What is a kurtosis distribution?
Kurtosis is a statistical measure that defines how heavily the tails of a distribution differ from the tails of a normal distribution. In other words, kurtosis identifies whether the tails of a given distribution contain extreme values.
What is the kurtosis of a 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.
How do you calculate kurtosis of a distribution?
x̅ is the mean and n is the sample size, as usual. m4 is called the fourth moment of the data set. m2 is the variance, the square of the standard deviation. The kurtosis can also be computed as a4 = the average value of z4, where z is the familiar z-score, z = (x−x̅)/σ.
What is the acceptable range of skewness and kurtosis for normal distribution of data?
The values for asymmetry and kurtosis between -2 and +2 are considered acceptable in order to prove normal univariate distribution (George & Mallery, 2010). Hair et al. (2010) and Bryne (2010) argued that data is considered to be normal if skewness is between ‐2 to +2 and kurtosis is between ‐7 to +7.
What does kurtosis tell us about data?
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. A uniform distribution would be the extreme case.
What are the three types of kurtosis?
There are three types of kurtosis: mesokurtic, leptokurtic, and platykurtic. Mesokurtic: Distributions that are moderate in breadth and curves with a medium peaked height.
Why is kurtosis so important?
Kurtosis is used as a measure to define the risk an investment carries. The nature of the investment to generate higher returns can also be predicted from the value of the calculated kurtosis. The greater the excess for any investment data set, the greater will be its deviation from the mean.
What does the kurtosis value tell us?
What is a good kurtosis value?
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 is unacceptable kurtosis?
Data with a skew above an absolute value of 3.0 and kurtosis above an absolute value of 8.0 are considered problematic.
What is the distribution if the coefficient of kurtosis is 3?
a normal distribution
For a normal distribution, the coefficient of kurtosis is equal to 3. Therefore a curve will be called platikurtic (meaning flatter than the normal distribution) if it has a kurtosis coefficient smaller than 3. It will be leptokurtic (meaning sharper than the normal distribution) if { \beta_2 } is greater than 3.
What are the types of kurtosis distribution?
The kurtosis of any univariate normal distribution is 3. It is common to compare the kurtosis of a distribution to this value. Distributions with kurtosis less than 3 are said to be platykurtic, although this does not imply the distribution is flat-topped as sometimes reported.
What is kurtosis?
From Wikipedia, the free encyclopedia. Jump to navigation Jump to search. fourth standardized moment in statistics. In probability theory and statistics, kurtosis (from Greek: κυρτός, kyrtos or kurtos, meaning “curved, arching”) is a measure of the “tailedness” of the probability distribution of a real -valued random variable.
What is the kurtosis of μ4?
where μ4 is the fourth central moment and σ is the standard deviation. Several letters are used in the literature to denote the kurtosis. A very common choice is κ, which is fine as long as it is clear that it does not refer to a cumulant.
What are the characteristics of data with high kurtosis?
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. Moment ratio and Percentile Coefficient of kurtosis are used to measure the kurtosis