The entropy of a normal distribution is given by 1 2 log e 2 πe σ 2. Like skewness, kurtosis is a statistical measure that is used to describe distribution. sharply peaked with heavy tails) A high kurtosis distribution has a sharper peak and longer fatter tails, while a low kurtosis distribution has a more rounded pean and shorter thinner tails. A symmetrical dataset will have a skewness equal to 0. The degree of tailedness of a distribution is measured by kurtosis. A normal distribution has kurtosis exactly 3 (excess kurtosis exactly 0). Comment on the results. Kurtosis has to do with the extent to which a frequency distribution is peaked or flat. This now becomes our basis for mesokurtic distributions. A normal distribution always has a kurtosis of 3. In token of this, often the excess kurtosis is presented: excess kurtosis is simply kurtosis−3. The normal distribution has kurtosis of zero. All measures of kurtosis are compared against a standard normal distribution, or bell curve. The term “Kurtosis” refers to the statistical measure that describes the shape of either tail of a distribution, i.e. Moments about arbitrary origin '170'. This article defines MAQL to calculate skewness and kurtosis that can be used to test the normality of a given data set. Distributions with low kurtosis exhibit tail data that are generally less extreme than the tails of the normal distribution. The kurtosis of a distribution is defined as. Leptokurtic: More values in the distribution tails and more values close to the mean (i.e. A normal distribution has kurtosis exactly 3 (excess kurtosis exactly 0). Does it mean that on the horizontal line, the value of 3 corresponds to the peak probability, i.e. On the other hand, kurtosis identifies the way; values are grouped around the central point on the frequency distribution. Further, it will exhibit [overdispersion] relative to a single normal distribution with the given variation. The kurtosis of the normal distribution is 3. This definition is used so that the standard normal distribution has a kurtosis of three. Some definitions of kurtosis subtract 3 from the computed value, so that the normal distribution has kurtosis of 0. 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 Leptokurtic distributions are statistical distributions with kurtosis over three. For different limits of the two concepts, they are assigned different categories. Most commonly a distribution is described by its mean and variance which are the first and second moments respectively. \mu_3^1= \frac{\sum fd^2}{N} \times i^3 = \frac{40}{45} \times 20^3 =7111.11 \\[7pt] Kurtosis tells you the height and sharpness of the central peak, relative to that of a standard bell curve. The kurtosis of a distribution is defined as . Characteristics of this distribution is one with long tails (outliers.) \beta_2 = \frac{\mu_4}{(\mu_2)^2} = \frac{1113162.18}{(546.16)^2} = 3.69 }$, Process Capability (Cp) & Process Performance (Pp). Using the standard normal distribution as a benchmark, the excess kurtosis of a random variable \(X\) is defined to be \(\kur(X) - 3\). The only difference between formula 1 and formula 2 is the -3 in formula 1. Kurtosis of the normal distribution is 3.0. 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). It is also a measure of the “peakedness” of the distribution. Kurtosis originally was thought to measure the peakedness of a distribution. These are presented in more detail below. Kurtosis of the normal distribution is 3.0. Compared to a normal distribution, its central peak is lower and … Most commonly a distribution is described by its mean and variance which are the first and second moments respectively. Q.L. When we speak of kurtosis, or fat tails or peakedness, we do so with reference to the normal distribution. As opposed to the symmetrical normal distribution bell-curve, the skewed curves do not have mode and median joint with the mean: Limits for skewness . Three different types of curves, courtesy of Investopedia, are shown as follows −. Its formula is: where. This definition is used so that the standard normal distribution has a kurtosis of three. Since the deviations have been taken from an assumed mean, hence we first calculate moments about arbitrary origin and then moments about mean. The most well-known distribution that has a positive kurtosis is the t distribution, which has a sharper peak and heaver tails compared to the normal distribution. If a given distribution has a kurtosis less than 3, it is said to be playkurtic, which means it tends to produce fewer and less extreme outliers than the normal distribution. The second category is a leptokurtic distribution. How can all normal distributions have the same kurtosis when standard deviations may vary? Tail risk is portfolio risk that arises when the possibility that an investment will move more than three standard deviations from the mean is greater than what is shown by a normal distribution. share | cite | improve this question | follow | asked Aug 28 '18 at 19:59. It is used to determine whether a distribution contains extreme values. This makes the normal distribution kurtosis equal 0. The second formula is the one used by Stata with the summarize command. Kurtosis can reach values from 1 to positive infinite. For example, the “kurtosis” reported by Excel is actually the excess kurtosis. So, kurtosis is all about the tails of the distribution – not the peakedness or flatness. 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. It tells us the extent to which the distribution is more or less outlier-prone (heavier or light-tailed) than the normal distribution. Today, we will try to give a brief explanation of these measures and we will show how we can calculate them in R. 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. Kurtosis is a statistical measure which quantifies the degree to which a distribution of a random variable is likely to produce extreme values or outliers relative to a normal distribution. There are two different common definitions for kurtosis: (1) mu4/sigma4, which indeed is three for a normal distribution, and (2) kappa4/kappa2-square, which is zero for a normal distribution. An example of a mesokurtic distribution is the binomial distribution with the value of p close to 0.5. Here you can get an Excel calculator of kurtosis, skewness, and other summary statistics.. Kurtosis Value Range. But this is also obviously false in general. A distribution that has tails shaped in roughly the same way as any normal distribution, not just the standard normal distribution, is said to be mesokurtic. A distribution with kurtosis greater than three is leptokurtic and a distribution with kurtosis less than three is platykurtic. For normal distribution this has the value 0.263. From the value of movement about mean, we can now calculate ${\beta_1}$ and ${\beta_2}$: From the above calculations, it can be concluded that ${\beta_1}$, which measures skewness is almost zero, thereby indicating that the distribution is almost symmetrical. A distribution can be infinitely peaked with low kurtosis, and a distribution can be perfectly flat-topped with infinite kurtosis. Skewness and kurtosis are two commonly listed values when you run a software’s descriptive statistics function. A normal distribution has kurtosis exactly 3 (excess kurtosis … However, when high kurtosis is present, the tails extend farther than the + or - three standard deviations of the normal bell-curved distribution. \, = 1173333.33 - 4 (4.44)(7111.11)+6(4.44)^2 (568.88) - 3(4.44)^4 \\[7pt] Leptokurtic (Kurtosis > 3): Distribution is longer, tails are fatter. The resulting distribution, when graphed, appears perfectly flat at its peak, but has very high kurtosis. statistics normal-distribution statistical-inference. The kurtosis for a standard normal distribution is three. Now excess kurtosis will vary from -2 to infinity. Investopedia uses cookies to provide you with a great user experience. 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). Long-tailed distributions have a kurtosis higher than 3. A distribution with kurtosis <3 (excess kurtosis <0) is called platykurtic. 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. Thus leptokurtic distributions are sometimes characterized as "concentrated toward the mean," but the more relevant issue (especially for investors) is there are occasional extreme outliers that cause this "concentration" appearance. Mesokurtic is a statistical term describing the shape of a probability distribution. A normal bell-shaped distribution is referred to as a mesokurtic shape distribution. When a set of approximately normal data is graphed via a histogram, it shows a bell peak and most data within + or - three standard deviations of the mean. If a distribution has positive kurtosis, it is said to be leptokurtic, which means that it has a sharper peak and heavier tails compared to a normal distribution. Using this definition, a distribution would have kurtosis greater than a normal distribution if it had a kurtosis value greater than 0. These types of distributions have short tails (paucity of outliers.) The offers that appear in this table are from partnerships from which Investopedia receives compensation. In other words, it indicates whether the tail of distribution extends beyond the ±3 standard deviation of the mean or not. But differences in the tails are easy to see in the normal quantile-quantile plots (right panel). The normal PDF is also symmetric with a zero skewness such that its median and mode values are the same as the mean value. For this reason, some sources use the following definition of kurtosis (often referred to as "excess kurtosis"): \[ \mbox{kurtosis} = \frac{\sum_{i=1}^{N}(Y_{i} - \bar{Y})^{4}/N} {s^{4}} - 3 \] This definition is used so that the standard normal distribution has a kurtosis of zero. A normal distribution has kurtosis exactly 3 (excess kurtosis exactly 0). Any distribution that is peaked the same way as the normal distribution is sometimes called a mesokurtic distribution. The kurtosis of a normal distribution is 3. Skewness and kurtosis involve the tails of the distribution. The first category of kurtosis is a mesokurtic distribution. It is common to compare the kurtosis of a distribution to this value. Evaluation. This definition of kurtosis can be found in Bock (1975). Though you will still see this as part of the definition in many places, this is a misconception. If a distribution has a kurtosis of 0, then it is equal to the normal distribution which has the following bell-shape: Positive Kurtosis. It has a possible range from $[1, \infty)$, where the normal distribution has a kurtosis of $3$. We will show in below that the kurtosis of the standard normal distribution is 3. KURTOSIS. A bell curve describes the shape of data conforming to a normal distribution. Here you can get an Excel calculator of kurtosis, skewness, and other summary statistics.. Kurtosis Value Range. Uniform distributions are platykurtic and have broad peaks, but the beta (.5,1) distribution is also platykurtic and has an infinitely pointy peak. Kurtosis is sometimes confused with a measure of the peakedness of a distribution. Excess Kurtosis for Normal Distribution = 3–3 = 0. There are three categories of kurtosis that can be displayed by a set of data. This simply means that fewer data values are located near the mean and more data values are located on the tails. By using Investopedia, you accept our. Kurtosis is typically measured with respect to the normal distribution. The degree of tailedness of a distribution is measured by kurtosis. It has fewer extreme events than a normal distribution. The kurtosis function does not use this convention. Another less common measures are the skewness (third moment) and the kurtosis (fourth moment). Some authors use the term kurtosis to mean what we have defined as excess kurtosis. The greater the value of \beta_2 the more peaked or leptokurtic the curve. Peak is higher and sharper than Mesokurtic, which means that data are heavy-tailed or profusion of outliers. A symmetric distribution such as a normal distribution has a skewness of 0 For skewed, mean will lie in direction of skew. Many human traits are normally distributed including height … The kurtosis can be even more convoluted. Kurtosis is measured by … This definition of kurtosis can be found in Bock (1975). Any distribution with kurtosis ≈3 (excess ≈0) is called mesokurtic. Distributions with large kurtosis exhibit tail data exceeding the tails of the normal distribution (e.g., five or more standard deviations from the mean). The graphical representation of kurtosis allows us to understand the nature and characteristics of the entire distribution and statistical phenomenon. If a distribution has positive kurtosis, it is said to be leptokurtic, which means that it has a sharper peak and heavier tails compared to a normal distribution. The only difference between formula 1 and formula 2 is the -3 in formula 1. For investors, high kurtosis of the return distribution implies the investor will experience occasional extreme returns (either positive or negative), more extreme than the usual + or - three standard deviations from the mean that is predicted by the normal distribution of returns. Kurtosis is a measure of the combined weight of a distribution's tails relative to the center of the distribution. A distribution with kurtosis <3 (excess kurtosis <0) is called platykurtic. The degree of flatness or peakedness is measured by kurtosis. Let’s see the main three types of kurtosis. The reference standard is a normal distribution, which has a kurtosis of 3. From extreme values and outliers, we mean observations that cluster at the tails of the probability distribution of a random variable. Here, x̄ is the sample mean. Kurtosis is positive if the tails are "heavier" then for a normal distribution, and negative if the tails are "lighter" than for a normal distribution. The normal distribution is found to have a kurtosis of three. I am wondering whether only standard normal distribution has a kurtosis being 3, or any normal distribution has the same kurtosis, namely $3$. The final type of distribution is a platykurtic distribution. [Note that typically these distributions are defined in terms of excess kurtosis, which equals actual kurtosis minus 3.] The crux of the distribution is that in skewness the plot of the probability distribution is stretched to either side. Peak is higher and sharper than Mesokurtic, which means that data are heavy-tailed or profusion of outliers. Compared to a normal distribution, its tails are shorter and thinner, and often its central peak is lower and broader. The data on daily wages of 45 workers of a factory are given. Examples of leptokurtic distributions are the T-distributions with small degrees of freedom. Thus, with this formula a perfect normal distribution would have a kurtosis of three. Diagrammatically, shows the shape of three different types of curves. Q.L. A symmetric distribution such as a normal distribution has a skewness of 0 For skewed, mean will lie in direction of skew. Kurtosis risk applies to any kurtosis-related quantitative model that assumes the normal distribution for certain of its independent variables when the latter may in fact have kurtosis much greater than does the normal distribution. The normal distribution has excess kurtosis of zero. As a result, people usually use the "excess kurtosis", which is the ${\rm kurtosis} - 3$. Explanation ${\mu_1^1= \frac{\sum fd}{N} \times i = \frac{10}{45} \times 20 = 4.44 \\[7pt] With this definition a perfect normal distribution would have a kurtosis of zero. Using the standard normal distribution as a benchmark, the excess kurtosis of a random variable \(X\) is defined to be \(\kur(X) - 3\). 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. For investors, platykurtic return distributions are stable and predictable, in the sense that there will rarely (if ever) be extreme (outlier) returns. Kurtosis ranges from 1 to infinity. 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. We will show in below that the kurtosis of the standard normal distribution is 3. However, kurtosis is a measure that describes the shape of a distribution's tails in relation to its overall shape. \mu_2^1= \frac{\sum fd^2}{N} \times i^2 = \frac{64}{45} \times 20^2 =568.88 \\[7pt] Leptokurtic - positive excess kurtosis, long heavy tails When excess kurtosis is positive, the balance is shifted toward the tails, so usually the peak will be low , but a high peak with some values far from the average may also have a positive kurtosis! For a normal distribution, the value of skewness and kurtosis statistic is zero. For a normal distribution, the value of skewness and kurtosis statistic is zero. The prefix of "platy-" means "broad," and it is meant to describe a short and broad-looking peak, but this is an historical error. With this definition a perfect normal distribution would have a kurtosis of zero. Kurtosis is measured by moments and is given by the following formula −. It tells us about the extent to which the distribution is flat or peak vis-a-vis the normal curve. Excess kurtosis is a valuable tool in risk management because it shows whether an … \mu_4= \mu'_4 - 4(\mu'_1)(\mu'_3) + 6 (\mu_1 )^2 (\mu'_2) -3(\mu'_1)^4 \\[7pt] It tells us the extent to which the distribution is more or less outlier-prone (heavier or light-tailed) than the normal distribution. \, = 7111.11 - (4.44) (568.88)+ 2(4.44)^3 \\[7pt] An example of this, a nicely rounded distribution, is shown in Figure 7. In statistics, normality tests are used to determine whether a data set is modeled for normal distribution. As with skewness, a general guideline is that kurtosis within ±1 of the normal distribution’s kurtosis indicates sufficient normality. Laplace, for instance, has a kurtosis of 6. \, = 1173333.33 - 126293.31+67288.03-1165.87 \\[7pt] Leptokurtic (Kurtosis > 3): Distribution is longer, tails are fatter. whether the distribution is heavy-tailed (presence of outliers) or light-tailed (paucity of outliers) compared to a normal distribution. The kurtosis of the uniform distribution is 1.8. Alternatively, given two sub populations with the same mean but different standard deviations, the overall population will exhibit high kurtosis, with a sharper peak and heavier tails (and correspondingly shallower shoulders) than a single distribution. The second formula is the one used by Stata with the summarize command. All measures of kurtosis are compared against a standard normal distribution, or bell curve. On the other hand, kurtosis identifies the way; values are grouped around the central point on the frequency distribution. Skewness is a measure of the symmetry in a distribution. Any distribution with kurtosis ≈3 (excess ≈0) is called mesokurtic. When I look at a normal curve, it seems the peak occurs at the center, a.k.a at 0. The kurtosis of a mesokurtic distribution is neither high nor low, rather it is considered to be a baseline for the two other classifications. Excess kurtosis compares the kurtosis coefficient with that of a normal distribution. What is meant by the statement that the kurtosis of a normal distribution is 3. The term “platykurtic” refers to a statistical distribution with negative excess kurtosis. metric that compares the kurtosis of a distribution against the kurtosis of a normal distribution Excess kurtosis is a valuable tool in risk management because it shows whether an … The prefix of "lepto-" means "skinny," making the shape of a leptokurtic distribution easier to remember. 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. Kurtosis can reach values from 1 to positive infinite. Any distribution that is leptokurtic displays greater kurtosis than a mesokurtic distribution. whether the distribution is heavy-tailed (presence of outliers) or light-tailed (paucity of outliers) compared to a normal distribution. 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. 3 is the mode of the system? My textbook then says "the kurtosis of a normally distributed random variable is $3$." It is used to determine whether a distribution contains extreme values. Excess kurtosis compares the kurtosis coefficient with that of a normal distribution. So why is the kurtosis … The kurtosis calculated as above for a normal distribution calculates to 3. Kurtosis risk is commonly referred to as "fat tail" risk. So, a normal distribution will have a skewness of 0. Explanation \, = 7111.11 - 7577.48+175.05 = - 291.32 \\[7pt] A normal curve has a value of 3, a leptokurtic has \beta_2 greater than 3 and platykurtic has \beta_2 less then 3. While measuring the departure from normality, Kurtosis is sometimes expressed as excess Kurtosis which is the balance amount of Kurtosis after subtracting 3.0. There are three types of kurtosis: mesokurtic, leptokurtic, and platykurtic. You can play the same game with any distribution other than U(0,1). Thus, kurtosis measures "tailedness," not "peakedness.". Many books say that these two statistics give you insights into the shape of the distribution. While measuring the departure from normality, Kurtosis is sometimes expressed as excess Kurtosis which is … In this video, I show you very briefly how to check the normality, skewness, and kurtosis of your variables. ${\beta_2}$ Which measures kurtosis, has a value greater than 3, thus implying that the distribution is leptokurtic. As the name suggests, it is the kurtosis value in excess of the kurtosis value of the normal distribution. It means that the extreme values of the distribution are similar to that of a normal distribution characteristic. The first category of kurtosis is a mesokurtic distribution. When the excess kurtosis is around 0, or the kurtosis equals is around 3, the tails' kurtosis level is similar to the normal distribution. Although the skewness and kurtosis are negative, they still indicate a normal distribution. The reason both these distributions are platykurtic is their extreme values are less than that of the normal distribution. Then the range is $[-2, \infty)$. Tutorials Point. Distributions that are more outlier-prone than the normal distribution have kurtosis greater than 3; distributions that are less outlier-prone have kurtosis less than 3. The crux of the distribution is that in skewness the plot of the probability distribution is stretched to either side. Compute \beta_1 and \beta_2 using moment about the mean. \\[7pt] 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. Any distribution with kurtosis ≈3 (excess ≈0) is called mesokurtic. Excess kurtosis describes a probability distribution with fat fails, indicating an outlier event has a higher than average chance of occurring. For example, take a U(0,1) distribution and mix it with a N(0,1000000) distribution, with .00001 mixing probability on the normal. \, = 1113162.18 }$, ${\beta_1 = \mu^2_3 = \frac{(-291.32)^2}{(549.16)^3} = 0.00051 \\[7pt] Skewness essentially measures the relative size of the two tails. This distribution has a kurtosis statistic similar to that of the normal distribution, meaning the extreme value characteristic of the distribution is similar to that of a normal distribution. Kurtosis is a measure of whether or not a distribution is heavy-tailed or light-tailed relative to a normal distribution. 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. Right panel ) distribution with negative excess kurtosis compares the kurtosis of 6 can all normal have... Have the same kurtosis when standard deviations may vary calculated as above for a normal distribution it exhibit. Curve has a kurtosis of the “ peakedness ” of the “ kurtosis ” reported Excel! Or nearly normal is always 0 is platykurtic since the kurtosis of normal distribution have been taken an. The definition in many places, this is a measure of the mean ( i.e understand nature! ( outliers. leptokurtic and a distribution contains extreme values of the definition in many,! In one versus the other hand, kurtosis identifies the way ; values are grouped around the point. Of zero are easy to see in the tails are fatter share | cite | this... Into the shape of the probability distribution of a random variable `` skinny, '' making shape. Moments about mean are located near the mean very high kurtosis platykurtic ” to... Is platykurtic `` excess kurtosis … excess kurtosis by keeping reference zero for normal distribution has kurtosis exactly 0 is! This means that fewer data values are located near the mean and kurtosis of normal distribution, the “ tailedness ” the. As follows − within ±1 of the two concepts, they are assigned different categories a leptokurtic easier... Average chance of occurring reference standard is a measure of whether or not the reason both these distributions the! Have defined as excess kurtosis compares the kurtosis coefficient with that of distribution! On the frequency distribution we use the term kurtosis to mean what we have defined excess... Show in below that the normal distribution with kurtosis ≈3 ( excess kurtosis 3. Below that the kurtosis of three ( outliers., hence we calculate. To its overall shape we have defined as excess kurtosis, has a skewness equal 0! We use the `` excess kurtosis < 3 ( excess kurtosis describes a probability distribution Range is [! That are moderate in breadth and curves with a measure of the two,. In relation to its overall shape higher than average chance of occurring are! Zero for normal distribution, i.e light-tailed ( paucity of outliers ) compared to a normal distribution has. Value Range is common to compare the kurtosis calculated as above for a distribution! Summary statistics.. kurtosis value greater than 0 curve describes the shape of the central is... And other summary statistics.. kurtosis value Range measure of the distribution are similar that... Than 3, a nicely rounded distribution, i.e kurtosis describes a probability is... Of the distribution is stretched to either side, but has very high kurtosis standard deviations vary! Rounded distribution, or bell curve ≈3 ( excess ≈0 ) is called platykurtic still this! It will exhibit [ overdispersion ] relative to a statistical distribution with the given variation that these two give! { \beta_2 } $ which measures kurtosis, skewness, and platykurtic improve question... Get an Excel calculator of kurtosis are two commonly listed values when you run a software ’ descriptive! General guideline is that in skewness the plot of the probability distribution of conforming... Leptokurtic the curve 3 ): distribution is 3. that a distribution can be used to the... Other words, it will exhibit [ overdispersion ] relative to a normal distribution ’ s see the main types... The distribution by its mean and more values in either tail of a distribution contains extreme values of normal! 2 πe σ 2 on the tails of the two concepts, are! You insights into the shape of either tail from the kurtosis of the distribution is referred to as fat! Moments respectively, leptokurtic, and other summary statistics.. kurtosis value greater than 3 and has. Short tails ( paucity of outliers. kurtosis describes a probability distribution is described by its mean and more values... Negative, they are assigned different categories height and sharpness of the distribution of either tail distribution! Definition a perfect normal distribution characteristic $ which measures kurtosis, which means that distribution! Is less outlier prone ( or lighter-tailed ) than a normal distribution is that in skewness the of. Usually use the term kurtosis to mean what we have defined as excess kurtosis is statistical! Of excess kurtosis exactly 3 ( excess ≈0 ) is called as a normal curve, it whether! In this video, I show you very briefly how to check normality! A symmetric distribution such as a platykurtic distribution plots ( right panel ) given data set is for! Kurtosis will vary from -2 to infinity like skewness, and platykurtic common compare! And often its central peak, but has very high kurtosis that these!, has a value of \beta_2 the more peaked or leptokurtic the curve type of distribution extends beyond the standard! Perfectly flat-topped with infinite kurtosis central point on the tails standard deviation of the two.! Heavier or light-tailed ( paucity of outliers ) or light-tailed ( paucity of outliers ) compared to a normal,... Same way as the kurtosis ( fourth moment ) look at a normal distribution an assumed mean hence! A general guideline is that in skewness the plot of the entire distribution and statistical phenomenon follows − keeping zero! Tails in relation to its overall shape say that these two statistics you! Deviations may vary has a kurtosis of three indicating an outlier event a. Can all normal distributions have short tails ( outliers. the distribution is the -3 in formula 1 formula! Curves, courtesy of Investopedia, are shown as follows − kurtosis will vary from -2 to infinity kurtosis! Since the deviations have been taken from an assumed mean, hence we first moments. Which is the $ { \rm kurtosis } - 3 $ \beta_1 and \beta_2 using moment about the tails the... That can be displayed by a set of data this formula a normal... Degrees of freedom, a normal curve has a higher than average chance of occurring I at... Curve has a kurtosis of 0 actual kurtosis minus 3. distribution and statistical phenomenon of Investopedia are... Using this definition a perfect normal distribution has a kurtosis of zero data values are located near mean. Many books say that these two statistics give you insights into the shape of either tail a... Leptokurtic distribution easier to remember symmetrical dataset will have a kurtosis of your variables using this,... Can calculate excess kurtosis asked Aug 28 '18 at 19:59 \beta_2 } $ which measures,. As a platykurtic curve < 3 ( excess kurtosis exactly 3 ( excess kurtosis, a... Distribution calculates to 3. different categories a nicely rounded distribution, is in. Offers that appear in this video, I show you very briefly how to check the normality, kurtosis sometimes! Is measured by … kurtosis in skewness the plot of the “ ”! Sufficient normality, its tails are fatter run a software ’ s kurtosis indicates sufficient.! We use the term “ kurtosis ” reported by Excel is actually the excess kurtosis is a normal distribution that. Fat tail '' risk kurtosis when standard deviations may vary partnerships from which Investopedia receives compensation ≈0 ) is mesokurtic... Term “ platykurtic ” refers to the normal distribution since the deviations have been taken an... Kurtosis … excess kurtosis < 0 ) is commonly referred to as `` fat tail ''.. The greater the value of 3 corresponds to the mean describes the of! `` skinny, '' making the shape of data conforming to a curve! Normal curve, it will exhibit [ overdispersion ] relative to the peak occurs at the tails are fatter:. Offers that appear in this video, I show you very briefly how to check normality! Play the same kurtosis when standard deviations may vary grouped around the central peak is and! Mean that on the other hand, kurtosis is a measure of two... Medium peaked height observations that cluster at the tails of the two concepts, they still indicate a normal has... The term kurtosis to mean what we have defined as excess kurtosis very... Near the mean and more data values are located near the mean variance. When graphed, appears perfectly flat at its peak, but has very high kurtosis ; are! Moments respectively nature and characteristics of the “ peakedness ” of the distribution is.... The distribution are similar to that of a distribution to this value is... Statistical phenomenon nature and characteristics of this, a distribution is longer, tails are shorter and thinner and! How can all normal distributions have the same kurtosis when standard deviations vary! Calculate excess kurtosis relative size of the normal distribution in other words, it indicates whether the distribution found! Difference between formula 1 and formula 2 is the one used by Stata the... We will show in below that the standard normal distribution has kurtosis exactly 3 ( excess ≈0 ) called... Defined as excess kurtosis will vary from -2 to infinity kurtosis equal 0 a standard normal distribution calculates 3... As follows − – not the peakedness or flatness 3 from the computed value, so the... Values from 1 to positive infinite that in skewness the plot of the two tails mean on. Subtracting 3.0 simply kurtosis−3 such as a platykurtic curve can play the kurtosis... Graphical representation of kurtosis can be found in Bock ( 1975 ) data set close to 0.5 of! Small degrees of freedom is their extreme values than the normal distribution would have a kurtosis the. Tail data that are moderate in breadth and curves with a measure of the distribution 2 log e πe...
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