Choose the Best Method for Estimation the Parameters of Probability Kappa Distribution
With practical application
A thesis
Submitted to College of Administration and Economic-Karbala University in partial fulfillment of the Requirements for the Degree of master of Science in statistics
By
Baqer Kareem Fahad
Under supervision
Asis. Prof. Dr. A Mahdi Wahhab Neamah
Abstract
Kappa distribution is considered one of the continouse distribution , whch is stuided the random behaivor for the important phenomenies for life and sciences . This distribution has developed by Hosking and other sientists . This distribution studies some natural phenomenonies such as falling rain and changing of the wether . This distribution is used for studying the discver of modren phenomenonies such as salor winds and plasma properties and other phenomenones from these points come the important of this distribution . There are more than one way and we will study in this thises search his furmela that cesuult from mix the distribution of Gamma and distribution of normal log ,by which we study the natural phenomenones . The searcher drived properties of distribution and use five mwthods for estimate the three parameters () of kappa disteribution after completed the math formela to get the final formula of these methods . These method are maximum liktihood ,L- moment . and for choosing the best one amony these method to estimate the three parameter of distribution . We use simulation to choose which method is bestof the paramters of distribution . We use test for ten groups of assuming data and five volums of samples ( 150 , 100 , 75 , 50 , 25 ) . The results were good to showed the best method which was LQ-moment sample , sizes . There for we use this method in oral side , which study phenomenon of rain fall on Baghdad city and we use oral data by main obsevation station of Baghdad city . We get these data from the central statistics .
Concluded in this thiese important Conclusions these are :
1 –Found that the best estimates to distribution of kappa was at the method of torque quantity linear .
2 –As stated in the experimental model turned out that the values of the estimated (θ,𝛃,α) very close with default values .
3 – When make a test of good matching (Goodness of fit ), and when compared to the value ( P-value ) to appose (Chi2) with ( 0.01 ) in side Applied The researcher Shows that The data in the station observations province of Baghdad behave a accordance with the hypothesis of alternative (H1: ) any spread the distribution of kappa .
In addition to the recommendations that were the most important :
1 – Expand the search to include the other six formulas other distribution Kappa as a result of importance in the study of phenomenon life and the phenomenon of climate change and the phenomena other space which studied distribution .
2 – Use anther modalisties change from thats use by researcher ( LH – Moment ) , ( TL – Moment ) and other Base methods to knon the rang of and accuracy of those methods .
