PLANCK

Overview

The PLANCK function computes values related to the Planck discrete exponential distribution, which describes the probability of a non-negative integer outcome with exponential decay. This function can return the probability mass function (PMF), cumulative distribution function (CDF), survival function (SF), inverse CDF (quantile/ICDF), inverse SF (ISF), mean, variance, standard deviation, or median for a given value.

For more details, see the scipy.stats.planck documentation .

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

Usage

To use the function in Excel:


=PLANCK(k, lambda, [mode], [loc])

k (float or 2D list, required): Value(s) at which to evaluate the distribution. For PMF, CDF, SF, ICDF, and ISF, this is the event count. For statistics modes, this is ignored and can be set to 0.
lambda (float, required): Shape parameter (>0).
mode (str, optional, default=“pmf”): Output type. One of "pmf", "cdf", "sf", "icdf", "isf", "mean", "var", "std", or "median".
loc (float, optional, default=0): Location parameter (shifts the distribution).

The function returns a scalar or 2D list of floats (for array input), or an error message (string) if the input is invalid. The output depends on the selected mode:

pmf: Probability mass function at k.
cdf: Cumulative distribution function at k.
sf: Survival function (1 - CDF) at k.
icdf: Inverse CDF (quantile) for probability k.
isf: Inverse survival function for probability k.
mean: Mean of the distribution.
var: Variance of the distribution.
std: Standard deviation of the distribution.
median: Median of the distribution.

Examples

Example 1: PMF at k=2, lambda=0.5

Inputs:

k	lambda	mode	loc
2	0.5	pmf	0

Excel formula:


=PLANCK(2, 0.5, "pmf", 0)

Expected output:

Result
0.1455

Example 2: CDF at k=2, lambda=0.5

Inputs:

k	lambda	mode	loc
2	0.5	cdf	0

Excel formula:


=PLANCK(2, 0.5, "cdf", 0)

Expected output:

Result
0.7769

Example 3: Survival Function at k=2, lambda=0.5

Inputs:

k	lambda	mode	loc
2	0.5	sf	0

Excel formula:


=PLANCK(2, 0.5, "sf", 0)

Expected output:

Result
0.2231

Example 4: Inverse CDF (ICDF) for probability k=0.5, lambda=0.5

Inputs:

k	lambda	mode	loc
0.5	0.5	icdf	0

Excel formula:


=PLANCK(0.5, 0.5, "icdf", 0)

Expected output:

Result
1

Example 5: Mean, Variance, Std, Median

Inputs:

k	lambda	mode	loc
0	0.5	mean	0
0	0.5	var	0
0	0.5	std	0
0	0.5	median	0

Excel formulas:


=PLANCK(0, 0.5, "mean", 0)
=PLANCK(0, 0.5, "var", 0)
=PLANCK(0, 0.5, "std", 0)
=PLANCK(0, 0.5, "median", 0)

Expected outputs:

Result
1.5415
3.9177
1.9793
1

Python Code


from scipy.stats import planck as scipy_planck
 
def planck(k, lambda_, mode="pmf", loc=0):
    """
    Compute Planck distribution values: PMF, CDF, SF, ICDF, ISF, mean, variance, std, or median.
 
    Args:
        k: Value(s) at which to evaluate (float or 2D list).
        lambda_: Shape parameter (float, >0).
        mode: Output type: 'pmf', 'cdf', 'sf', 'icdf', 'isf', 'mean', 'var', 'std', or 'median'.
        loc: Location parameter (float, default 0).
 
    Returns:
        Scalar or 2D list of floats, or error message (str) if invalid.
    """
    # Validate lambda_
    try:
        lam_val = float(lambda_)
        if lam_val <= 0:
            return "Invalid input: lambda must be > 0."
    except Exception:
        return "Invalid input: lambda must be a number."
    # Validate loc
    try:
        loc_val = float(loc)
    except Exception:
        return "Invalid input: loc must be a number."
    # Validate mode
    valid_modes = ["pmf", "cdf", "sf", "icdf", "isf", "mean", "var", "std", "median"]
    if not isinstance(mode, str) or mode not in valid_modes:
        return f"Invalid input: mode must be one of {valid_modes}."
    # Helper to process k (scalar or 2D list)
    def process_k(val):
        try:
            return float(val)
        except Exception:
            return None
    # Handle statistics
    if mode == "mean":
        return scipy_planck.mean(lam_val, loc=loc_val)
    if mode == "var":
        return scipy_planck.var(lam_val, loc=loc_val)
    if mode == "std":
        return scipy_planck.std(lam_val, loc=loc_val)
    if mode == "median":
        return scipy_planck.median(lam_val, loc=loc_val)
    # PMF, CDF, SF, ICDF, ISF
    def compute(val):
        kval = process_k(val)
        if kval is None:
            return "Invalid input: k must be a number."
        if mode == "pmf":
            return float(scipy_planck.pmf(kval, lam_val, loc=loc_val))
        elif mode == "cdf":
            return float(scipy_planck.cdf(kval, lam_val, loc=loc_val))
        elif mode == "sf":
            return float(scipy_planck.sf(kval, lam_val, loc=loc_val))
        elif mode == "icdf":
            return float(scipy_planck.ppf(kval, lam_val, loc=loc_val))
        elif mode == "isf":
            return float(scipy_planck.isf(kval, lam_val, loc=loc_val))
    # 2D list or scalar
    if isinstance(k, list):
        # 2D list
        if not all(isinstance(row, list) for row in k):
            return "Invalid input: k must be a scalar or 2D list."
        result = []
        for row in k:
            result_row = []
            for val in row:
                out = compute(val)
                if isinstance(out, str):
                    return out
                result_row.append(out)
            result.append(result_row)
        return result
    else:
        return compute(k)

Example Workbook

Link to Workbook