What does kurtosis represent?
What does kurtosis represent?
Kurtosis is a measure of the combined weight of a distribution’s tails relative to the center of the distribution. Kurtosis is sometimes confused with a measure of the peakedness of a distribution. However, kurtosis is a measure that describes the shape of a distribution’s tails in relation to its overall shape.
What is kurtosis of normal distribution?
Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution. That is, data sets with high kurtosis tend to have heavy tails, or outliers. Data sets with low kurtosis tend to have light tails, or lack of outliers.
What is a high kurtosis value?
It is used to describe the extreme values in one versus the other tail. It is actually the measure of outliers present in the distribution . High kurtosis in a data set is an indicator that data has heavy tails or outliers. This definition is used so that the standard normal distribution has a kurtosis of three.
What is kurtosis How is it measured?
In statistics, a measure of kurtosis is a measure of the “tailedness” of the probability distribution of a real-valued random variable. The standard measure of kurtosis is based on a scaled version of the fourth moment of the data or population. A distribution having a relatively high peak is called leptokurtic.
Why is kurtosis so important?
In finance, kurtosis is used as a measure of financial risk. Learn risk analysis. A large kurtosis is associated with a high risk for an investment because it indicates high probabilities of extremely large and extremely small returns.
Is high kurtosis good or bad?
Kurtosis is only useful when used in conjunction with standard deviation. It is possible that an investment might have a high kurtosis (bad), but the overall standard deviation is low (good). Conversely, one might see an investment with a low kurtosis (good), but the overall standard deviation is high (bad).
How much kurtosis is acceptable?
A kurtosis value of +/-1 is considered very good for most psychometric uses, but +/-2 is also usually acceptable. Skewness: the extent to which a distribution of values deviates from symmetry around the mean.
What does a kurtosis of 3 mean?
Kurtosis is a measure of the combined sizes of the two tails. If the kurtosis is greater than 3, then the dataset has heavier tails than a normal distribution (more in the tails). If the kurtosis is less than 3, then the dataset has lighter tails than a normal distribution (less in the tails).
Is negative kurtosis good?
A negative kurtosis implies platykurtosis. For the normal distribution the moment measure is equal to 3. This means your distribution is platykurtic or flatter as compared with normal distribution with the same M and SD.
Why high kurtosis is bad?
It is possible that an investment might have a high kurtosis (bad), but the overall standard deviation is low (good). Conversely, one might see an investment with a low kurtosis (good), but the overall standard deviation is high (bad). Kurtosis improves one’s understanding of volatility risk.
What is a bad kurtosis?
A negative kurtosis means that your distribution is flatter than a normal curve with the same mean and standard deviation. This means your distribution is platykurtic or flatter as compared with normal distribution with the same M and SD. The curve would have very light tails.
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.
What kind of kurtosis has a higher peak?
Leptokurtic distributions have positive kurtosis values. A leptokurtic distribution has a higher peak and taller (i.e. fatter and heavy) tails than a normal distribution.
What do you call a distribution with excess kurtosis?
A distribution with positive excess kurtosis is called leptokurtic, or leptokurtotic. “Lepto-” means “slender”. In terms of shape, a leptokurtic distribution has fatter tails.
What is the difference between skewness and kurtosis?
DEFINITION of ‘Kurtosis’. Like skewness, kurtosis is a statistical measure that is used to describe the distribution. Whereas skewness differentiates extreme values in one versus the other tail, kurtosis measures extreme values in either tail.