  Compound Poisson distributions and signed compound Poisson measures are used
for approximation of the Markov binomial distribution. The upper and lower
bound estimates are obtained for the total variation, local and Wasserstein
norms. In a special case, asymptotically sharp constants are calculated. For
the upper bounds, the smoothing properties of compound Poisson distributions
are applied. For the lower bound estimates, the characteristic function method
is used.
