RandomVariable

class pharmpy.model.RandomVariable(name, level, sympy_rv=None)

Bases: object

A single random variable

Parameters:

• name (str) – Name of the random variable

• level (str) – Name of the variability level. The default levels are IIV, IOV and RUV

• sympy_rv (sympy.RandomSymbol) – RandomSymbol to use for this random variable. See also the normal and joint_normal classmethods.

Examples

>>> import sympy
>>> import sympy.stats
>>> from pharmpy.model import RandomVariable
>>> name = "ETA(1)"
>>> sd = sympy.sqrt(sympy.Symbol('OMEGA(1,1)'))
>>> rv = RandomVariable(name, "IIV", sympy.stats.Normal(name, 0, sd))
>>> rv
ETA(1) ~ N(0, OMEGA(1,1))

See also

normal, joint_normal

Attributes Summary

free_symbols	Free symbols including random variable itself
joint_names	Names of all (including this) jointly varying rvs in a list
level
name	Name of the random variable
parameter_names	List of names of all parameters used in definition
sympy_rv	Corresponding sympy random variable

Methods Summary

copy()	Make copy of RandomVariable
joint_normal(names, level, mu, sigma)	Create joint normally distributed random variables
normal(name, level, mean, variance)	Create a normally distributed random variable
subs(d)	Substitute expressions

Attributes Documentation

free_symbols

Free symbols including random variable itself

joint_names

Names of all (including this) jointly varying rvs in a list

level

name

Name of the random variable

parameter_names

List of names of all parameters used in definition

sympy_rv

Corresponding sympy random variable

Methods Documentation

copy()

Make copy of RandomVariable

classmethod joint_normal(names, level, mu, sigma)

Create joint normally distributed random variables

Parameters:

• names (list) – Names of the random variables

• level (str) – Variability level

• mu (matrix or list) – Vector of the means of the random variables

• sigma (matrix or list of lists) – Covariance matrix of the random variables

Example

>>> from pharmpy.model import RandomVariable, Parameter
>>> omega_cl = Parameter("OMEGA_CL", 0.1)
>>> omega_v = Parameter("OMEGA_V", 0.1)
>>> corr_cl_v = Parameter("OMEGA_CL_V", 0.01)
>>> rv1, rv2 = RandomVariable.joint_normal(["IIV_CL", "IIV_V"], 'IIV', [0, 0],
...     [[omega_cl.symbol, corr_cl_v.symbol], [corr_cl_v.symbol, omega_v.symbol]])
>>> rv1
⎡IIV_CL⎤    ⎧⎡0⎤  ⎡ OMEGA_CL   OMEGA_CL_V⎤⎫
⎢      ⎥ ~ N⎪⎢ ⎥, ⎢                      ⎥⎪
⎣IIV_V ⎦    ⎩⎣0⎦  ⎣OMEGA_CL_V   OMEGA_V  ⎦⎭

classmethod normal(name, level, mean, variance)

Create a normally distributed random variable

Parameters:

• name (str) – Name of the random variable

• level (str) – Name of the variability level

• mean (expression or number) – Mean of the random variable

• variance (expression or number) – Variance of the random variable

Example

>>> from pharmpy.model import RandomVariable, Parameter
>>> omega = Parameter('OMEGA_CL', 0.1)
>>> rv = RandomVariable.normal("IIV_CL", "IIV", 0, omega.symbol)
>>> rv
IIV_CL ~ N(0, OMEGA_CL)

subs(d)

Substitute expressions

Parameters:

d (dict) – Dictionary of from: to pairs for substitution

Examples

>>> import sympy
>>> from pharmpy.model import RandomVariable, Parameter
>>> omega = Parameter("OMEGA_CL", 0.1)
>>> rv = RandomVariable.normal("IIV_CL", "IIV", 0, omega.symbol)
>>> rv.subs({omega.symbol: sympy.Symbol("OMEGA_NEW")})
>>> rv
IIV_CL ~ N(0, OMEGA_NEW)