PROBABILITY DENSITY FUNCTIONS OF n VECTORS ADDED WITH RANDOM DIRECTIONS.
NAVAL RESEARCH LAB WASHINGTON D C
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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
- Statistics and Probability