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The lognormal characteristic function. (English) Zbl 0721.60012
Summary: A number of different ways are examined of representing the characteristic function $$\phi$$ (t) of the lognormal distribution, which cannot be expanded in a Taylor series based on the moments. In § 2 the use of a finite Taylor series is examined. A method of summing the divergent formal expansion is discussed in § 3. In § 4 the fact that $$\phi$$ (t) is a boundary analytic function is exploited. Asymptotic approximation of the integral defining $$\phi$$ (t) is studied in § 5. Each approach produces some interesting information about the distribution.

MSC:
 6e+11 Characteristic functions; other transforms 6.2e+21 Asymptotic distribution theory in statistics 6.2e+11 Characterization and structure theory of statistical distributions
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References:
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