Estimation And Testing In The Burr Distribution With Three Parameters

The opening chapter gives a general development of the burr distribution with three parameters . Then introduces its application in Economics, Sociology, Euthenics and Actuaral Statistics.The burr distribution has often been used by actuary. So, it is significative to researth the burr distribution. The second and third parts introduce the burr_â…  distribution and fazrr_â…¡respectively.The second part is the keystone of this paper. Probability density function, moment, Fish information matrix, order statistics and parameter estimator of the burr_â…  distribution is introduced. The estimators including maximum likelihood estimator and interval estimator are analyzed. Based on the normal infer, some characters of maximum likelihood estimator are researched. Order statistics and its distributions of the burr_â…  distribution are introduced. Likelihood-ratio test is a important parameter test method which it is applied to the burr_â… distribution .The last part introduces the burr_â…¡ distribution with three parameters. Some of the basic characters including the mathematic characters, Fish information matrix, order statistics are introduced. The estimators including maximum likelihood estimator and interval estimator are analyzed. Based on the normal infer, some characters of maximum likelihood estimator are researched. Likelihood-ratio test is a important parameter test method which it is applied to the burr_â…¡ distribution. The burr distribution play key role in practical cases, such as income data exceed a fixed bound , hurricane loss and so on. It is important to research the burr distribution. At the end of this part we give a example to confirm that it is important to study the burr distribution with three parameters.