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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 9720946, 6 pages
https://doi.org/10.1155/2017/9720946
Research Article

Finsler Geometry for Two-Parameter Weibull Distribution Function

1Department of Electrical and Electronics Engineering, Engineering Faculty, Bilecik S.E. University, 11210 Bilecik, Turkey
2Department of Computer Engineering, Engineering Faculty, Bilecik S.E. University, 11210 Bilecik, Turkey

Correspondence should be addressed to Emrah Dokur

Received 19 December 2016; Accepted 16 February 2017; Published 9 March 2017

Academic Editor: Qin Yuming

Copyright © 2017 Emrah Dokur et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

To construct the geometry in nonflat spaces in order to understand nature has great importance in terms of applied science. Finsler geometry allows accurate modeling and describing ability for asymmetric structures in this application area. In this paper, two-dimensional Finsler space metric function is obtained for Weibull distribution which is used in many applications in this area such as wind speed modeling. The metric definition for two-parameter Weibull probability density function which has shape () and scale () parameters in two-dimensional Finsler space is realized using a different approach by Finsler geometry. In addition, new probability and cumulative probability density functions based on Finsler geometry are proposed which can be used in many real world applications. For future studies, it is aimed at proposing more accurate models by using this novel approach than the models which have two-parameter Weibull probability density function, especially used for determination of wind energy potential of a region.