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Document Type |
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Thesis |
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Document Title |
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A Study on The Goodness of Fit Tests for Burr Distribution دراسة عن اختبارات جودة التوفيق لتوزيع بير |
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Subject |
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A Study on The Goodness of Fit Tests for Burr Distribution |
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Document Language |
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Arabic |
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Abstract |
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المستخلص انجليزي
The compatibility of a set of observed sample values with any distribution can be checked by a goodness of fit tests. These tests designed for a null hypothesis, which is a statements about the form of the cumulative distribution function or probability function of parent population from which the sample is drawn.
The best known procedures for testing hypothesis are the classical goodness of fit tests based on the empirical distribution function (EDF) for continuous ungrouped data. A statistic measuring the difference between and will be called "EDF statistic". It is based on the vertical difference between and and it is conveniently divided into tow classes, the supermum class and the quadratic class.
The supermum statistics:
The form of this class: , and performed in this thesis with Kolmogorov –Smirnov test, and it's statistic is denoted by D.
The quadratic statistics:
A second and wide class of measures of discrepancy is given by:
where is suitable function which gives weight to the squared difference .
We will concerning two tests of this kind, they are:
a) Cramer – Von Mises (CVM) test when , and it's statistic is denoted by .
b) Anderson – Darling (AD) test when , and it's statistic is denoted by .
Where is the cumulative distribution function for the parent population. We can use these standard test when is completely specified with complete data and the tables of these tests be valid in this case. But if is contained unknown parameters must be estimated from the sample data or if the samples underling are censored, then these tests are inappropriate for use with it and critical values obtained from.
published tables of the complete samples with simple hypothesis are necessarily conservative.
In this thesis, we reviewed the modified Kolmogorov – Smirnov, Cramer – Von Mises and Anderson – Darling tests which are applicable to both simple or composite hypothesis and to complete or censored samples.
The aim of this thesis is to obtain tables of critical values for the modified KS, CVM and AD test statistics for the Burr distribution type III with unknown shape parameters c, k in the case of complete and type II censored samples. The powers of these test statistics are studied for six alternative distributions that is " Uniform, Logistic, Exponential, Weibull, Standard Normal, Chi-Square with one degree of freedom". Finally a power comparison of three test statistics were presented. |
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Supervisor |
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ABDULLAH ABDULFATTAH |
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Thesis Type |
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Master Thesis |
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Publishing Year |
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1422 AH
2000 AD |
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Added Date |
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Monday, February 16, 2015 |
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Researchers
| مها علي الدحلان | ALDAHLAN, MAHA ALI | Researcher | Master | |
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