Lognormal Probability Density Function

The lognormal distribution is a two-parameter distribution with parameters and . The pdf for this distribution is given by:

where = ln(T), where the T values are the times-to-failure, and

The lognormal pdf can be obtained, realizing that for equal probabilities under the normal and lognormal pdfs, incremental areas should also be equal, or:

Taking the derivative yields:

Substitution yields:

(1)

where: