Parameter estimation method based on beta-likelihood function

Distribution parameter estimation is a common method which is used in reliability data analysis to study the change rules of product reliability and evaluate the reliability level of the product. Learning from the beta distribution which is used to describe the product reliability in life test and evaluate the reasonable degree of estimator of reliability, we thought that reliability estimator is more reasonable if its probability density function is bigger in the beta distribution, raised a beta likelihood function to evaluate the reasonable level of the estimate in reliability analysis, discussed the distribution parameter estimation method when using this beta likelihood function, verified the method by simulation under the exponential distribution case and Weibull distribution case, and gave the corresponding application examples. The estimation method is based on abundant theoretic evidence, and is suitable for all kinds of distribution types. From the application examples, we know that estimation results are reasonable and believable. Maximum likelihood estimation method takes the samples' probability density function in the distribution to be estimated as the evaluation criteria, while, on the contrast, our method takes the cumulative incidence estimator as the evaluation criteria. So it is more applicable in the research on reliability and survival problems when concerning the cumulative occurrences.