NORM

Overview

The NORM function provides a unified interface to the main methods of the Normal (Gaussian) distribution, including PDF, CDF, inverse CDF, survival function, and distribution statistics.

Excel provides the NORM.DIST and NORM.INV functions, which can compute the PDF, CDF, and quantile (inverse CDF) for the normal distribution. The Python function in Excel here also supports the 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 Normal distribution is one of the most widely used probability distributions in statistics, natural sciences, and engineering. It is characterized by its bell-shaped curve and is defined by its mean (loc) and standard deviation (scale). The PDF is given by:

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

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

The Normal distribution is a continuous probability distribution that is symmetric about its mean. The parameters are:

loc: Mean of the distribution.
scale: Standard deviation (must be $> 0$ ).

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:


=NORM(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): Mean of the distribution.
scale (float, optional, default=1.0): Standard deviation. 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=0

Inputs:

value	loc	scale	method
0	0	1	pdf

Excel formula:


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

Expected output:

Result
0.398942

Example 2: CDF at x=1

Inputs:

value	loc	scale	method
1	0	1	cdf

Excel formula:


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

Expected output:

Result
0.841345

Example 3: Inverse CDF (Quantile) at q=0.841345

Inputs:

value	loc	scale	method
0.841345	0	1	icdf

Excel formula:


=NORM(0.841345, 0, 1, "icdf")

Expected output:

Result
1.000001

Example 4: Mean of the distribution

Inputs:

value	loc	scale	method
	0	1	mean

Excel formula:


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

Expected output:

Result
0.0

Python Code


from scipy.stats import norm as scipy_norm
import math
 
def norm(value=None, loc=0.0, scale=1.0, method="pdf"):
    """
    Normal (Gaussian) distribution function supporting multiple methods.
 
    Args:
        value: Input value (float), required for methods except 'mean', 'median', 'var', 'std'.
        loc: Mean (float, default: 0.0).
        scale: Standard deviation (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_norm(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.norm 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.norm 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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NORM

Overview

Usage

Examples

Python Code

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