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# Accession Number:

## AD0270477

# Title:

## SOME PROPERTIES OF A CLASS OF EVENT DISTRIBUTIONS WITH APPLICATIONS TO THE LEVEL CROSSINGS OF CONTINUOUS RANDOM PROCESSES

# Descriptive Note:

# Corporate Author:

## AERONAUTICAL SYSTEMS DIV WRIGHT-PATTERSON AFB OHIO DIRECTORATE OF ADVANCED SYSTEMS PLANNING

# Report Date:

## 1961-11-01

# Pagination or Media Count:

##
1.0

# Abstract:

## A class of event distributions in time is defined by specifying the behavior of the probability distribution functions including joint distribution functions of all orders in the limit as the time intervals approach zero. For this class of event distributions, it is shown that knowledge of the probability of an odd number of events occurring in a given interval of time is sufficient to calculate all the moments of the distribution, the first order probability distribution functions, and the probability density of the intervals between events. For the class of events defined by the level crossings of continuous random processes, the probability of an odd number of events in a given interval is readily calculable. However, there is no general method of determing whether the level crossings are included in the class of event distributions initially defined. In particular, for the zero crossings of ergodic gaussian processes with zero mean, evaluation of the resulting statistical functions reveals that the region of possible applicability is very small. However, within this region, there is one process for which experimental data is available. Comparison of calculated and experimental data for this particular process shows very good agreement. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#