estimating the survival function Maximum Likelihood and Cramér-Von Mises Method use of amixture distribution weibull and ailamujia with apractical application

Tow failure distributions were mixed ,weibull distribution and ailamujia distribution it's called weibull –ailamujia distribution which consists of four features, the two distributions were mixed by adding a mixing parameter ,the mixture of two distributions would be more efficient ,and representative of the data than the single distributions. A group of statistical properties of the mixture distribution were studied , such as the probability function ,the survival function and the failure rate function .classical estimation method were used to estimate the parameters of the mixture distribution, which are maximum likelihood of method ,the cramer –von mises method ,The method were compared using monte carlo simulations real data were taken regarding drug –resistant tuberculosis (TB) Multi Drug Resistance(MDR) methods were compared using the MSE statistical criterion ,and the result should a preference for the method cramer-von mises for having the lowest MSE