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: 

  y_norm = {distribution=normal, typical=0, sd=1}
  y_norm = {distribution=normal, mean=0, sd=1}
  

• Log-normal distribution, used with keyword lognormal:

  y_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 and max. By default, a=0 and b=1.

  y_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

  y_pbn = {distribution=probitnormal, typical=0.5, sd=0.6} 
  y_pbn = {distribution=probitnormal, mean=0, sd=0.6}