F_DIST

Overview

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

Excel provides the F.DIST and F.INV functions, which can compute the PDF, CDF, and quantile (inverse CDF) for the F-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 F-distribution is commonly used in statistics, especially in the analysis of variance (ANOVA), to compare variances between two populations. The PDF is given by:

f(x, df_1, df_2) = \frac{df_2^{df_2/2} \; df_1^{df_1/2} \; x^{df_1/2-1}}{(df_2 + df_1 x)^{(df_1+df_2)/2} \; B(df_1/2, df_2/2)}

for $x > 0$ , $df_1 > 0$ , $df_2 > 0$ .

The F-distribution is a continuous probability distribution that arises frequently as the null distribution of a test statistic, especially in ANOVA. The parameters df_1 and df_2 are the degrees of freedom for the numerator and denominator, 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:


=F_DIST(value, dfn, dfd, [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 $> 0$ )
- For icdf, isf: the probability $q$ (must be between 0 and 1)
- For mean, median, var, std: skip parameter
dfn (float, required): Numerator degrees of freedom. Must be $> 0$ .
dfd (float, required): Denominator degrees of freedom. 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	dfn	dfd	loc	scale	method
2	5	10	0	1	pdf

Excel formula:


=F_DIST(2, 5, 10, 0, 1, "pdf")

Expected output:

Result
0.162006

Example 2: CDF at x=2

Inputs:

value	dfn	dfd	loc	scale	method
2	5	10	0	1	cdf

Excel formula:


=F_DIST(2, 5, 10, 0, 1, "cdf")

Expected output:

Result
0.835805

Example 3: Inverse CDF (Quantile) at q=0.835805

Inputs:

value	dfn	dfd	loc	scale	method
0.835805	5	10	0	1	icdf

Excel formula:


=F_DIST(0.835805, 5, 10, 0, 1, "icdf")

Expected output:

Result
2.0

Example 4: Mean of the distribution

Inputs:

value	dfn	dfd	loc	scale	method
	5	10	0	1	mean

Excel formula:


=F_DIST( , 5, 10, 0, 1, "mean")

Expected output:

Result
1.25

Python Code


from scipy.stats import f as scipy_f
import math
 
def f_dist(value=None, dfn=1.0, dfd=1.0, loc=0.0, scale=1.0, method="pdf"):
    """
    Unified interface to the main methods of the F-distribution, including PDF, CDF, inverse CDF, survival function, and distribution statistics.
 
    Parameters:
        value (float, optional):
            For 'pdf', 'cdf', 'sf': the value x at which to evaluate the function (must be > 0)
            For 'icdf', 'isf': the probability q (must be between 0 and 1)
            For 'mean', 'median', 'var', 'std': skip parameter
        dfn (float): Numerator degrees of freedom. Must be > 0.
        dfd (float): Denominator degrees of freedom. Must be > 0.
        loc (float, optional): Location parameter. Default is 0.0.
        scale (float, optional): Scale parameter. Must be > 0. Default is 1.0.
        method (str, optional): One of 'pdf', 'cdf', 'icdf', 'sf', 'isf', 'mean', 'median', 'var', 'std'. Default is 'pdf'.
 
    Returns:
        float or str: The result of the requested method, or an error message if the input is invalid.
    """
    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:
        dfn = float(dfn)
        dfd = float(dfd)
        loc = float(loc)
        scale = float(scale)
    except Exception:
        return "Invalid input: dfn, dfd, loc, and scale must be numbers."
    if dfn <= 0 or dfd <= 0:
        return "Invalid input: dfn and dfd must be > 0."
    if scale <= 0:
        return "Invalid input: scale must be > 0."
    dist = scipy_f(dfn, dfd, loc, scale)
    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 <= 0:
            return "Invalid input: value must be > 0 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.f 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
    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.f 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 .

F_DIST

Overview

Usage

Examples

Python Code

Live Notebook

Live Demo