Maximum Likelihood Estimation And Application Of The Beta Exponential Geometric Distribution Parameters

The failure function with decreasing,increasing and inverting is called Beta exponential geometric distribution(BEG),which is an expansion of exponential geometric distribution(EG)and is generated by the logarithm of beta(?)random variable.Including generalized exponential geometric distribution(GEG),geometric exponential distribution(GE),and beta exponential distribution(BE).This article focuses on the maximum likelihood estimation and application of the beta exponential geometric distribution parameters.First,the problem of maximum likelihood estimation based on the beta exponential geometric distribution parameters under the full sample is studied.Solve the maximum likelihood estimate of unknown parameters.Using Newton iterative numerical method and MATLAB software for programming,101 fatigue life observation data obtained by 6061-T6 aluminum sheet parallel to the rolling direction at 18 oscillations per second(maximum stress of 31000 Psi per cycle)were substituted calculations are performed in the program to find the maximum likelihood estimates of the parameters.Secondly,the problem of maximum likelihood estimation based on beta exponential geometric distribution parameters under censored samples is studied.In the first step,the data is truncated and the first 70 data are taken.Using Newton iterative numerical method,combined with MATLAB software for programming,the 70 data are substituted into the program calculation,and the maximum likelihood estimate of the parameters under the censored sample is obtained.Finally,chi-square fitting test was performed on the 101 observed data.Test whether the data follow the beta exponential geometric distribution.The first step is to process and group the data to find the probability and frequency of occurrence of events falling on the interval.Then compare the calculated results.If the difference between the two is small,then accept the null hypothesis and accept that the data obey the geometric distribution of the beta index.