TEST_XKURT

Calculates the p-value of the statistical test for the population excess kurtosis (4th moment).

Syntax

TEST_XKURT(X)

X
is the data sample (a one dimensional array of cells (e.g. rows or columns)).

The data sample may include missing values (e.g. #N/A).
The test hypothesis for the population excess kurtosis:

$H_{o}: K=0$

$H_{1}: K\neq 0$

Where:
- $H_{o}$ is the null hypothesisⁱ.
- $H_{1}$ is the alternate hypothesis.
For the case in which the underlying population distribution is normal, the sample excess kurtosis also has a normal sampling distribution:

$\hat K \sim N(0,\frac{24}{T})$

Where:
- $\hat k$ is the sample excess kurtosis (i.e. 4th moment).
- $T$ is the number of non-missing values in the data sample.
- $N(.)$ is the normal (i.e. Gaussian) probability distribution function.
Using a given data sample, the sample excess kurtosis is calculated as:

$\hat K (x)= \frac{\sum_{t=1}^T(x_t-\bar x)^4}{(T-1)\hat \sigma^4}-3$

Where:
- $\hat K(x)$ is the sample excess kurtosis.
- $x_i$ is the i-th non-missing value in the data sample.
- $T$ is the number of non-missing values in the data sample.
- $\hat \sigma$ is the sample standard deviation.
The underlying population distribution is assumed normal (Gaussian).
This is a two-sides (i.e. two-tails) test, so the computed p-value should be compared with half of the significance level ( $\alpha/2$ ).

Example 1:

	Formula	Description (Result)
	=KURT($B$2:$B$20)	Sample excess kurtosis (-1.0517)
	=TEST_XKURT($B$2:$B$20)	p-value of the test when excess kurtosis = 0 (0.171)

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