In this paper was discussed the process of compounding two distributions using new compounding procedure which is connect a number of life time distributions ( continuous distribution ) where is the number of these distributions represent random variable distributed according to one of the discrete random distributions . Based on this procedure have been compounding zero – truncated poisson distribution with weibell distribution to produce new life time distribution having three parameter , Advantage of that failure rate function having many cases ( increasing , dicreasing , unimodal , bathtube) , and study the resulting distribution properties such as : expectation , variance , comulative function , reliability function and failure rate function . In addition to estimating the parameters of the resulting distribution by using three methods of estimation are maximum likelihood method ,minmum chi square method using Downhill simplex algorithm , percentile method. The comparison between them was depending on the statistical measure mean square error ( MSE ) by implementing simulation experiment using different samples size ( small , large , medium ) , which through their results was reached that minmum chi square method using Downhill simplex algorithm is the best to estimating the parameter and probability function for compound distribution .
