How are kurtosis and variability related?
When we say that kurtosis is relevant only when comparing to another curve with identical variance, it means that kurtosis measures something other than variance. Therefore peakedness is associated with fatter tails (and not thinner ones), which is why leptokurtic distributions have a higher kurtosis.
What is the kurtosis value of normal distribution?
A standard normal distribution has kurtosis of 3 and is recognized as mesokurtic. An increased kurtosis (>3) can be visualized as a thin “bell” with a high peak whereas a decreased kurtosis corresponds to a broadening of the peak and “thickening” of the tails. Kurtosis >3 is recognized as leptokurtic and <3.
Why is the kurtosis of a normal distribution 3?
The sample kurtosis is correspondingly related to the mean fourth power of a standardized set of sample values (in some cases it is scaled by a factor that goes to 1 in large samples). As you note, this fourth standardized moment is 3 in the case of a normal random variable.
What does kurtosis measure and what does it measure?
Therefore, kurtosis measures outliers only; it measures nothing about the “peak”. Many incorrect interpretations of kurtosis that involve notions of peakedness have been given. One is that kurtosis measures both the “peakedness” of the distribution and the heaviness of its tail.
How is the kurtosis and the skewness related?
Kurtosis and skewness are strongly related (the kurtosis must be at least 1 more than the square of the skewness; interpretation of kurtosis is somewhat easier when the distribution is nearly symmetric.
When is a kurtosis curve called a platykurtic curve?
If the curve of a distribution is more outlier prone (or heavier-tailed) than a normal or mesokurtic curve then it is referred to as a Leptokurtic curve. If a curve is less outlier prone (or lighter-tailed) than a normal curve, it is called as a platykurtic curve. Kurtosis is measured by moments and is given by the following formula −