LAPLACE

Overview

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

There are no similar native Excel functions for the Laplace distribution. The Python function in Excel here provides full support for the Laplace distribution, including PDF, CDF, quantile, survival, and distribution statistics.

The Laplace distribution, also known as the double exponential distribution, is used in various fields such as signal processing and finance. The PDF is given by:

f(x, loc, scale) = \frac{1}{2 \cdot scale} \exp\left(-\frac{|x - loc|}{scale}\right)

for $-\infty < x < \infty$ , $scale > 0$ .

The Laplace distribution is characterized by its location (loc) and scale (scale) parameters. The location parameter shifts the distribution, while the scale parameter stretches or compresses it.

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:


=LAPLACE(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
- 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=1

Inputs:

value	loc	scale	method
1	0	1	pdf

Excel formula:


=LAPLACE(1, 0, 1, "pdf")

Expected output:

Result
0.18394

Example 2: CDF at x=1

Inputs:

value	loc	scale	method
1	0	1	cdf

Excel formula:


=LAPLACE(1, 0, 1, "cdf")

Expected output:

Result
0.81606

Example 3: Inverse CDF (Quantile) at q=0.81606

Inputs:

value	loc	scale	method
0.81606	0	1	icdf

Excel formula:


=LAPLACE(0.81606, 0, 1, "icdf")

Expected output:

Result
1.0

Example 4: Mean of the distribution

Inputs:

value	loc	scale	method
	0	1	mean

Excel formula:


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

Expected output:

Result
0.0

Python Code


from scipy.stats import laplace as scipy_laplace
import math
 
def laplace(value=None, loc=0.0, scale=1.0, method="pdf"):
    """
    Laplace 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_laplace(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."
        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.laplace 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.laplace 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

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LAPLACE

Overview

Usage

Examples

Python Code

Live Notebook

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