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CONSERVATISM OF THE z CONFIDENCE INTERVAL

UNDER SYMMETRIC AND ASYMMETRIC DEPARTURES

FROM NORMALITY

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SANJIB BASU

*Department of Mathematical Sciences, Fulbright College of Arts and Sciences,*

University of Arkansas, 301 Science-Engineering Building, Fayetteville, AR 72701, U.S.A.
(Received April 22, 1996; revised September 11, 1997)

**Abstract.**
The robustness of the z-interval under
nonnormality is investigated by finding its infimum coverage
probability over suitably chosen broad class of
distributions. In the case of *n* = 1, the infimum coverage
probabilities over the normal scale mixture and the
symmetric unimodal families of distributions are obtained
analytically. For general *n*, the infimum problem is
theoretically reduced to a finite dimensional minimization
which is then obtained numerically. The obtained minimum
coverage probabilities are very close to the nominal
probabilities. These exact minimum coverage probabilities are
often notably sharper than the lower bounds given by the
Camp-Meidell-Gauss inequality. The family of general unimodal
distributions is considered next to investigate the possible
effect of asymmetry. The obtained infimum coverage
probabilities over this family are found to be the same as
the ones over the symmetric unimodal class.

*Key words and phrases*:
Camp-Meidell inequality,
coverage probability, normal scale mixture, robustness,
unimodal, z-interval.

**Source**
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