Research Article Open Access

Univariate Generalized Additive Models for Simulated Stationary and Non-Stationary Generalized Pareto Distribution

Mostafa Behzadi1, Mohd Bakri Adam1 and Anwar Fitrianto1
  • 1 Universiti Putra Malaysia, Malaysia

Abstract

Generalized additive models as a predictor in regression approaches, are made up over cubic spline basis and penalized regression splines. Despite of linear predictor in GLM, generalized additive models use a sum of smooth functions of covariates as a predictor. The data which are used in this study have generalized Pareto distribution and have been simulated by inversion method. The data are generated in two types, the stationary case and the non-stationary case. The method of root mean square of errors as a method of measurement is used for comparison between power of predictions which are based on penalized regression splines as a method in univariate generalized additive models and linear regression based on maximum likelihood estimation. The finding of this research illustrates that the amount of accuracy of estimation of parameter of location in UGAM approach as an alternative promising of modelling through each specialized GPD's models, has less RMSE in compare with MLE.

Journal of Mathematics and Statistics
Volume 13 No. 2, 2017, 169-176

DOI: https://doi.org/10.3844/jmssp.2017.169.176

Submitted On: 2 December 2014 Published On: 3 June 2017

How to Cite: Behzadi, M., Adam, M. B. & Fitrianto, A. (2017). Univariate Generalized Additive Models for Simulated Stationary and Non-Stationary Generalized Pareto Distribution. Journal of Mathematics and Statistics, 13(2), 169-176. https://doi.org/10.3844/jmssp.2017.169.176

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Keywords

  • Generalized Pareto Distribution
  • Univariate Generalized Additive Model
  • Smooth Function
  • Penalized Regression Spline
  • Cubic Spline Basis
  • Simulated Data
  • Maximum Likelihood Estimation
  • Root Mean Square of Errors