Probability distributions
This page summarizes the distributions available in Mlxtran. They can be used to define random variables in the [LONGITUDINAL] section (observations). They are also used by Monolix to automatically define random variables in the [INDIVIDUAL] section (individual parameters) within the .mlxtran Monolix project.
Normal distribution and the associated transformed
To define the normal distribution and its transformations, Monolix uses the typical
value of the distribution; as well as the standard deviation sd
of the associated normal distribution. For the logitnormal distribution, the min
and max
can also be specified (optional). Covariates and correlations between random effects are also automatically added in the [INDIVIDUAL] section.
Normal distribution, used with keyword
normal
:CODEy_norm = {distribution=normal, typical=0, sd=1} y_norm = {distribution=normal, mean=0, sd=1}
Log-normal distribution, used with keyword
lognormal
:CODEy_ln = {distribution=lognormal, typical=1, sd=0.3} y_ln = {distribution=lognormal, mean=0, sd=0.3}
Logit-normal distribution, used with keyword
logitnormal
:with a and b the bounds of the logit-normal distribution indicated in the optional arguments
min
andmax
. By default, a=0 and b=1.CODEy_lgn = {distribution=logitnormal, typical=0.5, sd=0.6, min=0, max=1} y_lgn = {distribution=logitnormal, mean=0, sd=0.6, min=0, max=1}
Probit-normal distribution, used with keyword
probitnormal
:, where
is the cumulative distribution function of the standard normal distribution
CODEy_pbn = {distribution=probitnormal, typical=0.5, sd=0.6} y_pbn = {distribution=probitnormal, mean=0, sd=0.6}