KURTOSIS

Overview

The KURTOSIS function computes the kurtosis (Fisher or Pearson) of a dataset. Kurtosis is a measure of the “tailedness” of the probability distribution of a real-valued random variable. This function flattens the input, ignores non-numeric values, and always omits NaN values (nan_policy is set to ‘omit’). Excel’s KURT function computes excess kurtosis (Fisher); this function allows both Fisher and Pearson forms. For more details, see the scipy.stats.kurtosis documentation .

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

Usage

To use the function in Excel:


=KURTOSIS(data, [fisher], [bias])

data (2D list, required): Data to compute kurtosis for. Must have at least two numeric elements after flattening.
fisher (bool, optional, default=True): If True, Fisher’s definition is used (normal ==> 0.0). If False, Pearson’s definition is used (normal ==> 3.0).
bias (bool, optional, default=True): If False, then the calculations are corrected for statistical bias.

The function returns a single value (float): the kurtosis of the data, or an error message (string) if the input is invalid. NaN values are always omitted.

Examples

Example 1: Fisher, bias=True

Inputs:

data				fisher	bias
1	2	3	4	TRUE	TRUE

Excel formula:


=KURTOSIS({1;2;3;4}, TRUE, TRUE)

Expected output:

Result
-1.36

Example 2: Pearson, bias=True Inputs:

data				fisher	bias
1	2	3	4	FALSE	TRUE

Excel formula:


=KURTOSIS({1;2;3;4}, FALSE, TRUE)

Expected output:

Result
1.64

Example 3: Fisher, bias=False Inputs:

data				fisher	bias
1	2	3	4	TRUE	FALSE

Excel formula:


=KURTOSIS({1;2;3;4}, TRUE, FALSE)

Expected output:

Result
-1.2

Example 4: Pearson, bias=False Inputs:

data				fisher	bias
1	2	3	4	FALSE	FALSE

Excel formula:


=KURTOSIS({1;2;3;4}, FALSE, FALSE)

Expected output:

Result
1.8

Python Code


 
from scipy.stats import kurtosis as scipy_kurtosis
 
def kurtosis(data, fisher=True, bias=True):
    """
    Computes the kurtosis (Fisher or Pearson) of a dataset.
    Flattens the input, ignores non-numeric values, and always omits NaN values (nan_policy is set to 'omit').
    This example function is provided as-is without any representation of accuracy.
    """
    # Flatten and filter numeric values
    try:
        flat = [float(x) for row in data for x in (row if isinstance(row, list) else [row]) if isinstance(x, (int, float, type(None))) and x is not None]
    except Exception:
        return "Two or more data elements are needed"
    if len(flat) < 2:
        return "Two or more data elements are needed"
    try:
        result = scipy_kurtosis(flat, fisher=fisher, bias=bias, nan_policy='omit')
        return round(float(result), 2)
    except Exception:
        return "Error computing kurtosis"

Live Demo

Example Workbook

Link to Workbook