Notice that kurtosis greater than or less than 3 corresponds to non-normal distribution shapes. 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. Let’s see the main three types of kurtosis. The second formula is the one used by Stata with the summarize command. When a set of approximately normal … Scenario A normal distribution has skewness and excess kurtosis of 0, so if your distribution is close to those values then it is probably close to normal. A negative value indicates a distribution which is more peaked than normal, and a positive kurtosis indicates a shape flatter than normal. Kurtosis of the normal distribution is 3.0. The normal PDF is also symmetric with a zero skewness such that its median and mode values are the same as the mean value. The "minus 3" at the end of this formula is often explained as a correction to make the kurtosis of the normal distribution equal to zero, as the kurtosis is 3 for a normal distribution. Here it doesn’t (12.778), so this distribution is also significantly non normal in terms of Kurtosis (leptokurtic). Here, x̄ is the sample mean. The normal distribution has a kurtosis value of 3. This definition of kurtosis can be found in Bock (1975). When kurtosis is equal to 0, the distribution is mesokurtic. BREAKING DOWN Kurtosis . Mesokurtic: This is the normal distribution; Leptokurtic: This distribution has fatter tails and a sharper peak.The kurtosis is “positive” with a value greater than 3; Platykurtic: The distribution has a lower and wider peak and thinner tails.The kurtosis is “negative” with a value greater than 3 Kurtosis is measured by moments and is given by the following formula − Formula The orange curve is a normal distribution. The only difference between formula 1 and formula 2 is the -3 in formula 1. MATH200B Program — Extra Statistics Utilities for TI-83/84 has a program to download to your TI-83 or TI-84. The excess kurtosis can take positive or negative values, as well as values close to zero. The entropy of a normal distribution is given by 1 2 log e 2 πe σ 2. https://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm KURTOSIS. A kurtosis value near zero indicates a shape close to normal. Here 2 X .363 = .726 and we consider the range from –0.726 to + 0.726 and check if the value for Kurtosis falls within this range. Tutorials Point. Kurtosis is a measure of the combined weight of a distribution's tails relative to the center of the distribution. With this definition a perfect normal distribution would have a kurtosis of zero. This property makes Kurtosis largely ignorant about the values lying toward the center of the distribution, and it makes Kurtosis sensitive toward values lying on the distribution’s tails. This means the kurtosis is the same as the normal distribution, it is mesokurtic (medium peak).. Kurtosis tells you the height and sharpness of the central peak, relative to that of a standard bell curve. Types of Kurtosis. The kurtosis of a mesokurtic distribution is neither high nor low, rather it is considered to be a baseline for the two other classifications. The kurtosis of the normal distribution is 3, which is frequently used as a benchmark for peakedness comparison of a given unimodal probability density. The following diagram gives a general idea of how kurtosis greater than or less than 3 corresponds to non-normal distribution shapes. Therefore, the excess kurtosis is found using the formula below: Excess Kurtosis = Kurtosis – 3 . The kurtosis of a normal distribution equals 3. 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