Omer L. Gebizlioglu

Advances on models, characterizations and applications

Preface Contributors The Shapes of the Probability Density, Hazard, and Reverse Hazard Functions Masaaki Sibuya Stochastic Ordering of Risks, Influence of Dependence, and A.S. Constructions Ludger Ruschendorf The q-Factorial Moments of Discrete q-Distributions and a Characterization of the Euler Distribution Ch.A. Charalambides and N. Papadatos On the Characterization of Distributions Through the Properties of Conditional Expectations of Order Statistics I. Bairamov and O. Gebizlioglu Characterization of the Exponential Distribution by Conditional Expectations of Generalized Spacings Erhard Cramer and Udo Kamps Some Characterizations of Exponential Distribution Based on Progressively Censored Order Statistics N. Balakrishnan and S.V. Malov A Note on Regressing Order Statistics and Record Values I. Bairamov and N. Balakrishnan Generalized Pareto Distributions and Their Characterizations Majid Asadi On Some Characteristic Properties of the Uniform Distribution G. Arslan, M. Ahsanullah, and I.G. Bairamov Characterizations of Multivariate Distributions Involving Conditional Specification and/or Hidden Truncation Barry C. Arnold Bivariate Matsumoto-Yor Property and Related Characterizations Konstancja Bobecka and Jacek Wesolowski First Principal Component Characterization of a Continuous Random Variable Carles M. Cuadras The Lawless-Wangs Operational Ridge Regression Estimator Under the LINEX Loss Function Esra Akdeniz and Fikri Akdeniz On the Distributions of the Reference Dose and Its Application in Health Risk Assessment Mehdi Razzaghi Subject Index

Comparison of certain value-at-risk estimation methods for the two-parameter Weibull loss distribution

The Weibull distribution is one of the most important distributions that is utilized as a probability model for loss amounts in connection with actuarial and financial risk management problems. This paper considers the Weibull distribution and its quantiles in the context of estimation of a risk measure called Value-at-Risk (VaR). VaR is simply the maximum loss in a specified period with a pre-assigned probability level. We attempt to present certain estimation methods for VaR as a quantile of a distribution and compare these methods with respect to their deficiency (Def) values. Along this line, the results of some Monte Carlo simulations, that we have conducted for detailed investigations on the efficiency of the estimators as compared to MLE, are provided.

Sarmanov distribution class for dependent risks and its applications

The essential input of risk management strategies is the underlying probability distribution of loss and ruin. The present work considers dependence of losses due to risk realizations. A new distribution for dependent risks is proposed from the Sarmanov Class with FGM distribution properties. Some risk ordering and loss control strategies are suggested.

Risk analysis under progressive type II censoring with binomial claim numbers

This paper presents a model of actuarial loss events that follow a progressive censoring scheme. Loss events are modelled according to this scheme regarding the claim number and size. Claim events at random time points are assumed to happen progressively in a given period due to each of an m number of claims that occur due to hazardous events, while a fixed number of n claims are anticipated to take place in total. Distribution of the resulting total loss amount is derived, and according to its properties, some risk management issues about reserves and solvency are discussed.

Asymptotic Distributions of Statistics Based on Order Statistics and Record Values and Invariant Confidence Intervals

In this chapter, we establish limit theorems for some statistics based on order statistics and record values. The finite-sample as well as asymptotic properties of statistics based on invariant confidence intervals are investigated and their use in statistical inference is outlined.