To match a failure probability distribution to test data requires, in general, two steps: 1. The procedure which determines what type of distribution matches the data in an acceptable way. 2. The estimate of the parameter(s) of the ‘accepted’ probability distribution which gives the ‘best fit’. Graphical methods are normally applied in Step 1. Often the required straight line does not fit the data plotted on a particular type of probability paper very well. The ‘fitting’ somehow becomes a subjective action. In this paper an analytical method is developed for Step 1, which does not utilize any graphical aids. The analytical method developed for Step 1 also provides simple methods for estimating parameter(s) and how good the ‘fit’ is. Two examples are worked out.