CHISQ

Overview

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

Excel provides the CHISQ.DIST and CHISQ.INV functions, which can compute the PDF, CDF, and quantile (inverse CDF) for the chi-squared 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 chi-squared distribution is widely used in statistics, especially in hypothesis testing and confidence interval estimation for variance. The PDF is given by:

f(x, k) = \frac{1}{2^{k/2} \Gamma \left( k/2 \right)} x^{k/2-1} \exp \left(-x/2 \right)

for $x > 0$ and $k > 0$ (degrees of freedom, denoted df).

The chi-squared distribution is a special case of the gamma distribution. The shape parameter (df) determines the degrees of freedom. 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:


=CHISQ(value, df, [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 $> loc$ )
- For icdf, isf: the probability $q$ (must be between 0 and 1)
- For mean, median, var, std: skip parameter
df (float, required): 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	df	loc	scale	method
2	3	0	1	pdf

Excel formula:


=CHISQ(2, 3, 0, 1, "pdf")

Expected output:

Result
0.207554

Example 2: CDF at x=2

Inputs:

value	df	loc	scale	method
2	3	0	1	cdf

Excel formula:


=CHISQ(2, 3, 0, 1, "cdf")

Expected output:

Result
0.427593

Example 3: Inverse CDF (Quantile) at q=0.427593

Inputs:

value	df	loc	scale	method
0.427593	3	0	1	icdf

Excel formula:


=CHISQ(0.427593, 3, 0, 1, "icdf")

Expected output:

Result
2.0

Example 4: Mean of the distribution

Inputs:

value	df	loc	scale	method
	3	0	1	mean

Excel formula:


=CHISQ( , 3, 0, 1, "mean")

Expected output:

Result
3.0

Python Code


from scipy.stats import chi2 as scipy_chi2
import math
 
def chisq(value=None, df=1.0, loc=0.0, scale=1.0, method="pdf"):
    """
    Chi-squared distribution function supporting multiple methods.
 
    Args:
        value: Input value (float), required for methods except 'mean', 'median', 'var', 'std'.
        df: Degrees of freedom (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:
        df = float(df)
        loc = float(loc)
        scale = float(scale)
    except Exception:
        return "Invalid input: df, loc, and scale must be numbers."
    if df <= 0:
        return "Invalid input: df must be > 0."
    if scale <= 0:
        return "Invalid input: scale must be > 0."
    dist = scipy_chi2(df, 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.chi2 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.chi2 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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CHISQ

Overview

Usage

Examples

Python Code

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