On the logistic midrange |
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Authors: | E Olusegun George Cecil C Rousseau |
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Institution: | (1) Memphis State University, Memphis, USA |
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Abstract: | Summary It is well-known that for a large family of distributions, the sample midrange is asymptotically logistic. In this article,
the logistic midrange is closely examined. Its distribution function is derived using Dixon's formula (Bailey (1935,Generalized Hypergeometric Series, Cambridge University Press, p. 13)) for the generalized hypergeometric function with unit argument, together with appropriate
techniques for the inversion of (bilateral) Laplace transforms. Several relationships in distribution are established between
the midrange and sample median of the logistic and Laplace random variables. Possible applications in testing for outliers
are also discussed. |
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Keywords: | Characteristic functions sample median logistic distribution Laplace distribution |
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