# 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`

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

Log-normal distribution, used with keyword

`lognormal`

:CODE`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.CODE`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 distributionCODE`y_pbn = {distribution=probitnormal, typical=0.5, sd=0.6} y_pbn = {distribution=probitnormal, mean=0, sd=0.6}`