JointNormalDistribution

class pharmpy.model.JointNormalDistribution(names, level, mean, variance)

Bases: Distribution

Joint distribution of random variables

Parameters:

• names (list) – Names of the random variables

• level (str) – Variability level

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

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

Example

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

Attributes Summary

free_symbols	Free symbols including random variable itself
level	Name of VariabilityLevel of the random variables
mean
names	Names of random variables of distribution
variance

Methods Summary

create(names, level, mean, variance)
evalf(parameters)
from_dict(d)
get_covariance(name1, name2)
get_variance(name)
latex_string([aligned])
replace(**kwargs)	Replace properties and create a new JointNormalDistribution
subs(d)	Substitute expressions
to_dict()

Attributes Documentation

free_symbols

Free symbols including random variable itself

level

mean

names

variance

Methods Documentation

classmethod create(names, level, mean, variance)

evalf(parameters)

classmethod from_dict(d)

get_covariance(name1, name2)

get_variance(name)

latex_string(aligned=False)

replace(**kwargs)

Replace properties and create a new JointNormalDistribution

subs(d)

Substitute expressions

Parameters:

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

Examples

>>> import sympy
>>> from pharmpy.model import JointNormalDistribution, Parameter
>>> omega1 = Parameter("OMEGA_CL", 0.1)
>>> omega2 = Parameter("OMEGA_V", 0.1)
>>> A = [[omega1.symbol, 0], [0, omega2.symbol]]
>>> dist = JointNormalDistribution.create(["IIV_CL", "IIV_V"], "IIV", [0, 0], A)
>>> dist = dist.subs({omega1.symbol: sympy.Symbol("OMEGA_NEW")})
>>> dist
        ⎡IIV_CL⎤    ⎧⎡0⎤  ⎡OMEGA_NEW     0   ⎤⎫
        ⎢      ⎥ ~ N⎪⎢ ⎥, ⎢                  ⎥⎪
        ⎣IIV_V ⎦    ⎩⎣0⎦  ⎣    0      OMEGA_V⎦⎭

to_dict()