TRANSFORMATION FOR STATISTICAL DISTRIBUTION APPROXIMATELY NORMAL BUT OF FINITE SAMPLE RANGE
Research and development rept. Aug 1965-Oct 1966
NAVAL UNDERSEA WARFARE CENTER SAN DIEGO CA
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In many cases statistical data are drawn from a population with approximately normal distribution but with bounded, rather than infinite, domain. The traditional approach is to use a truncated normal distribution, but if the population probability approaches zero at the bounds of the domain, serious errors in hypothesis testing may accompany truncation, since the tails of the assumed distribution are used in error probability and critical region computation. The truncated distribution is affine-transformed so that the abscissa is translated to the truncation points, and the curve above the new abscissa is given unit area then the curve is half-rectified. The result is a quasi-normal distribution having finite domain yet retaining many properties of the normal distribution. Exact sampling theory, tests of hypothesis methodology, illustrative applications from electronic component reliability evaluation and ocean data analysis, and tables of associated probabilities are presented.
- Statistics and Probability