I have used the BTYD Package in R to estimate the number of transactions that a customer is expected to make in the future. I have 2 questions: 1) Is the number of transactions always a non-integer value? 2) How do you validate the performance of the BTYD Model. I have made some R plots using the functions pnbd.PlotFrequencyInCalibration, pnbd.PlotFreqVsConditionalExpectedFrequency and pnbd.PlotRecVsConditionalExpectedFrequency. What exactly is the method used to validate the performance of BTYD Model? Can these plots be considered a measure of checking the performance of the model?