The Distribution of the Logarithm of the Sum of Two Log-Normal Variates

J. I. Naus

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

Let Z1, Z2 be two independent, identically distributed random variables whose logarithms are normally distributed. We derive the generating function, expectation, and variance of the logarithm of the sum of Z1 and Z2. The expressions for the expectation and variance involve the sums of rapidly converging series. Converging upper and lower bounds to the expectation are given to indicate the number of terms in the series that need to be evaluated to yield a specified number of significant places.

Original languageEnglish (US)
Pages (from-to)655-659
Number of pages5
JournalJournal of the American Statistical Association
Volume64
Issue number326
DOIs
StatePublished - Jun 1969

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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