MATH200B Program — Extra Statistics Utilities for TI-83/84 has a program to download to your TI-83 or TI-84. With this definition a perfect normal distribution would have a kurtosis of zero. The following diagram gives a general idea of how kurtosis greater than or less than 3 corresponds to non-normal distribution shapes. The second formula is the one used by Stata with the summarize command. 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. The orange curve is a normal distribution. This means the kurtosis is the same as the normal distribution, it is mesokurtic (medium peak).. When a set of approximately normal … The entropy of a normal distribution is given by 1 2 log e 2 πe σ 2. 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. Here, x̄ is the sample mean. Here it doesn’t (12.778), so this distribution is also significantly non normal in terms of Kurtosis (leptokurtic). This definition of kurtosis can be found in Bock (1975). Kurtosis of the normal distribution is 3.0. Let’s see the main three types of kurtosis. Kurtosis is a measure of the combined weight of a distribution's tails relative to the center of the distribution. 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. The kurtosis of a mesokurtic distribution is neither high nor low, rather it is considered to be a baseline for the two other classifications. A kurtosis value near zero indicates a shape close to normal. Notice that kurtosis greater than or less than 3 corresponds to non-normal distribution shapes. BREAKING DOWN Kurtosis . The excess kurtosis can take positive or negative values, as well as values close to zero. Therefore, the excess kurtosis is found using the formula below: Excess Kurtosis = Kurtosis – 3 . 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. If a curve is less outlier prone (or lighter-tailed) than a normal curve, it is called as a platykurtic curve. The types of kurtosis are determined by the excess kurtosis of a particular distribution. Kurtosis tells you the height and sharpness of the central peak, relative to that of a standard bell curve. 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 When kurtosis is equal to 0, the distribution is mesokurtic. KURTOSIS. https://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm The normal distribution has a kurtosis value of 3. 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. A negative value indicates a distribution which is more peaked than normal, and a positive kurtosis indicates a shape flatter than normal. 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. Tutorials Point. 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 kurtosis of a normal distribution equals 3. Types of Kurtosis. 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