WEIBULL_MIN

Overview

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

Excel provides the WEIBULL.DIST function, which can compute the PDF and CDF for the Weibull distribution. However, the Python function in Excel provided here supports additional features such as the inverse CDF (quantile), survival function, inverse survival function, and distribution statistics (mean, median, variance, standard deviation).

The Weibull minimum distribution is widely used in reliability engineering, survival analysis, and extreme value theory. The PDF is given by:

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

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

The shape parameter (c) controls the form of the distribution, while the location (loc) and scale (scale) parameters shift and stretch the distribution, respectively.

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:


=WEIBULL_MIN(value, c, [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
c (float, required): Shape parameter. Must be $> 0$ .
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	c	loc	scale	method
2	1.5	0	1	pdf

Excel formula:


=WEIBULL_MIN(2, 1.5, 0, 1, "pdf")

Expected output:

Result
0.125382

Example 2: CDF at x=2

Inputs:

value	c	loc	scale	method
2	1.5	0	1	cdf

Excel formula:


=WEIBULL_MIN(2, 1.5, 0, 1, "cdf")

Expected output:

Result
0.940894

Example 3: Inverse CDF (Quantile) at q=0.940894

Inputs:

value	c	loc	scale	method
0.940894	1.5	0	1	icdf

Excel formula:


=WEIBULL_MIN(0.940894, 1.5, 0, 1, "icdf")

Expected output:

Result
2.0

Example 4: Mean of the distribution

Inputs:

value	c	loc	scale	method
	1.5	0	1	mean

Excel formula:


=WEIBULL_MIN( , 1.5, 0, 1, "mean")

Expected output:

Result
0.902745

Python Code


from scipy.stats import weibull_min as scipy_weibull_min
import math
 
def weibull_min(value=None, c=1.0, loc=0.0, scale=1.0, method="pdf"):
    """
    Weibull minimum distribution function supporting multiple methods.
 
    Args:
        value: Input value (float), required for methods except 'mean', 'median', 'var', 'std'.
        c: Shape parameter (float, >0).
        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:
        c = float(c)
        loc = float(loc)
        scale = float(scale)
    except Exception:
        return "Invalid input: c, loc, and scale must be numbers."
    if c <= 0:
        return "Invalid input: c must be > 0."
    if scale <= 0:
        return "Invalid input: scale must be > 0."
    dist = scipy_weibull_min(c, 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.weibull_min 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.weibull_min 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 Notebook

Edit this function in a live notebook .

WEIBULL_MIN

Overview

Usage

Examples

Python Code

Live Notebook

Live Demo