estimation_mixture.py

import pandas as pd
import numpy as np

from scipy.optimize import minimize
from numpy.linalg import LinAlgError
from pycop import estimation, mixture, archimedean


def estim_mixture(data, opti_method, options={}):
    """
    Estimate the best-fitting three-component copula model for the given data.

    This function iterates over various combinations of copula families for a 
    three-component copula model and estimates the best-fitting model based on 
    the minimum IAD distance.

    Args:
        data (array-like): The input data for which to estimate the copula model.

    Returns:
        tuple: A tuple containing the following elements:
            - ctype (str): The best-fitting copula type as a string in the format "fam1-fam2-fam3".

    list of errors: When `allow_singular is False`, the input matrix must be symmetric positive definite
    """
    results = []
    for fam1 in ["clayton", "rgumbel", "rjoe", "rgalambos"]:
        for fam2 in ["gaussian", "frank", "fgm", "plackett"]: # 
            for fam3 in ["gumbel", "rclayton", "joe", "galambos" ]:
                coptype = f"{fam1}-{fam2}-{fam3}"
                cop = mixture([fam1, fam2, fam3])
                try:
                    param, cmle = estimation.fit_cmle_mixt(cop, data, opti_method, options=options)
                    iad_dist = estimation.IAD_dist(cop, data, param)
                    line = {"coptype": coptype, "param": param, "iad_dist": iad_dist}
                    LTC_cop = archimedean(family= coptype.split("-")[0]).LTDC(param[3])
                    LTDC = LTC_cop*param[0]
                    #print("cop:", coptype.split("-")[0], ", param:", param[3], ", LTDC:", LTDC)
                    results.append(line)
        
                except (LinAlgError, TypeError) as e:
                    #print(e)
                    continue
                
    # Find the best result based on the minimum IAD distance
    # Convert the list to a DataFrame
    df = pd.DataFrame(results)

    # Find the row with the minimum 'iad_dist'
    min_row = df.loc[df['iad_dist'].idxmin()]

    # Extract 'coptype' and 'param' values
    ctype, param = min_row['coptype'], min_row['param']

    return ctype, param