Zero And One Inflated Negative Binomial Model And Related Analysis

In areas such as Internet financial transactions and reliability engineering,number of transactions and failures are rare or not is superabundant,in particular,we often encounter excess zero and one in data samples.In order to fit data with excess zeros and excess ones and are overdispered,zero and one inflated negative binomial distribution(ZOINB distribution)and corresponding zero and one inflated negative binomial regression model(ZOINB regression model)are proposed.Bases on these,we discuss the implementation of EM algorithm for maximum likelihood estimation and Bayesian estimation of parameters.Firstly,in order to reduce the difficulty of parameter estimation,an EM algorithm for maximum likelihood estimation is proposed by introducing latent variables.In E step,we can obtain explicit expressions,and in M step,problem which we need to obtain the maximum of the highdimensional parameters converts to obtain the maximum of the lower-dimensional parameters respectively.Similarly,based on data augmentation,posterior sampling with high-dimensional parameters converts to latent variables sampling and posterior sampling with lower-dimensional parameters respectively.For these two estimation methods,we simplify the probem by introducing data augmentation.Secondly,based on the theory,a large number of simulations were performed to illustrate the correctness of the model and the validity of the EM algorithm and Bayesian posterior sampling.Finally,a study of real data is used to show the validity of the model proposed.Further,we also use the zero and one inflated possion model to fit the data and the results show that zero and one inflated negative binomial model performs better than the zero and one inflated possion model.