Minimum K-S estimator using PH-transform technique
Keywords:
Minimum K-S estimator, H-transform technique, Grid search techniqueAbstract
In this paper, we propose an improvement of the Minimum Kolmogorov-Smirnov (K-S) estimator using proportional hazards transform (PH-transform) technique. The data of experiment is 47 fire accidents data of an insurance company in Thailand. This experiment has two operations, the first operation, we minimize K-S statistic value using grid search technique for nine distributions; Rayleigh distribution, gamma distribution, Pareto distribution, log-logistic distribution, logistic distribution, normal distribution, Weibull distribution, log-normal distribution, and exponential distribution and the second operation, we improve K-S statistic using PH-
transform. The result appears that PH-transform technique can improve the Minimum K-S estimator. The algorithms give better the Minimum K-S estimator for seven distributions; Rayleigh distribution, logistic distribution, gamma distribution, Pareto distribution, log-logistic distribution, normal distribution, Weibull distribution, log-normal distribution, and exponential distribution while the Minimum K-S estimators of normal distribution and logistic distribution are unchanged.
References
Khotama, S., Thongjunthug, T., Sangaroon, K., & Klongdee, W., (2015). On approximating the minimum initial capital of fire insurance with
the finite-time ruin probability using a simulation Approach. KKU Research Journal, 20 (3),267-271.
Leonard, A.A., & Mark, M.M., (2015). Probability and Statistics with applications(2 nd ed.). America, MA: ACTEX Publications, Inc.
Sinsomboonthong, S.(2015). Statistical Distributions (10 th ed.). Bangkok, MA, Chamchuree products company, Ltd.
Wang, S. (1995) Insurance pricing and increased limits ratemaking by proportional hazard transforms. Insurance: Mathematics and
Economics, 17, 43-54.
Weber, M.D., Leemis, L.M., & Kincaid, R.K. (2006) Minimum Kolmogorov-Smirnov test statistic parameter estimates. Journal of
Statistical Computation and Simulation, 76(3), 195-206. Doi:10.1080/00949650412331321098.
Wieczorek, J. (2009). finite sample properties of minimum kolmogorov-smirnov estimator an maximum likelihood estimator for right
censored data: Portland state university (Thesis).
