I need to sample a random variable from truncated distribution
everytime in MCMC.  Suppose, the upper (a) and lower (b) bounds are
far from the location parameter (c) and the scale parameter is
relatively small, i.e,. b<=a<=c, and c is far greater than a and b. 
The chance to sample using slice sampling is trivival.  It's almost
impossible to sample it from such a truncated distribution.  However,
the problem is quite often in some cases.  What should I do in dealing
with this scenario?

Many thanks,
Nicole
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