Abstract
Problem statement: The study and research of survival or reliability or life time belong to the same area of study but they may belong to a different area of application. In survival analysis one can use several life time distribution, exponential distribution with mean life time θ is one of them. To estimate this parameter and survival function we must be used estimation procedures with less MSE and MPE. Approach: The only statistical theory that combined modeling inherent uncertainty and statistical uncertainty is Bayesian statistics. The theorem of Bayes provided a solution to how learn from data. Bayes theorem was depending on prior and posterior distribution and standard Bayes estimator depends on Jeffery prior information. In this study we annexed Jeffery prior information to get the modify Bayes estimator and then compared it with standard Bayes estimator and maximum likelihood estimator to find the best (less MSE and MPE). Results: when we derived Bayesian and Maximum likelihood of the scale parameter and survival functions. Simulation study was used to compare between estimators and Mean Square Error (MSE) and Mean Percentage Error (MPE) of estimators are computed. Conclusion: The new proposed estimator of modify Bayes estimator in parameter and survival function was the best estimator (less MSE and MPE) when we compared it with standard Bayes and maximum likelihood estimator.
Highlights
Survival analysis refers to the techniques used to study the time to occurrence of some event in a population and is often called time to event analysis
A Bayesian approach to hypothesis testing is presented by Fernandez[2]. He studied the problem of estimating the mean lifetime, hazard rate and survival function of exponential lifetime model
Maximum likelihood estimation: We have the set of random lifetime t1, t1,...tn and a vector of unknown parameters θ = (θ1,... θn), the ith element of the score vector is: Ui (θ) =
Summary
Survival analysis refers to the techniques used to study the time to occurrence of some event in a population and is often called time to event analysis. The survival function S(t) is defined as the probability that human being will surviving at time period t. The two parameter of exponential distribution was used when failure will never occur prior to some specified time to. T ≥ to, the probability density function of exponential distribution becomes: f ( t; θ) = 1 θ exp − t. A Bayesian approach to hypothesis testing is presented by Fernandez[2]. He studied the problem of estimating the mean lifetime, hazard rate and survival function of exponential lifetime model. Hahn[3] show that it is not always Jeffrey’ prior applied to panel models with fixed effects yields posterior inference free from the incidental parameter problem. In[4] derived Bayesian and non Bayesian estimators of the shape parameter and reliability in case of complete and censored samples and the MSE of estimators are computed
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