Characteristics of the Lognormal Distribution

The lognormal distribution is a distribution skewed to the right.
The pdf starts at zero, increases to its mode and decreases thereafter.

The characteristics of the lognormal distribution can be exemplified by examining the two parameters, the log-mean, () and the log-std, () and the effect they have on the pdf.

Looking at the Log-mean ()

The parameter, , or the log-mean life, or the MTTF’ in terms of the logarithm of the T’s is also the scale parameter and is a unitless number.
For the same the pdf's skewness increases as increases.

Looking at the Log-std ()

The parameter , or the standard deviation of the T’s in terms of their logarithm or of their , is also the shape parameter and not the scale parameter as in the normal pdf. It is a unitless number and assumes only positive values.
The degree of skewness increases as increases, for a given .
For values significantly greater than 1, the pdf rises very sharply in the beginning, i.e. for very small values of T near zero, and essentially follows the ordinate axis, peaks out early, and then decreases sharply like an exponential pdf or a Weibull pdf with 0 < β < 1.