  The directional precision of the sample mean estimator was calculated
analytically for the offset exponential and normal distributions in
three-dimensional space both for a finite sample and for limiting cases. It was
shown that the spherical projection of the sample mean of the shifted
exponential distribution has connections with modified Bessel functions and
with hypergeometric functions. It was shown explicitly how the distribution of
the sample mean of the exponential pdf converges near the mode to the normal
distribution. Approximation formulae for the distribution of the sample mean of
the shifted exponential distribution and for its directional precision and for
the precision of the estimation of the direction of shift of the normal
distribution were obtained.
