All Theses and Dissertations


Master of Science in Mathematics


Department of Mathematical Sciences

Date of Award

Spring 2020


Dr. Junaid Alam Khan

Second Advisor

Dr. Zaheer Uddin

Committee Member 1

Dr. Khursheed A. Siddiqui

Committee Member 2

Dr. M. Shoaib Saleem, University of Okara, Okara

Committee Member 3

Dr. Hisham Bin Zubair Syed, Chairperson-Department of Mathematical Sciences, IBA

Project Type


Access Type

Restricted Access


ix, 54


In this study Maximum entropy probability distribution functions are employed to fit the wind speed data from two different geographical locations in the Netherlands. A comparative study of the two investigated coastal sites viz. Debilt and Berkhout for the wind power density is presented in this study. The presented study has focal point to appraise the suitability and precision of the fitted distribution function to the measured wind speed data for two sites in the Netherlands. Comparison is made between the wind powers densities obtained by using the fitted functions based on Maximum Entropy Principle (MEP). Investigations on recorded daily wind speed data are performed at hourly basis, obtained from weather site of the Netherlands of two different locations for a period of four years, i.e. from 2015 to 2018. A computer program has been developed to implement this principle on record data. The wind potentials are calculated for each month of years mentioned above. In case of MEP-based function a probability density function is defined as a system of (N+1) non-linear equations containing (N+1) Lagrange multipliers. Three different methods such as Newton Raphson Method and Method of Moments, Maximum Likelihood Method and Least Square Method are discussed to find out Lagrange Parameter of the distribution. Out of three methods, Parameter estimation is performed by the Least Square Method, and the model is judged by three goodness of fit tests, Chi Squared Error, Kolmogorov- Simonov Test and Root Mean Square Error. The tests confirm the appropriateness of MEP-based function for modeling measured wind speed data. The expected frequencies (wind speed) and average wind speed of the months are calculated by the computer program which displays the graphs in the form of histograms and polygons. In last comparison of average velocities from 2015-2018 shows that both towns have the same wind effect in some specific months like January, February, November and December. Computer Sciences.

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