Optimal Threshold from a Mixture of Two Distributions

• Activity Number: 516
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Chong Sun Hong+ and Jae Seon Joo*
• Companies: SKK University and KWDI
• Keywords: CAP ; ROC ; Discriminatory ; Total Accuracy ; True Rate

Abstract

Assume a mixture of two distributions for credit evaluation studies with a parameter space consisting of default and non-default states. From this mixture, we discuss three methods for estimating thresholds to minimize the sum of errors that lead to mistaken predictions that borrowers in default are not in default, or that borrowers not in default are in default. By using statistical hypothesis tests, an optimal threshold can be identified as a critical value. Two other optimal thresholds used to maximize classification accuracy measures, 'total accuracy' and 'true rate', are estimated as equations related to these probability density functions of ROC and CAP curves. These optimal thresholds are obtained using normal mixtures with a range of means and variances. The error sums corresponding to each optimal threshold are obtained and compared