EXPON

Overview

The EXPON function provides a unified interface to the main methods of the Exponential distribution, including PDF, CDF, inverse CDF, survival function, and distribution statistics.

Excel provides the EXPON.DIST function, which can compute the PDF and CDF for the exponential distribution. The Python function in Excel here also supports the inverse CDF (quantile), survival function, inverse survival, and distribution statistics (mean, median, variance, standard deviation), as well as location and scale parameters, which are not available in native Excel functions.

The Exponential distribution is commonly used to model the time between events in a Poisson process. The PDF is given by:

f(x, loc, scale) = \frac{1}{scale} \exp\left(-\frac{x - loc}{scale}\right)

for $x \geq loc$ , $scale > 0$ .

The Exponential distribution is a continuous probability distribution with a single scale parameter (sometimes parameterized by rate $\lambda = 1/scale$ ). It is a special case of the gamma distribution.

For more details, see the official SciPy documentation .

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

Usage

To use the function in Excel:


=EXPON(value, [loc], [scale], [method])

value (float, required for pdf, cdf, icdf, sf, isf):
- For pdf, cdf, sf: the value $x$ at which to evaluate the function (must be $\geq loc$ )
- For icdf, isf: the probability $q$ (must be between 0 and 1)
- For mean, median, var, std: skip parameter
loc (float, optional, default=0.0): Location parameter.
scale (float, optional, default=1.0): Scale parameter. Must be $> 0$ .
method (string, optional, default=“pdf”): One of pdf, cdf, icdf, sf, isf, mean, median, var, std.

Method	Description	Output
`pdf`	Probability Density Function: $f(x)$ , the likelihood of a specific value $x$ .	Density at $x$
`cdf`	Cumulative Distribution Function: $P(X \leq x)$ , the probability that $X$ is less than or equal to $x$ .	Probability
`icdf`	Inverse CDF (Quantile Function): Returns $x$ such that $P(X \leq x) = q$ for a given probability $q$ .	Value $x$
`sf`	Survival Function: $P(X > x)$ , the probability that $X$ is greater than $x$ .	Probability
`isf`	Inverse Survival Function: Returns $x$ such that $P(X > x) = q$ for a given probability $q$ .	Value $x$
`mean`	Mean (expected value) of the distribution.	Mean value
`median`	Median of the distribution.	Median value
`var`	Variance of the distribution.	Variance
`std`	Standard deviation of the distribution.	Standard deviation

The function returns a single value (float): the result of the requested method, or an error message (string) if the input is invalid.

Examples

Example 1: PDF at x=2

Inputs:

value	loc	scale	method
2	0	1	pdf

Excel formula:


=EXPON(2, 0, 1, "pdf")

Expected output:

Result
0.1353

Example 2: CDF at x=2

Inputs:

value	loc	scale	method
2	0	1	cdf

Excel formula:


=EXPON(2, 0, 1, "cdf")

Expected output:

Result
0.8647

Example 3: Inverse CDF (Quantile) at q=0.8647

Inputs:

value	loc	scale	method
0.8647	0	1	icdf

Excel formula:


=EXPON(0.8647, 0, 1, "icdf")

Expected output:

Result
2.0003

Example 4: Mean of the distribution

Inputs:

value	loc	scale	method
	0	1	mean

Excel formula:


=EXPON( , 0, 1, "mean")

Expected output:

Result
1.0

Python Code


from scipy.stats import expon as scipy_expon
import math
 
def expon(value=None, loc=0.0, scale=1.0, method="pdf"):
    """
    Exponential distribution function supporting multiple methods.
 
    Args:
        value: Input value (float), required for methods except 'mean', 'median', 'var', 'std'.
        loc: Location parameter (float, default: 0.0).
        scale: Scale parameter (float, default: 1.0, >0).
        method: Which method to compute (str): 'pdf', 'cdf', 'icdf', 'sf', 'isf', 'mean', 'median', 'var', 'std'. Default is 'pdf'.
 
    Returns:
        Result of the requested method (float or str), or an error message (str) if input is invalid.
 
    This example function is provided as-is without any representation of accuracy.
    """
    valid_methods = ['pdf', 'cdf', 'icdf', 'sf', 'isf', 'mean', 'median', 'var', 'std']
    if not isinstance(method, str) or method.lower() not in valid_methods:
        return f"Invalid method: {method}. Must be one of {valid_methods}."
    method = method.lower()
    try:
        loc = float(loc)
        scale = float(scale)
    except Exception:
        return "Invalid input: loc and scale must be numbers."
    if scale <= 0:
        return "Invalid input: scale must be > 0."
    dist = scipy_expon(loc, scale)
    # Methods that require value
    if method in ['pdf', 'cdf', 'icdf', 'sf', 'isf']:
        if value is None:
            return f"Invalid input: missing required argument 'value' for method '{method}'."
        try:
            value = float(value)
        except Exception:
            return "Invalid input: value must be a number."
        if method in ['pdf', 'cdf', 'sf'] and value < loc:
            return "Invalid input: value must be >= loc for this method."
        try:
            if method == 'pdf':
                result = dist.pdf(value)
            elif method == 'cdf':
                result = dist.cdf(value)
            elif method == 'sf':
                result = dist.sf(value)
            elif method == 'isf':
                if not (0 <= value <= 1):
                    return "Invalid input: value (probability) must be between 0 and 1 for isf."
                result = dist.isf(value)
            elif method == 'icdf':
                if not (0 <= value <= 1):
                    return "Invalid input: value (probability) must be between 0 and 1 for icdf."
                result = dist.ppf(value)
        except Exception as e:
            return f"scipy.stats.expon error: {e}"
        if isinstance(result, float):
            if math.isnan(result):
                return "Result is NaN (not a number)"
            if math.isinf(result):
                return "inf" if result > 0 else "-inf"
        return result
    # Methods that do not require value
    try:
        if method == 'mean':
            result = dist.mean()
        elif method == 'median':
            result = dist.median()
        elif method == 'var':
            result = dist.var()
        elif method == 'std':
            result = dist.std()
    except Exception as e:
        return f"scipy.stats.expon error: {e}"
    if isinstance(result, float):
        if math.isnan(result):
            return "Result is NaN (not a number)"
        if math.isinf(result):
            return "inf" if result > 0 else "-inf"
    return result

Live Demo

Example Workbook

Link to Workbook