The probability density estimation of the number of software failures in the event of clustering or clumping of the software failures is the subject of this paper. A discrete compound Poisson (CP) prediction model, as opposed to a Poisson (P) process, is proposed for the random variable (rv) X(rem), which is the remaining number of software failures. The compounding distributions, which are assumed to govern the failure sizes at Poisson arrivals, are respectively taken to be geometric when failures are forgetful and logarithmic-series (LSD) when failures are contagious. The expected value (mu) of X(rem) of CP is calculated as a function of the time-dependent Poisson and compounding distribution based on the failures experienced. Also, the q (variance/mean) parameter for the remaining number of failures, q(rem) is best estimated by q(past) from the failures already experienced. Then, one obtains the pdf of the remaining number of failures estimated by CP(mu,q). The CP model suggests that the CP is superior to Poisson where clumping of failures exists. Its predictive validity is comparable to Musa-Okumoto's (MO) Log-Poisson Model for certain software failure data with q > 1 when software failures clump within the same CPU second or unit time.