Parameter Estimation of the Generalized Pareto Distribution By using a Plotting Position

Abstract

The objective of this research is to propose the parameter estimation methods of the generalized Pareto distribution. A modified plotting position method was optimized and compared with maximum likelihood estimator and probability weighted moments methods then applied them thru the financial data. The parameter estimation with a modified plotting position method results showed the lowest in bias value and root mean square error for small sample size. The maximum likelihood estimator method showed the lowest in bias value and root mean square error for large sample size. For applied data of securities of company True Corporation PCL or company (TRUE) found that the Value at Risk of maximum likelihood estimator, probability weighted moments and modified plotting position methods that fit at quantile 95% equals 0.1066, 0.1080 and 0.1084 respectively and quantile 99% equals 0.1838, 0.1801 and 0.1796 respectively. Therefore, if investors are to invest in this securities of company (TRUE). There is a high investment risk. However, the Value at Risk is just a preliminary guide to invest in the stock market. If investors are interested in investing, they should consider other factors. Keywords: Generalized Pareto Distribution, Plotting Position, Value at Risk, Quantile Estimation