretations, are investigated. The univariate distribution has four parameters, whereas the bivariate distribution has five parameters. We propose to use an EM algorithm to estimate the unknown parameters. According to extensive simulation studies, we see that the effectiveness of the proposed algorithm, and the performance is quite satisfactory. A bivariate data set is analyzed and it is observed that the proposed models and the EM algorithm work quite well in practice.

scholarly journals Extended Odd Fréchet-G Family of Distributions

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Suleman Nasiru
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Data Set ◽  
New Class ◽  
New Family ◽  
Rate Functions ◽  
The Given ◽  
Family Of Distributions

The need to develop generalizations of existing statistical distributions to make them more flexible in modeling real data sets is vital in parametric statistical modeling and inference. Thus, this study develops a new class of distributions called the extended odd Fréchet family of distributions for modifying existing standard distributions. Two special models named the extended odd Fréchet Nadarajah-Haghighi and extended odd Fréchet Weibull distributions are proposed using the developed family. The densities and the hazard rate functions of the two special distributions exhibit different kinds of monotonic and nonmonotonic shapes. The maximum likelihood method is used to develop estimators for the parameters of the new class of distributions. The application of the special distributions is illustrated by means of a real data set. The results revealed that the special distributions developed from the new family can provide reasonable parametric fit to the given data set compared to other existing distributions.

Differentially Fed Artificial Neural Networks for Speech Signal Prediction

2011 ◽  
pp. 309-323
Author(s):  
Manjunath Ramachandra Iyer
Keyword(s):  
Personal Identification ◽  
Final Decision ◽  
Personal Identification Number ◽  
Limited Data ◽  
Data Set ◽  
New Class ◽  
Signal Prediction ◽  
Speaker Authentication ◽  
Artificial Neural ◽  
Security Checks

Speaker authentication has become increasingly important. It goes with the other forms of security checks such as user login and personal identification number and has a say in the final decision about the authenticity. One of the issues with the authentication algorithms is that the automated devices that take the call have to work with a limited data set. In this chapter, a new class of intelligent element called differentially fed artificial neural network has been introduced to predict the data and use it effectively. It keeps the model simple and helps in taking online and crisp decisions with the available limited data.

Incentivized Actions in Freemium Games

2020 ◽  
Author(s):  
Lifei Sheng ◽  
Christopher Thomas Ryan ◽  
Mahesh Nagarajan ◽  
Yuan Cheng ◽  
Chunyang Tong
Keyword(s):  
Operations Management ◽  
Sufficient Conditions ◽  
Problem Definition ◽  
Data Set ◽  
New Class ◽  
Recent Innovation ◽  
Markov Decision ◽  
Managerial Implications ◽  
Operational Issues ◽  
Data Driven Decisions

Problem definition: Games are the fastest-growing sector of the entertainment industry. Freemium games are the fastest-growing segment within games. The concept behind freemium is to attract large pools of players, many of whom will never spend money on the game. When game publishers cannot earn directly from the pockets of consumers, they employ other revenue-generating content, such as advertising. Players can become irritated by revenue-generating content. A recent innovation is to offer incentives for players to interact with such content, such as clicking an ad or watching a video. These are termed incentivized (incented) actions. We study the optimal deployment of incented actions. Academic/practical relevance: Removing or adding incented actions can essentially be done in real-time. Accordingly, the deployment of incented actions is a tactical, operational question for game designers. Methodology: We model the deployment problem as a Markov decision process (MDP). We study the performance of simple policies, as well as the structure of optimal policies. We use a proprietary data set to calibrate our MDP and derive insights. Results: Cannibalization—the degree to which incented actions distract players from making in-app purchases—is the key parameter for determining how to deploy incented actions. If cannibalization is sufficiently high, it is never optimal to offer incented actions. If cannibalization is sufficiently low, it is always optimal to offer. We find sufficient conditions for the optimality of threshold strategies that offer incented actions to low-engagement users and later remove them once a player is sufficiently engaged. Managerial implications: This research introduces operations management academics to a new class of operational issues in the games industry. Managers in the games industry can gain insights into when incentivized actions can be more or less effective. Game designers can use our MDP model to make data-driven decisions for deploying incented actions.

scholarly journals Multivariate Student versus Multivariate Gaussian Regression Models with Application to Finance

2019 ◽  
Vol 12 (1) ◽  
pp. 28
Author(s):  
Thi Nguyen ◽  
Anne Ruiz-Gazen ◽  
Christine Thomas-Agnan ◽  
Thibault Laurent
Keyword(s):  
Maximum Likelihood ◽  
Covariance Matrix ◽  
Mean Squared Error ◽  
Financial Assets ◽  
Multivariate Normal ◽  
Graphical Tool ◽  
Data Generating Process ◽  
Competing Models ◽  
Heavy Tailed ◽  
Gaussian Regression

To model multivariate, possibly heavy-tailed data, we compare the multivariate normal model (N) with two versions of the multivariate Student model: the independent multivariate Student (IT) and the uncorrelated multivariate Student (UT). After recalling some facts about these distributions and models, known but scattered in the literature, we prove that the maximum likelihood estimator of the covariance matrix in the UT model is asymptotically biased and propose an unbiased version. We provide implementation details for an iterative reweighted algorithm to compute the maximum likelihood estimators of the parameters of the IT model. We present a simulation study to compare the bias and root mean squared error of the ensuing estimators of the regression coefficients and covariance matrix under several scenarios of the potential data-generating process, misspecified or not. We propose a graphical tool and a test based on the Mahalanobis distance to guide the choice between the competing models. We also present an application to model vectors of financial assets returns.

scholarly journals Count data regression modeling: an application to spontaneous abortion

2020 ◽  
Vol 17 (1) ◽  
Author(s):  
Prashant Verma ◽  
Prafulla Kumar Swain ◽  
Kaushalendra Kumar Singh ◽  
Mukti Khetan
Keyword(s):  
Spontaneous Abortion ◽  
Count Data ◽  
Regression Modeling ◽  
Data Regression
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