Holgate, P. The lognormal characteristic function. (English) Zbl 0721.60012 Commun. Stat., Theory Methods 18, No. 12, 4539-4548 (1989). 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. Cited in 4 Documents MSC: 60E10 Characteristic functions; other transforms 62E20 Asymptotic distribution theory in statistics 62E10 Characterization and structure theory of statistical distributions Keywords:summation methods; saddle point method; characteristic function; lognormal distribution; Asymptotic approximation PDF BibTeX XML Cite \textit{P. Holgate}, Commun. Stat., Theory Methods 18, No. 12, 4539--4548 (1989; Zbl 0721.60012) Full Text: DOI References: [1] Aitchison J., The lognormal distribution (1957) · Zbl 0081.14303 [2] Crow E.L., Lognormal distributions (1988) · Zbl 0644.62014 [3] De Bruin N.G., Asymptotic methods in analysis (1961) [4] Hardy G.H., Divergent Series (1949) · Zbl 0032.05801 [5] Heyde C.C., J. Roy, Statist Soc. B 25 pp 392– (1963) [6] DOI: 10.1137/1126095 · Zbl 0488.60024 · doi:10.1137/1126095 [7] Lukacs E., Characteristic functions (1970) · Zbl 0201.20404 [8] Thorin O., Scand. Act J pp 121– (1977) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.