Parameters Estimation And Hypothetical Testing Of Bivariate Generalized Exponential Distribution

There are many ways for parameter estimation,and the most used one is maximum likelihood estimate.In the process of calculating the maximum likelihood estimation,it is often encountered that the analytical solution cannot be obtained.Usually in this case,an iterative algorithm is used to solve it.In the process of solving the log-likelihood equation,there is a method that is the numerical analysis method of Newton iteration.In this thesis,the maximum likelihood estimation and application of binary generalized exponential distribution parameters are mainly considered,and testing the goodness of fit of the data used to prove that the data is available.Firstly,the maximum likelihood estimation problem of the binary generalized exponenti al distribution parameters under full sample is studied.Among them,the maximum likelihood estimation for solving unknown parameters when some parameters are known.Using the numerical method of Newton iteration,the MATLAB language is used to substitute the real data of the respective 100-meter race results and marathon scores of 55 countries provided in the IAAF 1984 Los Angeles Olympics track and field statistics manual,and the maximum likelihood estimation of the parameters is obtained.Secondly,the maximum likelihood estimation of unknown parameters is solved for the binary generalized exponential distribution under censored samples.The method used is also to assume that some of the parameters are known to solve the maximum likelihood estimate of the unknown parameters.This article truncates the real data and takes the results of the first 44 countries.Using Newton's iterative algorithm,using MATLAB language to program,then bring the data of 44 countries into,and then obtain the maximum likelihood estimation of the parameters.Finally,a fitting test was performed on the 1984 Olympic data used.In order to prove that this data comes from the binary generalized exponential distribution,this thesis performs a goodness-of-fit test on this data.First,the data is grouped,then the data is processed,and the probability and frequency of the event falling in the interval are obtained.The result is that the difference between the two is small,and the original hypothesis can be accepted,and then the data is obtained from the binary generalized exponential distribution.