The common problem in risk analysis of correctly specifying a probability distribution about an estimate in situations when few data are available is examined. In the absence of data, experts are sometimes used to give a lowest and highest conceivable estimate. Triangular distributions are well suited for these situations when only a low, high, and most likely estimate are given. A problem, however, exists from the failure to adjust for biases when estimating extreme values. Various types of biases, which narrow the range of extreme estimates, are explored. A method is suggested for accounting for these biases by placing extreme estimates at specified percentile points rather than endpoints of a triangular distribution. Since most Monte Carlo models require end points of a triangular distribution, a closed‐form expression for identifying the end points given two percentile points and a most likely point is derived. This method has been used extensively in developing cost risk estimates for the Ballistic Missile Defense Organization (BMDO
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