Parameter Estimation Of Commonly Used Survival Distribution Based On Randomly Censored Data

Survival analysis is a subject to evaluate and forecast biologic survival time that can be generally defined as the duration of an appointed state. From the mathematical point of view, survival analysis is a type of statistical analysis towards one or more non-negative random variables. Because its analysis method is of great applications in many fields, such as biomedicine, reliability, service system and socio-economy, survival analysis has already been an important branch of modern mathematical statistics.When it can be assumed that the sample is from some distribution, we would naturally like to use parameter estimation method. Due to some practical reasons, however, measuring data is always being censored, which would result in some troubles in statistical analysis. The most common type of censoring is randomly right censoring, in which case the survival time is randomly censored and no fewer than the right censored time.Censored data is incomplete. The EM algorithm introduced by Dempster et al. in 1977 can be viewed as an iterative algorithm to calculate the MLE based on incomplete data, and it performs well.In this paper, EM algorithm is used to estimate the parameters of exponential distribution, Weibull distribution and lognormal distribution based on randomly right censored data. For exponential distribution, the acquired estimate expression is the same as the result obtained by other method in reference [8]; for Weibull distribution, the author prove that γ satisfies a non-linear equation and λ is afunction of y; for lognormal distribution, a iterative algorithm for parameter estimation is proposed, which is the expansion of some results in Wolynetz's Ph.D. thesis.Furthermore, computer simulation aimed at Weibull distribution and lognormal distribution is processed, and results show that the provided method is feasible and easy to implement.