Academic journal article IUP Journal of Applied Economics

Movie Rankings and Greatest Accuracy Credibility Theory: An Alternate Modeling Approach

Academic journal article IUP Journal of Applied Economics

Movie Rankings and Greatest Accuracy Credibility Theory: An Alternate Modeling Approach

Article excerpt

(ProQuest: ... denotes formulae omitted.)

Introduction

Credibility theory is basically a set of quantitative tools, policies and procedures which allows an insurer to adjust future premiums based on past experience on a particular risk or group of risks. Credibility theory ultimately relies on the combination of experience estimates from historical data as well as base estimates in order to develop formulas. The formulas are used to replicate past experiences, and are then tested against actual data.

Credibility theory has been used over a considerable period of time in one form or another mainly in different areas of the insurance industry. Areas such as property, casualty accident and health have benefitted from using credibility theory because claims occur at a relatively high rate and the pricing horizon is relatively short. This provides sufficient recent experience to use for future expectations.

There are three basic approaches to credibility theory: classical credibility (also known as limited fluctuation credibility), Bühlmann credibility (also known as greatest accuracy credibility) and Bayesian credibility. Of these, Bühlmann credibility has a statistical modelbased approach and is more theoretically sound and robust. Due to these advantages of Bühlmann credibility over other approaches, we will apply it to the movie ranking problem in this study contrary to the previous studies of Das and Chakrabarti (2016) that had approached the same problem by applying the principles of Bayesian credibility theory.

Greatest accuracy credibility or Bühlmann credibility attempts to produce linear estimates which will minimize the estimate and the quantity being estimated. Instead of concentrating on the stability of the experience, this theory focuses on the homogeneity of the estimate within the portfolio. However, it is assumed in this model that past experiences are independent and identically distributed components with respect to each year. Although this assumption makes the model simple, it is impractical as it does not allow for variations in exposure or size. These variations are dealt with in the Bühlmann-Straub model.

Traditionally any form of the theory of credibility was applied by actuaries and insurers as a method to calculate the future risk premium by combining the individual risk experience with the class risk experience. Hence, its application was confined to a large extent in the insurance industry domain only. However, recent researches have justified the fact that the application of the theory can be diversified and extended to other unlikely domain as well. One such diverse and interesting application is its usage in ranking movies. The primary aim is to apply credibility theory to achieve more accurate and reliable movie rankings based on user's votes. The goal is to eventually help investors to reduce uncertainty about their decision to finance (or not) a new motion picture. Since user's votes comprise a dynamic subset of the whole population of movie goers, the movie rating problem focuses on the homogeneity of the voting group. Hence the appropriateness of the application of greatest accuracy credibility theory in movie ranking problem is ascertained. Further, in our study, we will justify the statistical robustness of credibility theory as an efficient method to rank movies as claimed in the previous studies concerning the same topic.

The paper is organized as follows: a review of the related literature on greatest accuracy credibility theory is followed by justification of the present study and objectives. Subsequently we will apply Bühlmann modeling and Bühlmann-Straub modeling to movie ranking problem. Numerical calculations are followed by interpretation of the same to justify the suitability and effectiveness of Bühlmann-Straub modeling over Bühlmann modeling to achieve more accurate movie rankings. Finally, the conclusion is presented along with the scope for further research. …

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