Abstract
An expression is obtained for the distribution of a convolution of independent and identically distributed logistic random variables by directly inverting the characteristic function. This distribution is shown to be closely approximated by a student'st distribution when both distribution are standardized. Moreover, by showing that some of the analytic simplicity and statistical properties that are manifest in the single logistic also obtain in the convolution, an application of the convolution as a dose-response curve in the bio-assay problem is suggested.
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Research sponsored in parts by the Air Force Office of Scientific Research, Air Force Systems Command, USAF under Grant No. AFOSR-77-3360, by the Office of Naval Research under contract number N00014-76-0001 and by the African American Institute. The United States Government is authorized to reproduce and distribute reprints for Governmental purposes not withstanding any copyright notation here on.
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George, E.O., Mudholkar, G.S. On the convolution of logistic random variables. Metrika 30, 1–13 (1983). https://doi.org/10.1007/BF02056895
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DOI: https://doi.org/10.1007/BF02056895