Kurtosis of the normal distribution is 3.0. 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 kurtosis value near zero indicates a shape close to normal. Kurtosis tells you the height and sharpness of the central peak, relative to that of a standard bell curve. BREAKING DOWN Kurtosis . This definition of kurtosis can be found in Bock (1975). MATH200B Program — Extra Statistics Utilities for TI-83/84 has a program to download to your TI-83 or TI-84. 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. This means the kurtosis is the same as the normal distribution, it is mesokurtic (medium peak).. When kurtosis is equal to 0, the distribution is mesokurtic. 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. Tutorials Point. KURTOSIS. The second formula is the one used by Stata with the summarize command. 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 following diagram gives a general idea of how kurtosis greater than or less than 3 corresponds to non-normal distribution shapes. 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. Therefore, the excess kurtosis is found using the formula below: Excess Kurtosis = Kurtosis – 3 . A negative value indicates a distribution which is more peaked than normal, and a positive kurtosis indicates a shape flatter than normal. 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. The only difference between formula 1 and formula 2 is the -3 in formula 1. 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 excess kurtosis can take positive or negative values, as well as values close to zero. If a curve is less outlier prone (or lighter-tailed) than a normal curve, it is called as a platykurtic curve. Notice that kurtosis greater than or less than 3 corresponds to non-normal distribution shapes. When a set of approximately normal … The normal distribution has a kurtosis value of 3. The kurtosis of a normal distribution equals 3. Types of Kurtosis. 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. 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 types of kurtosis are determined by the excess kurtosis of a particular distribution. 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 entropy of a normal distribution is given by 1 2 log e 2 πe σ 2. Let’s see the main three types of kurtosis. Here, x̄ is the sample mean. https://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm The orange curve is a normal distribution. Here it doesn’t (12.778), so this distribution is also significantly non normal in terms of Kurtosis (leptokurtic). 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