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Note on the probability distribution of a small number of vectors

  • S. A. Vincenz (a1) and J. McG. Bruckshaw (a2)

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In this note the problem of random flights is considered for the case of a small number of vectors, each vector possessing the same constant magnitude. A formula is developed which permits the calculation of the probability function of the sum of N + 1 such vectors if the function of the sum of N vectors is known. The formulae for the probability distributions up to N = 8 are quoted and some of their practical applications mentioned.

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(1)Bruckshaw, J. M. and Vincenz, S. A.Mon. Not. R. Astr. Soc., Geophys. Suppl. 6 (1954), 579.
(2)Chandrasekhar, S.Rev. Mod. Phys. 15 (1943), 1.
(3)Fisher, Sir RonaldProc. Roy. Soc. A, 217 (1953), 295.
(4)Rayleigh, LordTheory of sound (London, 1878).
(5)Rayleigh, LordPhil. Mag. 37 (1919), 321.
(6)Vincenz, S. A.Ph.D. Thesis, Imperial College (London, 1952).
(7)Vincenz, S. A.Mon. Not. R. Astr. Soc., Geophys. Suppl. 6 (1954), 590.
(8)Watson, G. S.Mon. Not. R. Astr. Soc., Geophys. Suppl. 7 (1956), 160.

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