Editing Binomial distribution (section)

=== Ratio of two binomial distributions ===

This result was first derived by Katz and coauthors in 1978.<ref name=Katz1978>{{cite journal |last1=Katz |first1=D. |display-authors=1 |first2=J. |last2=Baptista |first3=S. P. |last3=Azen |first4=M. C. |last4=Pike |year=1978 |title=Obtaining confidence intervals for the risk ratio in cohort studies |journal=Biometrics |volume=34 |issue=3 |pages=469–474 |doi=10.2307/2530610 |jstor=2530610 }}</ref>

Let {{nowrap|''X'' ~ B(''n'', ''p''<sub>1</sub>)}} and {{nowrap|''Y'' ~ B(''m'', ''p''<sub>2</sub>)}} be independent. Let {{nowrap|1=''T'' = (''X''/''n'') / (''Y''/''m'')}}.

Then log(''T'') is approximately normally distributed with mean log(''p''<sub>1</sub>/''p''<sub>2</sub>) and variance {{nowrap|((1/''p''<sub>1</sub>) − 1)/''n'' + ((1/''p''<sub>2</sub>) − 1)/''m''}}.