My earlier answer wasn't "real-life", but there are certainly examples for
which the distr. is a mixture of a normal and, with small probability, a
distribution with prob. mass far to the right. I remember a client who had
some rat swimming-time data. He came to me because some of the rats
drowned, but I noticed that a few rats had very large times, so that the
distr. of times seemed to be a mixture of this kind. It turned out that
some rats were able to "hang" along the side of the tub, and achieve very
large times. I used that example for years to motivate nonparametric methods.
One correction for my first message: In the sentence
"Let X be a std. normal cdf with prob .999 and be 1 million with prob.
0.001. X has cdf F(x)" replace "cdf" by "random variable."
.
Jim Stapleton
Professor and Graduate Director
Dept. of Statistics and Probability
Michigan State University
517-355-9678
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