# Accession Number:

## ADA051557

# Title:

## Confidence Intervals Associated with Random Signal Processing.

# Descriptive Note:

## Memorandum rept.,

# Corporate Author:

## TRACOR INC AUSTIN TEX

# Personal Author(s):

# Report Date:

## 1968-12-31

# Pagination or Media Count:

## 39.0

# Abstract:

When a random signal is sampled and digitally analyzed, the results of the analysis are estimates of the true parameters or statistics describing the random signal. In many cases there exists difficulty in assigning a level of confidence to such an estimate. That is, the estimate can never be said to equal the true parameter value, but can be said to lie within specified confidence limits, or error bars, with a given probability. The confidence limits are highly dependent upon the characteristics of the particular random signal being analyzed and the parameter being estimated. This memorandum contains the necessary procedures for determining confidence intervals for several types of estimates that occur frequently in sonar signal analysis. Covered in Section 2 are confidence intervals for the sample mean and sample variance from a normal population. Section 3 contains a description of the chi-square goodness-of-fit test, used to test the equivalence of a measured probability density function for sampled data to some hypothesized density function. Section 4 describes the Kolmogorov K statistic, used to set a confidence band about an entire probability distribution function and a binomial statistic, used to set confidence limits about each point on an empirical distribution function.

# Descriptors:

# Subject Categories:

- Statistics and Probability
- Acoustic Detection and Detectors