THE IMPACTS OF INDIVIDUAL INFORMATION ON LOSS RESERVING

2020 ◽  
pp. 1-45
Author(s):  
Zhigao Wang ◽  
Xianyi Wu ◽  
Chunjuan Qiu
Keyword(s):  
Information Model ◽  
Statistical Properties ◽  
Unknown Parameters ◽  
Asymptotic Behaviors ◽  
Computation Procedure ◽  
General Insurance ◽  
Loss Reserving ◽  
Portfolio Size ◽  
Better Than ◽  
Individual Information

Abstract The projection of outstanding liabilities caused by incurred losses or claims has played a fundamental role in general insurance operations. Loss reserving methods based on individual losses generally perform better than those based on aggregate losses. This study uses a parametric individual information model taking not only individual losses but also individual information such as age, gender, and so on from policies themselves into account. Based on this model, this study proposes a computation procedure for the projection of the outstanding liabilities, discusses the estimation and statistical properties of the unknown parameters, and explores the asymptotic behaviors of the resulting loss reserving as the portfolio size approaching infinity. Most importantly, this study demonstrates the benefits of individual information on loss reserving. Remarkably, the accuracy gained from individual information is much greater than that from considering individual losses. Therefore, it is highly recommended to use individual information in loss reserving in general insurance.

scholarly journals New class of Lindley distributions: properties and applications

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Duha Hamed ◽  
Ahmad Alzaghal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Data Sets ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Lindley Distribution ◽  
New Class

AbstractA new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

scholarly journals Maximum Product of Spacing Parameter Estimation of Gompertz Rayleigh Distribution and Application to Rainfall Datasets

2021 ◽  
pp. 41-59
Author(s):  
Hussein Ahmad Abdulsalam ◽  
Sule Omeiza Bashiru ◽  
Alhaji Modu Isa ◽  
Yunusa Adavi Ojirobe
Keyword(s):  
Goodness Of Fit ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Rainfall Data ◽  
Parameter Estimates ◽  
Data Sets ◽  
Unknown Parameters ◽  
Exponentiated Weibull ◽  
Integrated Hazard

Gompertz Rayleigh (GomR) distribution was introduced in an earlier study with few statistical properties derived and parameters estimated using only the most common traditional method, Maximum Likelihood Estimation (MLE). This paper aimed at deriving more statistical properties of the GomR distribution, estimating the three unknown parameters via a competitive method, Maximum Product of Spacing (MPS) and evaluating goodness of fit using rainfall data sets from Nigeria, Malaysia and Argentina. Properties of statistical distributions including distribution of smallest and largest order statistics, cumulative or integrated hazard function, odds function, rth non-central moments, moment generating function, mean, variance and entropy measures for GomR distribution were explicitly derived. The fitted data sets reveal the flexibility of GomR distribution over other distributions been compared with. Simulation study was used to evaluate the consistency, accuracy and unbiasedness of the GomR distribution parameter estimates obtained from the method of MPS. The study found that GomR distribution could not provide a better fit for Argentine rainfall data but it was the best distribution for the rainfall data sets from Nigeria and Malaysia in comparison with the distributions; Generalized Weibull Rayleigh (GWR), Exponentiated Weibull Rayleigh (EWR), Type (II) Topp Leone Generalized Inverse Rayleigh (TIITLGIR), Kumarawamy Exponential Inverse Raylrigh (KEIR), Negative Binomial Marshall-Olkin Rayleigh (NBMOR) and Exponentiated Weibull (EW). Furthermore, the estimates from MPSE were consistent as the sample size increases but not as efficient as those from MLE.

scholarly journals Statistical properties and different methods of estimation of transmuted Rayleigh distribution

2017 ◽  
Vol 40 (1) ◽  
pp. 165-203 ◽  
Author(s):  
Sanku Dey ◽  
Enayetur Raheem ◽  
Saikat Mukherjee
Keyword(s):  
Stochastic Ordering ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Statistical Properties ◽  
Point Of View ◽  
Strength Parameter ◽  
Residual Lifetime ◽  
Mean Deviation ◽  
Unknown Parameters ◽  
Anderson Darling

This article addresses the various properties and different methods of estimation of the unknown parameters of the Transmuted Rayleigh (TR) distribution from the frequentist point of view. Although, our main focus is on estimation from frequentist point of view,  yet, various mathematical and statistical properties of the TR distribution (such as quantiles, moments, moment generating function, conditional moments,  hazard rate, mean residual lifetime, mean past lifetime,  mean deviation about mean and median, the stochastic ordering,  various entropies, stress-strength parameter  and order statistics) are derived.  We briefly describe different frequentist methods of estimation approaches, namely, maximum likelihood estimators, moments estimators, L-moment estimators, percentile based estimators, least squares estimators, method of maximum product of spacings,  method of Cram\'er-von-Mises, methods of Anderson-Darling and right-tail Anderson-Darling and compare them using extensive numerical simulations. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, the potentiality of the model is analyzed by means of two real data sets which is further illustrated by obtaining bias and standard error of the estimates and the bootstrap percentile confidence intervals using bootstrap resampling.

scholarly journals GM(1,1;λ) with Constrained Linear Least Squares

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 278
Author(s):  
Ming-Feng Yeh ◽  
Ming-Hung Chang
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Model Fitting ◽  
Ordinary Least Squares ◽  
Linear Least Squares ◽  
Unknown Parameters ◽  
Constrained Problems ◽  
Linear Least Squares Problems ◽  
Ordinary Least Squares Method ◽  
Better Than

The only parameters of the original GM(1,1) that are generally estimated by the ordinary least squares method are the development coefficient a and the grey input b. However, the weight of the background value, denoted as λ, cannot be obtained simultaneously by such a method. This study, therefore, proposes two simple transformation formulations such that the unknown parameters, and can be simultaneously estimated by the least squares method. Therefore, such a grey model is termed the GM(1,1;λ). On the other hand, because the permission zone of the development coefficient is bounded, the parameter estimation of the GM(1,1) could be regarded as a bound-constrained least squares problem. Since constrained linear least squares problems generally can be solved by an iterative approach, this study applies the Matlab function lsqlin to solve such constrained problems. Numerical results show that the proposed GM(1,1;λ) performs better than the GM(1,1) in terms of its model fitting accuracy and its forecasting precision.

Using Weibull Distribution for Modeling Bimodal Diffusion Curves: A Naive Framework to Study Product Life Cycle

2019 ◽  
Vol 16 (07) ◽  
pp. 1950050
Author(s):  
Adarsh Anand ◽  
Richie Aggarwal ◽  
Ompal Singh
Keyword(s):  
Weibull Distribution ◽  
Product Life Cycle ◽  
Scale Parameter ◽  
Functional Model ◽  
Real Life ◽  
Step Function ◽  
Unknown Parameters ◽  
Consumer Durables ◽  
Study Product ◽  
Better Than

With the purpose of understanding differing shapes of sales curve (unimodal and bimodal) this paper discusses a naive way for viewing the diffusion process for consumer durables. In this paper, a step functional model involving two-step Weibull distribution with four unknown parameters is characterized wherein the shape of the density function of the models depends upon the shape and scale parameter of Weibull distribution. Empirical analysis on real life sales datasets indicates that the Weibull step function model is more flexible and fits better than the other models.

An Additive NHPP-Based Reliability Model of Wireless Sensor Networks

2014 ◽  
Vol 602-605 ◽  
pp. 3206-3212
Author(s):  
Bo Zhao ◽  
Jian Feng Yang ◽  
Ming Zhao ◽  
Qi Li ◽  
Yan Liu
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Wireless Sensor ◽  
Reliability Model ◽  
Unknown Parameters ◽  
Failure Data ◽  
Better Than

As the Wireless Sensor Networks (WSNs) are widely implemented in various fields recent years, the quality of WSNs has been increasingly concerned. WSNs can usually be divided into sub-nets, which assumed to work or fail independently. Through the failure data of those sub-nets, the additive NHPP model for reliability evaluation is composed, and then the maximum likelihood estimation is applied to estimate the unknown parameters in the model. Finally, the simulation shows that the additive NHPP model is better than general NHPP model under certain circumstances.

Efficient Parametric Optimization for Expensive Single Objective Problems

2021 ◽  
pp. 1-12
Author(s):  
Jonathan Weaver-Rosen ◽  
Richard Malak
Keyword(s):  
Adaptive Sampling ◽  
Parametric Optimization ◽  
Optimization Problems ◽  
Test Problems ◽  
Surface Model ◽  
High Fidelity ◽  
Unknown Parameters ◽  
Element Analysis ◽  
Better Than

Abstract Parametric optimization solves optimization problems as a function of uncontrollable or unknown parameters. Such an approach allows an engineer to gather more information than traditional optimization procedures during design. Existing methods for parametric optimization of computationally or monetarily expensive functions can be too time-consuming or impractical to solve. Therefore, new methods for the parametric optimization of expensive functions need to be explored. This work proposes a novel algorithm that leverages the advantages of two existing optimization algorithms. This new algorithm is called the efficient parametric optimization (EPO) algorithm. EPO enables adaptive sampling of a high-fidelity design space using an inexpensive low-fidelity response surface model. Such an approach largely reduces the required number of expensive high-fidelity computations. The proposed method is benchmarked using analytic test problems and used to evaluate a case study requiring finite element analysis. Results show that EPO performs as well as or better than the existing alternative, P3GA, for these problems given an allowable number of function evaluations.

scholarly journals Statistical inference on the accelerated competing failure model from the inverse weibull distribution under progressively type-II censored data

2021 ◽  
pp. 97-97
Author(s):  
Ying Wang ◽  
Zai-Zai Yan
Keyword(s):  
Confidence Intervals ◽  
Normal Approximation ◽  
Likelihood Method ◽  
Failure Model ◽  
Unknown Parameters ◽  
Bootstrap Confidence Intervals ◽  
Inverse Weibull Distribution ◽  
Type Ii Censored Data ◽  
Censored Sample ◽  
Better Than

In this paper, the parameter estimation is discussed by using the maximum likelihood method when the available data have the form of progressively censored sample from a constant-stress accelerated competing failure model. Normal approximation and bootstrap confidence intervals for the unknown parameters are obtained and compared numerically. The simulation results show that bootstrap confidence intervals perform better than normal approximation. A thermal stress example is discussed.

A Comparative Study of EDF Tests for Normality and Exponentiality

2014 ◽  
Vol 602-605 ◽  
pp. 2004-2010
Author(s):  
Yan Su ◽  
Xia Ying Su
Keyword(s):  
Monte Carlo ◽  
Test Statistics ◽  
Exponential Distributions ◽  
Test Procedures ◽  
Unknown Parameters ◽  
Monte Carlo Algorithms ◽  
Wide Range ◽  
Anderson Darling ◽  
Tests For Normality ◽  
Better Than

In this paper, the modified EDF test procedures for testing the normal and exponential distributions with unknown parameters are suggested. The Monte Carlo algorithms are given to approximate the critical values of the EDF test statistics for a wide range of sample sizes. The power simulations show that the Anderson-Darling (AD) test is on the whole better than other EDF tests considered, in particular when the alternative departs from the true distribution in the tails.

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