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

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