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GEOM

Overview

The GEOM function computes values related to the Geometric distribution, a discrete probability distribution that describes the number of trials needed to get the first success in repeated, independent Bernoulli trials, each with the same probability of success. 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.geom documentation .

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

Usage

To use the function in Excel:

=GEOM(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 trial count (k >= 1). For statistics modes, this is ignored and can be set to 1.
  • p (float, required): Probability of success (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:

kpmodeloc
30.5pmf0

Excel formula:

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

Expected output:

Result
0.125

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

Inputs:

kpmodeloc
30.5cdf0

Excel formula:

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

Expected output:

Result
0.875

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

Inputs:

kpmodeloc
30.5sf0

Excel formula:

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

Expected output:

Result
0.125

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

Inputs:

kpmodeloc
0.50.5icdf0

Excel formula:

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

Expected output:

Result
1

Example 5: Mean, Variance, Std, Median

Inputs:

kpmodeloc
10.5mean0
10.5var0
10.5std0
10.5median0

Excel formulas:

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

Expected outputs:

Result
2
2
1.4142
1

Python Code

from scipy.stats import geom as scipy_geom
 
def geom(k, p, mode="pmf", loc=0):
    """
    Compute Geometric 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 of success (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 (inclusive)."
    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_geom.mean(p_val, loc=loc_val)
    if mode == "var":
        return scipy_geom.var(p_val, loc=loc_val)
    if mode == "std":
        return scipy_geom.std(p_val, loc=loc_val)
    if mode == "median":
        return scipy_geom.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_geom.pmf(kval, p_val, loc=loc_val))
        elif mode == "cdf":
            return float(scipy_geom.cdf(kval, p_val, loc=loc_val))
        elif mode == "sf":
            return float(scipy_geom.sf(kval, p_val, loc=loc_val))
        elif mode == "icdf":
            return float(scipy_geom.ppf(kval, p_val, loc=loc_val))
        elif mode == "isf":
            return float(scipy_geom.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 

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