An Investigation of the Applicability of the Product Limit Estimate to the Statistical Analysis of Sonar Detection Distributions

Abstract

The application of the product limit estimate (PL estimate) to the analysis of sonar detection range data was examined using an empirical approach. A sonar detection distribution was assumed to be known and target lateral range distributions corresponding to likely operational scenarios were derived. These distributions were used in a computer simulation to generate sample fleet exercise reconstruction data. For data of small sample sizes, the PL estimates of the sonar detection distribution were compared with the known distribution and were found to be reasonably accurate approximations for all tactical situations tested. The PL estimates clearly outperformed the more readily computable, yet always optimistic, reduced sample (or empirical survival function) estimates. Finally, confidence intervals about the estimate were computed by using the jackknife procedure and the apparent optimism of the resulting confidence intervals was noted. Confidence interval baseline data is provided for future comparison with results from the estimates generated from small sample sizes. Further research is indicated to improve the usefulness of the jackknife to this application.