The Reduced Cumulative Distribution Function (rCDF) is the maximal lower bound for the Cumulative Distribution Function (CDF). It is equivalent to the inverse of the Conditional Value at Risk (CVaR), or one minus the Buffered Probability of Exceedance (bPOE). This paper introduces the Reduced Probability Density Function (rPDF), the derivative of the rCDF. We first explore the relation between rCDF and other risk measures. Then we describe three means of calculating the rPDF for a distribution, depending on what is known about the distribution. For functions with a closed-form formula for bPOE, we derive closed-form formulae for rPDF. We also examine using these formulae for parameter estimation with the maximum likelihood method. Further, we describe formulas for rPDF based on a numerical bPOE when there is a closed-form formula for CVaR but no closed-form formula for bPOE. Finally, we give a method for numerically calculating rPDF for an empirical distribution, and compare the results with other methods for known distributions.