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 is 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  $$0<\beta <1$$.