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