Barniv, Ran, John Hathorn, Abraham Mehrez, and Douglas Kline, "Confidence Intervals for the Probability of Insolvency in the Insurance Industry", Journal of Risk and Insurance, Vol. 66, No. 1, (March 1999), pp. 125-137.

Abstract: Recent literature use logit analysis for point estimators of the probability of insolvency for each insurer based on financial statements data. These studies focus on selecting predictors, comparing classification techniques, and measuring classification accuracy. Our analysis differs from the previous literature by explicating and developing confidence intervals which provide measures of statistical reliability for the estimators and thus enhance the results of prior research. The main purpose of this article is to provide and illustrate a method of constructing confidence intervals for insolvency probabilities. We examine various measures of the confidence intervals, such as their minimum lengths and minimum upper bounds. Two examples show a substantial improvement (reduction) in the length and the minimum upper bound of the confidence intervals at the optimal level of the financial accounting variables. A third example depicts a confidence interval for the probability of failure for an insolvent insurer. Implications for researchers and users of financial accounting information are briefly discussed.

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