Following the same reasoning through a probabilistic approach would have led to 3 lognormal distributions
for the [AF.sub.A], [AF.sub.H] and [AF.sub.S], with percentiles ranges of 1([P.sub.0.05])-3([P.sub.0.95]), 1([P.sub.0.05])-10([P.sub.0.95]), and 1([P.sub.0.05])-3([P.sub.0.95]), respectively.
We then developed an automated workflow with standardized decision rules for assigning conceptual models and magnitudes of effect, default uncertainty distributions based largely on the WHO/ IPCS (2014) review, and a simplified calculation approach using lognormal distributions
that has been validated for accuracy.
 compared different regression mixture models including the model whose all components are Gaussian distributions and the model with mixture of Gaussian and lognormal distributions
to estimate urban arterial travel time.
In this study, both initial background particles and sources take lognormal distributions
, and the background particle size distribution is characterized by its GMD of 500 nm, TPN of 4.34 x [10.sup.1]0 #/[m.sup.3], and GSD of 1.32.
In this paper, we used the generalized p values, proposed by Tsui and Weerahandi  and Weerahandi , to find new generalized p values for testing: (1) one population variance, (2) the difference between two population variances, and (3) the ratio of population variances of lognormal distributions
when coefficients of variation are known.
In this study, the best fit for the distribution of frame sizes was lognormal distribution
among gamma, Weibull, and lognormal distributions
For instance, using a simulation study, Shevchenko (2010) shows that for light-tail lognormal severity distributions, the shifting approach might induce significant bias in comparison to the truncation approach, but this bias becomes insignificant for heavy-tail lognormal distributions
. Meanwhile, simulation studies performed by Cavallo et al.
Then, we obtained statistical simulations of time-dependent responses with normal and lognormal distributions
, which were subsequently summarized in order to obtain the statistical distribution of the injury risk.
The result from a Matlab programming shows a lower failure probability value 0.016 for the present condition and 0.0251-0.032 for the future condition when using lognormal distributions
. Even by using a Monte Carlo simulation, the result is still lower than the original case having normal distribution random variables.
The new fifth edition features new problems, updated applications, and new material on Pareto and lognormal distributions
, prediction intervals, dummy variables in multiple regression models, and equality of population distributions.
The best-fit distribution for electric gains was normal, while occupancy more closely resembled lognormal distributions
. The means and scaling factors for each distribution are also shown in Table 2.
Model Ms- Assuming non-informative lognormal distributions
as a prior for all the parameters: M, b, c ~ lognormal (m, 106), with p mean estimated by the frequentist method.