Bob Wheeler wrote:
> It is a form of the bivariate normal. If x is the
> distance from the aim point, then the density is
> (x/s^2)exp(-x^2/(2s^2)), and s is the common
> standard deviation. There is substantial data to
> show that this is a reasonable description of the
> pattern for small arms fire.
A practical consequence of this density which Bob didn't mention is that
the probability of obtaining a distance less than or equal to r from the
density's center (i.e., the [cumulative] distribution function) is given
by 1 - exp(-r^2/(2s^2)). Also, one should note that:
1. Both the quantity "x" in Bob's expression and the quantity "r" in
mine range from 0 to +infinity.
and:
2. In practical applications, the probability density's center may not
be located at the *aiming* point (i.e., the hit locations may be
incorrect "on average"). The probability of obtaining a distance from
the *aiming point* less than or equal to r cannot be expressed in closed
form in that case, but useful numerical approximations are available --
e.g., see the chapter on 'Probability Functions' in 'Handbook of
Mathematical Functions,' by Abramowitz and Stegun.
Charles Metz
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