# Accession Number:

## AD0691770

# Title:

## PROBABILITY DENSITY FUNCTIONS OF n VECTORS ADDED WITH RANDOM DIRECTIONS.

# Descriptive Note:

## Interim rept.,

# Corporate Author:

## NAVAL RESEARCH LAB WASHINGTON D C

# Personal Author(s):

# Report Date:

## 1969-07-17

# Pagination or Media Count:

## 15.0

# Abstract:

The probability density function of the resultant amplitude of n vectors in two dimensions, added with random directions, was calculated through an integral transformation which takes a probability density function for k components into a probability density function for k 1 components. Examples were calculated to show the qualitative aspects of the density functions for 2, 3, and 4 components, with arbitrarily given magnitudes. For n or 5, the probability distribution rapidly approaches the Rayleigh distribution. The method also allows the use of a Rayleigh vector as one of the components. Author

# Descriptors:

# Subject Categories:

- Statistics and Probability