In the probabilistic approach, each AF is replaced by a lognormal distribution
based on empirical observations to identify, median, standard deviation, and percentiles.
As before, the lognormal distribution
for a had a median of 1, an expectation of 1.13, and a standard deviation of 0.6.
We also conducted additional simulations where the survival times were derived from a lognormal distribution
. The estimates of power under alternative configurations of [[mu].sub.k] are given in Table 4.
 used the lognormal distribution
to calibrate fragility curves in 2000.
In this article, we assume that severity is modeled by lognormal distribution
while frequency is modeled by Poisson distribution.
6 shows the generated random numbers and discretization process when the failure model follows Poisson distribution with parameter [lambda]=4, and the restoration model follows a Lognormal distribution
with parameters p=1, [delta]=0.2.
For example, the right tail of the '5pt base' distribution is much longer in Figure 8 than in Figures 5, 6, 7, while the accumulation of probability at 1 for the '3pt_base' condition in Figure 8 is due to simulations from the longer right tail of the lognormal distribution
This holds true for Fisk distribution regarding log- likelihood, BIC and chi-square criteria while lognormal distribution
is showing slight improvement on the basis of SAE and SSE criteria.
It is estimated , that IRW has the form of lognormal distribution
with parameters depending on the age of the person consuming water.
Other reasons for utilizing the lognormal distribution
are that it is strictly positive, it can approximate sums of positive random variables, it can represent the relationship between capacity and activity time, and it can represent the ratio between actual and estimated activity time .
Neither the normal, lognormal, Weibull, nor gamma distributions provided good fits for the micronized copper group (Anderson-Darling P values < 0.01), although based on the lowest [AIC.sub.c], the lognormal distribution
appeared to better describe the distribution.