Template:Ald characteristics

Characteristics

 * 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 $$({{\overline{T}}^{\prime }})$$ and the log-std ($${{\sigma }_}$$), and the effect they have on the $$pdf$$. Looking at the Log-Mean $$({{\overline{T}}^{\prime }})$$
 * The parameter, $$\bar{{T}'}$$, or the log-mean life, or the  $$MTT{F}'$$ in terms of the logarithm of the  $${T}'s$$  is also the scale parameter and a unitless number.
 * For the same $${{\sigma }_}$$  the  $$pdf$$ 's skewness increases as  $$\bar{{T}'}$$  increases.



Looking at the Log-STD $$({{\sigma }_})$$

 * The parameter $${{\sigma }_}$$, or the standard deviation of the  $${T}'s$$  in terms of their logarithm or of their  $${T}'$$, 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 $${{\sigma }_}$$  increases, for a given  $$\bar{{T}'}$$.
 * For $${{\sigma }_}$$  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  $$0<\beta <1$$.