الفهرس 
Probability DistributionsOnly 14 pages are availabe for public view
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Abstract
Many researchers always face difficulties in applying the traditional estimation methods due to the complex mathematical formula of some distributions that contain at least two parameters. This thesis aims to formulate a future vision on developing estimation methods by describing and analyzing their reality. Therefore, new statistical methods are proposed to estimate the parameters of some distributions. In addition, the thesis introduced strengths and weaknesses for some trends in mathematical statistics to overcome the difficulties facing researchers in various applications. This thesis supports the field of mathematical statistics by proposing innovative statistical methods for estimation and prediction.
This thesis proposed three algorithms to the problem of solar energy prediction and Percentile Root Estimation (PR) of three-parameters distributions. The first algorithm named Algorithm of Change Rate Matrix (CRM) depends on creating a matrix of solar energy change rates for each month separately during successive years. CRM is characterized by not relying on the transition matrix or Markov model. The second algorithm named Algorithm of Converting Dataset to Markov model (CDM) depends on the transition states of the solar energy and Markov model for a month during successive years. The results were compared with the actual values to validate the algorithms CRM and CDM. Moreover, they can be performed on other data in various applications. The third algorithm PR applied on the distributions Lognormal, Fatigue lifetime, Erlang, Fréchet and Pert which it was validated using Goodness-fit-tests, Anderson-Darling test. Moreover, it was found to be more accurate than the maximum likelihood estimation method.
Moreover, the thesis provided a new algorithm to estimate the three parameters of log-Pearson distribution called algorithm of percentile roots (PR). The effectiveness of PR was tested by the Anderson-Darling test which accepted the results at a high-level of significance. The estimated parameters by PR were very close to EasyFit program’s results. In addition, they were somewhat more accurate than the MLE method. The analyzed data is a data set of the number of bank transactions in the Kingdom of Saudi Arabia.