Skewness. Moments about arbitrary origin '170'. The "skinniness" of a leptokurtic distribution is a consequence of the outliers, which stretch the horizontal axis of the histogram graph, making the bulk of the data appear in a narrow ("skinny") vertical range. It is also a measure of the “peakedness” of the distribution. It is common to compare the kurtosis of a distribution to this value. \mu_3 = \mu'_3 - 3(\mu'_1)(\mu'_2) + 2(\mu'_1)^3 \\[7pt] The term “Kurtosis” refers to the statistical measure that describes the shape of either tail of a distribution, i.e. Kurtosis originally was thought to measure the peakedness of a distribution. Diagrammatically, shows the shape of three different types of curves. Dr. Wheeler defines kurtosis as: The kurtosis parameter is a measure of the combined weight of the tails relative to the rest of the distribution. Any distribution that is peaked the same way as the normal distribution is sometimes called a mesokurtic distribution. whether the distribution is heavy-tailed (presence of outliers) or light-tailed (paucity of outliers) compared to a normal distribution. Examples of leptokurtic distributions are the T-distributions with small degrees of freedom. However, kurtosis is a measure that describes the shape of a distribution's tails in relation to its overall shape. Characteristics of this distribution is one with long tails (outliers.) Any distribution that is leptokurtic displays greater kurtosis than a mesokurtic distribution. I am wondering whether only standard normal distribution has a kurtosis being 3, or any normal distribution has the same kurtosis, namely $3$. ${\beta_2}$ Which measures kurtosis, has a value greater than 3, thus implying that the distribution is leptokurtic. Distributions with kurtosis less than 3 are said to be platykurtic, although this does not imply the distribution is "flat-topped" as is sometimes stated. For investors, platykurtic return distributions are stable and predictable, in the sense that there will rarely (if ever) be extreme (outlier) returns. However, when high kurtosis is present, the tails extend farther than the + or - three standard deviations of the normal bell-curved distribution. The term “platykurtic” refers to a statistical distribution with negative excess kurtosis. Any distribution with kurtosis ≈3 (excess ≈0) is called mesokurtic. It is used to determine whether a distribution contains extreme values. In statistics, normality tests are used to determine whether a data set is modeled for normal distribution. The prefix of "lepto-" means "skinny," making the shape of a leptokurtic distribution easier to remember. Normal distribution kurtosis = 3; A distribution that is more peaked and has fatter tails than normal distribution has kurtosis value greater than 3 (the higher kurtosis, the more peaked and fatter tails). If a distribution has a kurtosis of 0, then it is equal to the normal distribution which has the following bell-shape: Positive Kurtosis. Kurtosis is a measure of whether or not a distribution is heavy-tailed or light-tailed relative to a normal distribution. A distribution can be infinitely peaked with low kurtosis, and a distribution can be perfectly flat-topped with infinite kurtosis. When I look at a normal curve, it seems the peak occurs at the center, a.k.a at 0. The final type of distribution is a platykurtic distribution. This definition is used so that the standard normal distribution has a kurtosis of three. My textbook then says "the kurtosis of a normally distributed random variable is $3$." Since the deviations have been taken from an assumed mean, hence we first calculate moments about arbitrary origin and then moments about mean. Kurtosis is sometimes confused with a measure of the peakedness of a distribution. Peak is higher and sharper than Mesokurtic, which means that data are heavy-tailed or profusion of outliers. The kurtosis can be even more convoluted. Kurtosis is measured by moments and is given by the following formula −. On the other hand, kurtosis identifies the way; values are grouped around the central point on the frequency distribution. With this definition a perfect normal distribution would have a kurtosis of zero. Its formula is: where. Kurtosis is sometimes reported as “excess kurtosis.” Excess kurtosis is determined by subtracting 3 from the kurtosis. Kurtosis ranges from 1 to infinity. sharply peaked with heavy tails) Kurtosis in statistics is used to describe the distribution of the data set and depicts to what extent the data set points of a particular distribution differ from the data of a normal distribution. All measures of kurtosis are compared against a standard normal distribution, or bell curve. The first category of kurtosis is a mesokurtic distribution. Thus, with this formula a perfect normal distribution would have a kurtosis of three. Leptokurtic (Kurtosis > 3): Distribution is longer, tails are fatter. It has fewer extreme events than a normal distribution. This definition of kurtosis can be found in Bock (1975). Some definitions of kurtosis subtract 3 from the computed value, so that the normal distribution has kurtosis of 0. The histogram shows a fairly normal distribution of data with a few outliers present. Excess kurtosis describes a probability distribution with fat fails, indicating an outlier event has a higher than average chance of occurring. So why is the kurtosis … The offers that appear in this table are from partnerships from which Investopedia receives compensation. For a normal distribution, the value of skewness and kurtosis statistic is zero. Excess kurtosis is a valuable tool in risk management because it shows whether an … The normal distribution has excess kurtosis of zero. With this definition a perfect normal distribution would have a kurtosis of zero. share | cite | improve this question | follow | asked Aug 28 '18 at 19:59. Skewness essentially measures the relative size of the two tails. Further, it will exhibit [overdispersion] relative to a single normal distribution with the given variation. This simply means that fewer data values are located near the mean and more data values are located on the tails. A distribution with kurtosis <3 (excess kurtosis <0) is called platykurtic. Because kurtosis compares a distribution to the normal distribution, 3 is often subtracted from the calculation above to get a number which is 0 for a normal distribution, +ve for leptokurtic distributions, and –ve for mesokurtic ones. The kurtosis calculated as above for a normal distribution calculates to 3. Computational Exercises . Many human traits are normally distributed including height … This article defines MAQL to calculate skewness and kurtosis that can be used to test the normality of a given data set. We will show in below that the kurtosis of the standard normal distribution is 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. Kurtosis of the normal distribution is 3.0. An example of a mesokurtic distribution is the binomial distribution with the value of p close to 0.5. 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