LOGSER

Overview

The LOGSER function computes values related to the Log-Series (Logarithmic) distribution, a discrete probability distribution describing the number of occurrences in a sequence of independent events, each with a fixed probability. This function supports probability mass function (PMF), cumulative distribution function (CDF), survival function (SF), inverse CDF (quantile/ICDF), inverse SF (ISF), mean, variance, standard deviation, and median for a given value.

Excel Comparison: Excel does not provide a native function for the Log-Series distribution. The Python LOGSER function enables direct calculation of PMF, CDF, quantiles, and statistics, which are not available in Excel. It also supports array inputs and robust error handling for Excel integration.

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

Usage

To use the function in Excel:


=LOGSER(k, p, [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 (k >= 1). For statistics modes, this is ignored and can be set to 1.
p (float, required): Probability parameter (0 < p < 1).
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=3, p=0.5

Inputs:

k	p	mode	loc
3	0.5	pmf	0

Excel formula:


=LOGSER(3, 0.5, "pmf", 0)

Expected output:

Result
0.0601

Example 2: CDF at k=3, p=0.5

Inputs:

k	p	mode	loc
3	0.5	cdf	0

Excel formula:


=LOGSER(3, 0.5, "cdf", 0)

Expected output:

Result
0.9618

Example 3: Survival Function at k=3, p=0.5

Inputs:

k	p	mode	loc
3	0.5	sf	0

Excel formula:


=LOGSER(3, 0.5, "sf", 0)

Expected output:

Result
0.0382

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

Inputs:

k	p	mode	loc
0.5	0.5	icdf	0

Excel formula:


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

Expected output:

Result
1

Example 5: Mean, Variance, Std, Median

Inputs:

k	p	mode
1	0.5	mean
1	0.5	var
1	0.5	std
1	0.5	median

Excel formulas:


=LOGSER(1, 0.5, "mean", 0)
=LOGSER(1, 0.5, "var", 0)
=LOGSER(1, 0.5, "std", 0)
=LOGSER(1, 0.5, "median", 0)

Expected outputs:

Result
1.4427
0.804
0.8967
1

Python Code


from scipy.stats import logser as scipy_logser
 
def logser(k, p, mode="pmf", loc=0):
    """
    Compute Log-Series distribution values: PMF, CDF, SF, ICDF, ISF, mean, variance, std, or median.
 
    Args:
        k: Value(s) at which to evaluate (float or 2D list).
        p: Probability parameter (float, 0 < p < 1).
        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 p
    try:
        p_val = float(p)
        if not (0 < p_val < 1):
            return "Invalid input: p must be between 0 (exclusive) and 1 (exclusive)."
    except Exception:
        return "Invalid input: p 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_logser.mean(p_val, loc=loc_val)
    if mode == "var":
        return scipy_logser.var(p_val, loc=loc_val)
    if mode == "std":
        return scipy_logser.std(p_val, loc=loc_val)
    if mode == "median":
        return scipy_logser.median(p_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_logser.pmf(kval, p_val, loc=loc_val))
        elif mode == "cdf":
            return float(scipy_logser.cdf(kval, p_val, loc=loc_val))
        elif mode == "sf":
            return float(scipy_logser.sf(kval, p_val, loc=loc_val))
        elif mode == "icdf":
            return float(scipy_logser.ppf(kval, p_val, loc=loc_val))
        elif mode == "isf":
            return float(scipy_logser.isf(kval, p_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)

Live Demo

Example Workbook

Link to Workbook