MULTIVARIATE_HYPERGEOM

=MULTIVARIATE_HYPERGEOM(x, m, n, [method], [size])

=MULTIVARIATE_HYPERGEOM({3,2,1}, {10,8,6}, {6})

=MULTIVARIATE_HYPERGEOM({3,2,1}, {10,8,6}, {6}, "logpmf")

=MULTIVARIATE_HYPERGEOM(, {10,8,6}, {6}, "mean")

=MULTIVARIATE_HYPERGEOM(, {10,8,6}, {6}, "cov")

from scipy.stats import multivariate_hypergeom as scipy_multivariate_hypergeom
from typing import List, Optional, Union
 
def multivariate_hypergeom(
    x: Optional[List[List[int]]] = None,
    m: Optional[List[List[int]]] = None,
    n: Optional[List[int]] = None,
    method: str = 'pmf',
    size: Optional[int] = None
) -> Union[List[List[Optional[float]]], str]:
    """
    Computes probability mass function, log-PMF, mean, variance, covariance, or draws random samples from a multivariate hypergeometric distribution.
 
    Args:
        x: 2D list of int values. Number of objects of each type drawn from the population. Required for 'pmf' and 'logpmf'.
        m: 2D list of int values. Number of objects of each type in the population.
        n: List of int values. Number of samples drawn from the population.
        method: Which method to compute (str): 'pmf', 'logpmf', 'mean', 'var', 'cov', 'rvs'. Default is 'pmf'.
        size: Number of samples to draw if method is 'rvs'. Optional.
 
    Returns:
        2D list of results for each input, or an error message (str) if input is invalid.
 
    This example function is provided as-is without any representation of accuracy.
    """
    # Validate method
    valid_methods = {'pmf', 'logpmf', 'mean', 'var', 'cov', 'rvs'}
    if method not in valid_methods:
        return f"Invalid method: {method}. Must be one of {sorted(valid_methods)}."
 
    # Validate m
    if not isinstance(m, list) or not all(isinstance(row, list) and all(isinstance(val, int) for val in row) for row in m):
        return "Invalid input: m must be a 2D list of integers."
    if len(m) != 1:
        return "Invalid input: m must be a 2D list with exactly one row (Excel passes population as [[...]])."
    if len(m[0]) < 2:
        return "Invalid input: m must be a 2D list with at least two columns."
 
    # Validate n
    if not isinstance(n, list) or not all(isinstance(val, int) for val in n):
        return "Invalid input: n must be a list of integers."
    if len(n) != 1:
        return "Invalid input: n must be a list with exactly one element (Excel passes sample size as [n])."
 
    # Validate x for pmf/logpmf
    if method in {'pmf', 'logpmf'}:
        if not isinstance(x, list) or not all(isinstance(row, list) and all(isinstance(val, int) for val in row) for row in x):
            return "Invalid input: x must be a 2D list of integers for pmf/logpmf."
        if len(x) != 1:
            return "Invalid input: x must be a 2D list with exactly one row."
        if len(x[0]) != len(m[0]):
            return "Invalid input: x must have the same number of columns as m."
 
    # Validate size for rvs
    if method == 'rvs' and size is not None:
        if not isinstance(size, int) or size < 1:
            return "Invalid input: size must be a positive integer."
 
    # Try to create the distribution
    try:
        m_arr = m[0]
        n_val = n[0]
        dist = scipy_multivariate_hypergeom(m_arr, n_val)
    except Exception as e:
        return f"scipy.multivariate_hypergeom error: {e}"
 
    # Compute result
    try:
        if method == 'pmf':
            result = dist.pmf(x[0])
            return [[float(result)]]
        elif method == 'logpmf':
            result = dist.logpmf(x[0])
            return [[float(result)]]
        elif method == 'mean':
            result = dist.mean()
            return [list(map(float, result))]
        elif method == 'var':
            result = dist.var()
            return [list(map(float, result))]
        elif method == 'cov':
            cov = dist.cov()
            # cov is a 2D numpy array
            return [list(map(float, row)) for row in cov.tolist()]
        elif method == 'rvs':
            if size is not None:
                samples = dist.rvs(size=size)
                # samples: shape (size, k)
                if hasattr(samples, 'tolist'):
                    samples = samples.tolist()
                return [list(map(int, row)) for row in samples]
            else:
                sample = dist.rvs()
                if hasattr(sample, 'tolist'):
                    sample = sample.tolist()
                return [list(map(int, sample))]
    except Exception as e:
        return f"scipy.multivariate_hypergeom error: {e}"
    return "Unknown error."