"""
.. _plot_b17_lognormal_mixture:

17. Mixture with lognormal distribution
=======================================

Bayesian estimation of a mixture of logit models.
The mixing distribution is distributed as a log normal.

Michel Bierlaire, EPFL
Sat Nov 15 2025, 18:20:02
"""

from IPython.core.display_functions import display

import biogeme.biogeme_logging as blog
from biogeme.bayesian_estimation import (
    BayesianResults,
    get_pandas_estimated_parameters,
)
from biogeme.biogeme import BIOGEME
from biogeme.expressions import Beta, DistributedParameter, Draws, exp
from biogeme.models import loglogit
# %%
# See the data processing script: :ref:`swissmetro_data`.
from swissmetro_data import (
    CAR_AV_SP,
    CAR_CO_SCALED,
    CAR_TT_SCALED,
    CHOICE,
    SM_AV,
    SM_COST_SCALED,
    SM_TT_SCALED,
    TRAIN_AV_SP,
    TRAIN_COST_SCALED,
    TRAIN_TT_SCALED,
    database,
)

logger = blog.get_screen_logger(level=blog.INFO)
logger.info('Example b17_lognormal_mixture.py')

# %%
# The scale parameters must stay away from zero. We define a small but positive lower bound
POSITIVE_LOWER_BOUND = 1.0e-5
# %%
# Parameters to be estimated.
asc_car = Beta('asc_car', 0, None, None, 0)
asc_train = Beta('asc_train', 0, None, None, 0)
asc_sm = Beta('asc_sm', 0, None, None, 1)
b_cost = Beta('b_cost', 0, None, None, 0)

# %%
# Define a random parameter, normally distributed, designed to be used
# for Monte-Carlo simulation.
b_time_param = Beta('b_time', 0, None, None, 0)

# %%
# It is advised not to use 0 as starting value for the following parameter.
b_time_s = Beta('b_time_s', 1, POSITIVE_LOWER_BOUND, 2, 0)

# %%
# Define a random parameter, log normally distributed, designed to be used
# for Monte-Carlo simulation.
b_time_eps = Draws('b_time_eps', 'NORMAL')
b_time_rnd = DistributedParameter(
    'b_time_rnd', -exp(b_time_param + b_time_s * b_time_eps)
)

# %%
# Definition of the utility functions.
v_train = asc_train + b_time_rnd * TRAIN_TT_SCALED + b_cost * TRAIN_COST_SCALED
v_swissmetro = asc_sm + b_time_rnd * SM_TT_SCALED + b_cost * SM_COST_SCALED
v_car = asc_car + b_time_rnd * CAR_TT_SCALED + b_cost * CAR_CO_SCALED

# %%
# Associate utility functions with the numbering of alternatives.
v = {1: v_train, 2: v_swissmetro, 3: v_car}

# %%
# Associate the availability conditions with the alternatives.
av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP}

# %%
# Conditional to b_time_rnd, we have a logit model (called the kernel).
conditional_log_probability = loglogit(v, av, CHOICE)

# %%
# %%
# Create the Biogeme object.
the_biogeme = BIOGEME(database, conditional_log_probability)
the_biogeme.model_name = 'b17_lognormal_mixture'

# %%
# Estimate the parameters.
try:
    results = BayesianResults.from_netcdf(
        filename=f'saved_results/{the_biogeme.model_name}.nc'
    )
except FileNotFoundError:
    results = the_biogeme.bayesian_estimation()

print(results.short_summary())

# %%
pandas_results = get_pandas_estimated_parameters(estimation_results=results)
display(pandas_results)