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.
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.
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.