Asymmetric Density for Risk Claim-Size Data: Prediction and Bimodal Data Applications

Abstract

A new, flexible claim-size Chen density is derived for modeling asymmetric data (negative and positive) with different types of kurtosis (leptokurtic, mesokurtic and platykurtic). The new function is used for modeling bimodal asymmetric medical data, water resource bimodal asymmetric data and asymmetric negatively skewed insurance-claims payment triangle data. The new density accommodates the “symmetric”, “unimodal right skewed”, “unimodal left skewed”, “bimodal right skewed” and “bimodal left skewed” densities. The new hazard function can be “decreasing–constant–increasing (bathtub)”, “monotonically increasing”, “upside down constant–increasing”, “monotonically decreasing”, “J shape” and “upside down”. Four risk indicators are analyzed under insurance-claims payment triangle data using the proposed distribution. Since the insurance-claims data are a quarterly time series, we analyzed them using the autoregressive regression model AR(1). Future insurance-claims forecasting is very important for insurance companies to avoid uncertainty about big losses that may be produced from future claims.

Risk Analysis and Estimation of a Bimodal Heavy-Tailed Burr XII Model in Insurance Data: Exploring Multiple Methods and Applications

“…C tion some of these works, especially the recent ones; for example, see Figueiredo et al [3], Shrahili et al [22], and Mohamed et al ( [23,24]). Hence, this important aspect of actuarial science requires a lot of effort to employ probability distributions in the field of actuarial science and to treat, evaluate, and forecast risks.…”

“…Shrahili et al [22], and Mohamed et al ( [23,24]). Hence, this important aspect of actuarial science requires a lot of effort to employ probability distributions in the field of actuarial science and to treat, evaluate, and forecast risks.…”

“…In the statistical and actuarial literature, there is a dearth of works that have used probability distributions in the field of processing and analyzing actuarial risks. We mention some of these works, especially the recent ones; for example, see Figueiredo et al [3], Shrahili et al [22], and Mohamed et al ( [23,24]). Hence, this important aspect of actuarial science requires a lot of effort to employ probability distributions in the field of actuarial science and to treat, evaluate, and forecast risks.…”

“…In this section, using a U.K. Motor Non-Comprehensive account as a concrete example, we look at the insurance claims payment triangle. Convenience led us to pick the genesis era from 2007 to 2013 (see Charpentier [34], Shrahili et al [22], Mohamed et al [23,24]).…”

Short-Term Insurance Claims Payments Forecasting with Holt-Winter Filtering and Residual Analysis

“…Following Shrahili et al (2021), Mohamed et al (2022) define a new size-of-loss synthetic autoregressive model for the left skewed insurance claims datasets. In order to choose the optimal model, the technique essentially involves examining the insurance claims using all feasible ARIMA models.…”