Maximum Likelihood Estimation And Application Of Multi-parameter Odd Log-Logistic Generalized Gompertz Model For Complex Censored Data

This paper mainly considers the maximum likelihood estimation and application of multi-parameter odd log-logistic generalized Gompertz(OLLGG)model under complex censored data(interval-censored data,left truncated and right censored data).These complex censored data are very important data types in many disciplines.It is one of the frontier and hot issues in modern statistics research.Interval censored failure time data often appear in biomedical,industrial engineering and other fields,and the analysis of such data mainly relies on some parameter model methods.Left-truncated and right-deleted data is also a common data type in the fields of finance and survival analysis.In recent years,scholars have conducted a lot of research on this data type.OLLGG is a particularly flexible four-parameter distribution,which generalizes exponents,generalized exponents and generalized Gompertz distributions,and has better fitting than its sub-models and some generalized Gompertz distributions.The risk function of the generalized Gompertz distribution can only increase or be constant,which does not provide a reasonable fit for modeling the bathtub shaped risk function.However,the OLLGG model has flexible risk shape,which is very effective for modeling different data sets with different shapes,which is an important feature of reliability research.The first part mainly discusses the estimation problem of multi-parameter regression model based on four-parameter OLLGG distribution under interval-censored data.Compared with other models,multi-parameter regression is no longer the regression relationship between single parameter and covariable in the form of standard risk function regression.It provides the idea of multi-parameter regression modeling and generates a flexible regression model.In addition,it can also establish a failure time distribution parameter and covariable model under the assumption of failure time model to relax the proportional risk hypothesis,supplement the deficiency of the single regression model on the assumption,and the estimation process is simpler and easier to realize.Firstly,the background of interval censored data is introduced.Secondly,based on OLLGG distribution,a multi-parameter regression model is proposed to describe the correlation between distribution parameters and covariables by linear regression.The maximum likelihood estimation method is used to estimate the parameters in the model,and the simulation results verify the effectiveness of the model.Finally,the proposed model was compared with the proportional dominance model and applied to the data of HIV infection in hemophiliacs.It was found that the proposed model had a flexible fitting effect on the data.The second part mainly discusses the estimation problem of the multi-parameter regression model of OLLGG distribution under left truncated and right censored data.Multi-parameter regression not only generates a flexible regression model,but also establishes the failure time distribution parameter and covariable model under the failure time model hypothesis to relax the proportional risk hypothesis,it complements the deficiency of the traditional single model in the aspect of hypothesis,so that the estimation process is simple and conducive to implementation.Firstly,the data types of left truncated and right censored data and the research status at home and abroad are introduced.Secondly,based on OLLGG distribution,a multi-parameter regression model is proposed to describe the relationship between the four parameters and covariables in the distribution by linear regression.Then the corresponding likelihood function is given and the maximum likelihood estimation method is used to estimate the parameters.The simulation results verify the effectiveness of the multi-parameter OLLGG model with left truncated and right censored data.Finally,the proposed model is compared with the classical proportional dominance model,and the maximum likelihood estimation is applied to the death time data set of 462 elderly residents in the retirement center of Palo Alto,California,respectively.It is found that the proposed model has a flexible fitting effect on the data.