Author name:
ليماء عبد الجبار داود الحلفي
Supervisor name:
انتصار عريبي فدعم الدوري
Abstract:
من المشاكل التي تواجه محلل البيانات هو معرفة الانموذج الاحصائي الملائم الذي يصف الظاهرة المدروسة, ومن اكثر النماذج شيوعا ما يدعى بالتوزيع الاحتمالي(Probability distribution) ولكن الجزء المهم في عملية تحليل البيانات والتي قد تكون مشكلة في بعض الاحيان هي ا | One of the problems which the data analyst has faced is how he can know the appropriate statistical models which describe the studied phenomenon. The most popular models is called (contribution probability ), but the most important part of the data analysis process which can be a problem sometimes , is to find appropriate contribution probability for data to present and analysis data through which reasoning the dimensions of the studied phenomenon accurately. One of these contributions is (Generalize Lambda Distribution) with its four parameters which has been studied by researchers Ramberg and Schmeiser in (1972 - 1974) and others in later periods, they take its importance and usage, it is a continuous probability contribution known through (Quantile function), and it is consider as one of the Quantile distributions, characterized by having four parameters, making it more flexible, public and takes various forms, its importance appears in stimulating studies as the form of definition imply as a simple algorithm for generating random numbers , and also it can be near to many continuous probability contributions such as (regular, whipple, exponent, normal, F. distribution) etc., depending on its parameters values, this feature gave it a special importance in its ease of use in the simulation of distribution which has no closed inverse function, as well as compensation the lost value of the data to which access is difficult to determine its real phenomenon through its capability in stimulation a statistical models. This contribution can be appropriate for data when it is unknown data distribution, it is also an alternative representation of data for distribution in the mixture of data which are difficult to present in some cases in single contribution without resorting to a mixture of distribution, these features enabled the researchers in dealing with one contribution for one phenomenon or different states of the same phenomenon instead of dealing with different contributions, for this features the (GLD) contribution has been used in many areas, including quantity control, reliability, metrological and others, it is the distribution which is appropriate for many phenomenon that showed its importance in solving the great problem of appropriate data through evaluating its parameters and performing well - conformity test. In this thesis the Generalize Lambda Distribution has been used as a model for the times of the failure to estimate the reliability function as in sometimes it is difficult to determine the appropriate probability distribution at failure times. The GLD has its ability to present failure times whether its distribution is known or unknown this was due to the features which it has. Its importance has been studied in two forms (RSGLD, FMKLGLD) and evaluated its four parameters (?_1,? ??_2,? ??_3,? ??_4) by using (moments, linear moments, ratios percentage, and least squares) methods, with the numerial algorithm method (Downhill Simplex) which accompanied the evaluating method. Also the researcher has been reached to a method in which evaluation is made by the expanding of numerical work method which accompanied with evaluation methods, and named (Downhill simplex) (D.S.M) method.A test of well - conformity for harmonizing data for distribution after estimating its parameters has been done by using (Kolmogorov - Smirnov) (K - S) test After that it was addressed to estimate the reliability function through quintile function being the only one closed formula for distribution. The researcher has depended upon an experimental way by carrying out a stimulation experience according to a program made with (Matlab) language for both distribution formats, and for (small, medium, and large) sample sizes and different presumptive parameter models for the purpose of comparison between the methods of parameters estimation depending on the statistical standard Mean Square Error (MSE), when the standard comparison were applied to the parameters estimator and to the distribution that represented by quantile function, the conclusion was that the Downhill Simplex Method (D.S.M.) is the best among the other superior methods of both distribution formats, for it has the smallest value of (MSE) , then the reliability function was established by superior methods.Practical application has been made in the research to experimental a real data taken from Wasit General Company for textile industrial/textile department to find out the failure time of the machines to estimate the reliability function of it by the best methods that have been reached through the experimental side.According to all the above, the most important conclusions and recommendations have presented, as well as future research. The main conclusion that the thesis has been concluded is that the expansion of algorithm mechanism (Downhill Simplex) to work on their own through the distribution quantile function to find the capabilities of the four parameter values (?_1,? ??_2,? ??_3,? ??_4) had approved its highly efficient in finding the values of the distribution capabilities for both versions. The researcher has been recommended many recommendations including that in the absence of an appropriate data under consideration for certain distribution, it is possible to use Generalize Lambda Distribution as it is a distribution which appropriate to many continuous phenomena, as it could be an alteration to use of nonparametric method which are less efficient than parametric methods.Key words : appropriate statistical model, Generalize Lambda Distribution, Quantile function, algorithm (Downhill Simplex), test (Kolmogorov - Smirnov), reliability function
