What are the advantages and disadvantages? Why and how can researchers find it? What is the ideal limit 1,2,3 etc?
The skewness and kurtosis are standardized moments of the random variable, unless you are defining the excess kurtosis, which is then the standardized cumulant.
Simply, the skewness defines the asymmetry of the distribution about the median. The kurtosis is a measure of the intensity of the distribution (or how peaked it is). Both are used to describe a distribution for random variables.
I am not sure what you mean by an ideal limit, it entirely depends on what distribution you are investigating. There are standard formulae for the skewness and kurtosis, but be careful that you are using the correct one for the kurtosis depending on what you want to know.
For a quick formula the nth standardized moment is m = E((x-mu)^n)/sigma^n, where mu is the mean and sigma is the standard deviation. Skewness is the third standard moment and standard kurtosis is the fourth.
Apply the formula and see what you come up with. Skewness will be positive or negative depending on the weighting of the distribution and kurtosis will be positive and the larger the magnitude the tighter the distribution about the mean.
I hope this helps a little.
Chris
The skewness and kurtosis are standardized moments of the random variable, unless you are defining the excess kurtosis, which is then the standardized cumulant.
Simply, the skewness defines the asymmetry of the distribution about the median. The kurtosis is a measure of the intensity of the distribution (or how peaked it is). Both are used to describe a distribution for random variables.
I am not sure what you mean by an ideal limit, it entirely depends on what distribution you are investigating. There are standard formulae for the skewness and kurtosis, but be careful that you are using the correct one for the kurtosis depending on what you want to know.
For a quick formula the nth standardized moment is m = E((x-mu)^n)/sigma^n, where mu is the mean and sigma is the standard deviation. Skewness is the third standard moment and standard kurtosis is the fourth.
Apply the formula and see what you come up with. Skewness will be positive or negative depending on the weighting of the distribution and kurtosis will be positive and the larger the magnitude the tighter the distribution about the mean.
I hope this helps a little.
Chris
Skewness is a measure of symmetry, or more precisely, the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the center point.
Kurtosis is a measure of whether the data are peaked or flat relative to a normal distribution. That is, data sets with high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have heavy tails. Data sets with low kurtosis tend to have a flat top near the mean rather than a sharp peak. A uniform distribution would be the extreme case.
Kurtosis does not measure anything about the peak; that is erroneous historical information. You can have nearly all values of kurtosis and a flat peak, and you can have nearly all values of kurtosis with an infinitely pointy peak. Rather, kurtosis measures tail weight of the distribution. The heavier the tail (where "heaviness" is a combination of remoteness and mass, like leverage), the higher the kurtosis. For data, high kurtosis in manifested by the presence of outlier(s). See Article Kurtosis as Peakedness, 1905-2014. RIP
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