JARQUE_BERA

Overview

The JARQUE_BERA function performs the Jarque-Bera goodness of fit test for normality. This test evaluates whether the sample data has skewness and kurtosis matching a normal distribution. It is commonly used in statistics and econometrics to assess the normality of residuals or data samples. The test statistic is calculated as:

JB = \frac{n}{6} \left( S^2 + \frac{(K-3)^2}{4} \right)

where $n$ is the sample size, $S$ is the sample skewness, and $K$ is the sample kurtosis. The p-value is computed based on the chi-squared distribution with 2 degrees of freedom. For more details, see the scipy.stats.jarque_bera documentation .

This example function is provided as-is without any representation of accuracy.

Usage

To use the function in Excel:


=JARQUE_BERA(x)

x (2D list, required): Sample data. Must contain at least two elements. Ideally, use more than 2000 elements for the test to be valid.

The function returns a 1-row, 2-column array: the test statistic and the p-value. If the input is invalid, an error message is returned as a string.

Examples

Example 1: Normal Data

Inputs:

x
0.1
-0.2
0.3
0.0
0.2
-0.1

Excel formula:


=JARQUE_BERA({0.1;-0.2;0.3;0.0;0.2;-0.1})

Expected output:

Statistic	P-value
0.40231836734693943	0.8177822436106005

Example 2: Skewed Data

Inputs:

x
1.0
2.0
3.0
4.0
5.0
6.0

Excel formula:


=JARQUE_BERA({1;2;3;4;5;6})

Expected output:

Statistic	P-value
0.40231836734693854	0.8177822436106008

Example 3: Small Sample

Inputs:

x
2.5
2.7
2.9
3.1
3.3
3.5

Excel formula:


=JARQUE_BERA({2.5;2.7;2.9;3.1;3.3;3.5})

Expected output:

Statistic	P-value
0.40231836734693843	0.8177822436106009

Example 4: Data with Outlier

Inputs:

x
0.0
0.1
0.2
0.3
0.4
5.0

Excel formula:


=JARQUE_BERA({0;0.1;0.2;0.3;0.4;5})

Expected output:

Statistic	P-value
3.463994184620268	0.17693070994138124

This means the function returns the test statistic and p-value for the Jarque-Bera test for each input sample.

Python Code


from scipy.stats import jarque_bera as scipy_jarque_bera
 
def jarque_bera(x):
    """
    Perform the Jarque-Bera goodness of fit test for normality.
 
    Args:
        x: 2D list. Sample data (ideally >2000 elements).
 
    Returns:
        2D list. Test statistic and p-value, or an error message (str) if input is invalid.
 
    This example function is provided as-is without any representation of accuracy.
    """
    # Validate input
    if not isinstance(x, list) or len(x) < 2:
        return "Invalid input: x must be a 2D list with at least two elements."
    # Flatten 2D list to 1D
    try:
        flat = []
        for row in x:
            if isinstance(row, list):
                flat.extend(row)
            else:
                flat.append(row)
        data = [float(val) for val in flat]
    except Exception:
        return "Invalid input: x must contain only numeric values."
    if len(data) < 2:
        return "Invalid input: x must contain at least two numeric values."
    try:
        res = scipy_jarque_bera(data)
        # Try to access statistic and pvalue attributes if present
        if hasattr(res, 'statistic') and hasattr(res, 'pvalue'):
            stat = float(res.statistic)
            pval = float(res.pvalue)
        elif isinstance(res, (tuple, list)) and len(res) == 2:
            stat, pval = float(res[0]), float(res[1])
        else:
            return f"scipy.stats.jarque_bera unexpected result: {res}"
        # Disallow nan/inf
        if any([s is None or isinstance(s, str) or s != s or s == float('inf') or s == float('-inf') for s in [stat, pval]]):
            return [["error", "error"]]
        return [[stat, pval]]
    except Exception as e:
        return f"scipy.stats.jarque_bera error: {e}"

Example Workbook

Link to Workbook