Which of the following is a type of wild cat? Kurtosis definition, the state or quality of flatness or peakedness of the curve describing a frequency distribution in the region about its mode. Kurtosis. Another feature to consider when talking about a distribution is the shape of the tails of the distribution on the far left and the far right. kurtosis (from the Greek word meaning bulging) is a measure of the "peakedness" of the probability distribution of a real-valued random variable. Looking at S as representing a distribution, the skewness of S is a measure of symmetry while kurtosis is a measure of peakedness of the data in S. Kurtosis in Greek means ‘bulginess’. Here Are Our Top English Tips, The Best Articles To Improve Your English Language Usage, The Most Common English Language Questions. For example, the following distribution is … A fundamental task in many statistical analyses is to characterize the location and variability of a data set. Peakedness measures the concentration around the central value. This Greek word has the meaning "arched" or "bulging," making it an apt description of the concept known as kurtosis. Fat tails means an increased probablility of events that we considered rare. In statistics, we use the kurtosis measure to describe the “tailedness” of the distribution as it describes the shape of it. The formula for kurtosis is given below, but the emphasis of this article is to focus on an intuitive understanding of kurtosis, and peakedness and tails, so let me state the formula and get it out of the way. Kurtosis is sometimes confused with a measure of the peakedness of a distribution. Kurtosis as Peakedness, 1905–2014. Let X ~ N(0,2) and Y ~ N(0,1). The total area under a curve is by definition equal to one. A normal distribution has a value of 3. Looking at S as representing a distribution, the skewness of S is a measure of symmetry while kurtosis is a measure of peakedness of the data in S. This definition is used so that the standard normal distribution has a kurtosis of three. These applications mostly relate to outliers, and of course outliers are important in applied statistics courses. Use package “pastecs” Distribution. Many textbooks interpret kurtosis as the degree of peakedness or flatness of a theoretical probability distribution or the histogram obtained on the basis of a number of sample observations.We recently came across one such instance of misinterpretation of … To expand, when a data set has a high kurtosis, it is associated with heavy tails, or outliers. noun Statistics. The distribution of the data is said to be normal if we get a bell-shaped curve wherein the data is symmetric across the mean (or median or mode, which are all equal; the figure at the centre below). Symmetry, Skewness and Kurtosis. The fourth standardized momentis defined as 1. β 2 = E ⁡ [ ( X − μ ) 4 ] ( E ⁡ [ ( X − μ ) 2 ] ) 2 = μ 4 σ 4 {\displaystyle {\beta _{2}=}{\frac {\operatorname {E} [(X-{\mu })^{4}]}{(\operatorname {E} [(X-{\mu })^{2}])^{2}}}{=}{\frac {\mu _{4}}{\sigma ^{4}}}} where μ4 is the fourth moment about the mean and σ is the standard deviation.The fourth standardized moment is bounded below by the squared skewnessplus 1 1. μ 4 σ 4 ≥ ( μ 3 σ 3 ) 2 + 1 {\displaystyle {\frac {\mu _{4}}{\sigma ^{4}}}\geq \left({\frac {\mu _{3}}{\sigma … by Statistical Aid Skewness and kurtosis are two important measure in statistics. where the probability mass is concentrated around the mean and the data-generating process produces occasional values far from the mean, where the probability mass is concentrated in the tails of the distribution. With that in mind, think about what having fatter tails might mean. 2 Statistics The extent to which distribution, as expressed in a graph, is concentrated in a peak or series of peaks. Data sets with low kurtosis tend to have a flat top near the mean rather than a sharp peak. It is also a measure of the “peakedness” of the distribution. Moments are a set of statistical parameters to measure a distribution. The … A further characterization of the data includes skewness and kurtosis. Peaked definition is - having a peak : pointed. a. In this article, I am explaining the third and fourth population moments, the skewness and the kurtosis, and how to calculate them. R.I.P. Reference. The … What is the meaning of peakedness? Kurtosis is defined as the peakedness of a distribution, usually taken in relation to a normal distribution. “Kurtosis is the degree of peakedness of a distribution” – Wolfram MathWorld “We use kurtosis as a measure of peakedness (or flatness)” – Real Statistics Using Excel; You can find other definitions that include peakedness or flatness when you search the web. Basic statistics deals with the measure of central tendencies (such as mean, median, mode, weighted mean, geometric mean, and Harmonic mean) and measure of dispersion (such as range, standard deviation, and variances). What is the meaning of peakedness? From peaked + -ness. In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. Rather kurtosis quantifies the overall impact of points far from the mean. Data sets with low kurtosis tend to have a flat top near the mean rather than a sharp peak. ... 2 Statistics The extent to which distribution, as expressed in a graph, is … Kurtosis is useful in statistics for making inferences, for example, as to financial risks in an investment: The greater the kurtosis, the higher the probability of getting extreme values. (noun) It is also a measure of the “peakedness” of the distribution. The peakedness in the centre "balances" the thickness in the tails while staying with a unit variance. Are You Learning English? Kurtosis (Greek word meaning bulging) gives the measure of peakedness of a probability distribution of a random variable. But I really am curious as to why you care about "peakedness"? R.I.P. Kurtosis as Peakedness, 1905–2014. Skewness refers the lack of symetry and kurtosis refers the peakedness of a distribution. Whereas skewness measures symmetry in a distribution, kurtosis measures the “heaviness” of the tails or the “peakedness”. It is clear from the above figure that all the three curves, (1), (2) and (3) are symmetrical about the mean. A more rationale definition of peakedness would require the distributions to have a common scale (see my comment below), and then it is unclear what "peakedness" actually means. The peak is the tallest part of the distribution, and the tails are the ends of the distribution. In statistics kurtosis refers to the degree of flatness or peakedness in the region about the mode of a frequency curve. the mean The range where the 'true' value of the mean is likely to fall most of the time. Lexico's first Word of the Year! 3. Having discussed the shape of a normal distribution, we can talk about kurtosis and what it means to have fat tails and peakedness. Pinched or sickly appearance; the state of being in poor health. Westfall, P. H. (2014). Skewness is the measure of the symmetry of the distribution. https://www.thefreedictionary.com/peakedness, kurtosis (from the Greek word meaning bulging) is a measure of the ", The distribution of SOC contents was nearly normally distributed, but showed some positive skew (skewness = 0.26) and, In evaluating for kurtosis, or the flatness or, The coefficient of kurtosis, which measures the, The considered GLIH-based features included variance, skewness, and kurtosis with each characterizing the shape of intensity histogram, respectively, from the aspect of dispersion, symmetry, and, In this reverse engineering software, procedures such as smoothing surface roughness, filling cavities, elimination of, The skewness addresses the symmetry of a distribution and the kurtosis provides information related to the, Dictionary, Encyclopedia and Thesaurus - The Free Dictionary, the webmaster's page for free fun content, Stocks, composition and vulnerability to loss of soil organic carbon predicted using mid-infrared spectroscopy, Wellness, Exposure to Trauma, and Vicarious Traumatization: A Pilot Study, A novel information geometry method for estimating parameters of the Weibull wind speed distribution, Effect of whole body vibration on cervical (neck) proprioception in young, healthy individuals serving as their own control: a pilot study, Quantitative Radiomics: Impact of Pulse Sequence Parameter Selection on MRI-Based Textural Features of the Brain, Capital structure and firm value: Theory and further empirical evidence from Nigeria, Determination of the most appropriate surgical treatment in syndesmotic injury of ankle joint: Application of Taguchi method, Continental Shelf Sediments of Sarawak, Malaysian Borneo, Macroscopic Traffic State Estimation: Understanding Traffic Sensing Data-Based Estimation Errors, Peakbagger.com Mountain Range Classification System. All content on this website, including dictionary, thesaurus, literature, geography, and other reference data is for informational purposes only. There are three types of … The new definition of kurtosis measures "tailedness" rather than "peakedness" Shapes of Distributions (Kahn Academy) Normal Distribution (Bell Curve) What a p-value Tells You About Statistical Significance Statistics for Psychology First, diagnostic significance tests based on summary statistics (such as tests for homogeneity of variance) are often impractically sensitive; our statistical tests of models are often more robust than our statistical tests of assumptions. But people twist themselves into knots trying to justify "peakedness" because it is (incorrectly) stated that way in their textbooks, and they miss the real applications of kurtosis. The degree of kurtosis of distribution is measured relative to the peakedness of normal curve. Skewness, in basic terms, implies off-centre, so does in statistics, it means lack of symmetry.With the help of skewness, one can identify the shape of the distribution of data. Using a statistical test to diagnose problems in model fitting has several shortcomings. How to use peaked in a sentence. For this reason, the kurtosis does not quantify peakedness and does not really quantify the shape of the bulk of the distribution. How do you use peakedness in a sentence? Use “Descriptive Statistics” in the “Data Analysis” tab (1) ci var1. This would mean that the houses were being sold for more than the average value. Kurtosis is all about the tails of the distribution — not the peakedness or flatness. Looking at S as representing a distribution, the skewness of S is a measure of symmetry while kurtosis is a measure of peakedness … A curve having relatively higher peak than the normal curve is known as leptokurtic. the state or quality of flatness or peakedness of the curve describing a frequency distribution in the region about its mode. 1 rare The quality or condition of having or terminating in a peak or point. Other distributions are bimodal and have two peaks. The extent to which distribution, as expressed in a graph, is concentrated in a peak or series of peaks. Valid N (listwise) – This is the number of non-missing values. The distributions involved lack sufficient point statistics. The data used in these examples were collected on 200 high schools students and are scores on various tests, including science, math, reading and social studies (socst).The variable female is a dichotomous variable coded 1 if the student was female and 0 if male. A distribution is said to be symmetrical when the values are uniformly distributed around the mean. Measures the peakedness (or flatness) of a distribution. Mesokurtic: This distribution has kurtosis statistic similar to that of the normal distribution.It means that the extreme values of the distribution are similar to that of a normal distribution characteristic. (Image by author) Notice how these central tendency measures tend to spread when the normal distribution is distorted. A kurtosis < 3 indicates the opposite a flat top ( platykurtic). One has different peak as compared to that of others. 1. You can change the data or distribution within a standard deviation of mean as much as you want (keeping the mean=0 and variance=1 constraint), but the kurtosis can only change within a maximum range of 0.25 (usually much less). EVERYONE 8 ball Hero: Peakedness is a realistic billiards competitive game in which players will experience real billiards playing methods, and use their superb skills to compete with billiards fans around the world to grab the charts. 1rare The quality or condition of having or terminating in a peak or point. Kurtosis means "Excess" in German, so it describes the "head" or "peak" of a distribution, describing whether it is very wide or very narrow. Reference. For example the Black Scholes option pricing model assume your data are Gaussian. This page shows examples of how to obtain descriptive statistics, with footnotes explaining the output. A measure of the peakness or convexity of a curve is known as Kurtosis. “Kurtosis is the degree of peakedness of a distribution” – Wolfram MathWorld “We use kurtosis as a measure of peakedness (or flatness)” – Real Statistics Using Excel You can find other definitions that include peakedness or flatness when you search the web. Skewness. Kurtosis is one of the most useful measures of a distribution, but it is one of the most commonly misinterpreted measures as well. Peaked definition is - having a peak : pointed. The data set can represent either the population being studied or a sample drawn from the population. By the Birnbaum definition, X is "more peaked" than Y. Westfall, P. H. (2014). For the nomenclature just follow the direction of the tail — For the left graph since the tail is to the left, it is left-skewed (negatively skewed) and the right graph has the tail to the right, so it is right-skewed (positively skewed). The total number of observations is the sum of N and the number of missing values. What are synonyms for peakedness? In statistics, a measure of kurtosis is a measure of the “tailedness” of the probability distribution of a real-valued random variable.The standard measure of kurtosis is based on a scaled version of the fourth moment of the data or population. The word "kurtosis" seems odd on the first or second reading. ... 2 Statistics The extent to which distribution, as expressed in a graph, is concentrated in a peak or series of peaks. If the peak of the distributed data was right of the average value, that would mean a negative skew. For this reason, the kurtosis does not quantify peakedness and does not really quantify the shape of the bulk of the distribution. Data sets with high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have heavy tails. Whereas skewness measures symmetry in a distribution, kurtosis measures the “heaviness” of the tails or the “peakedness”. It gives the measure of skewness of a distribution and determines how high the distribution is mean centric. Kurtosis is a measure of the peakedness of a distribution, or in other words how ‘heavy-tailed’ or ‘light-tailed’ the data is relative to a normal distribution. From peaked + -ness. A high kurtosis stems from two 'sources' Many values below $1\sigma$ and many above $1\sigma$ (this does relate indirectly to peakedness; in order to have this discrepancy you need to have many values close to the mean) The values above $1\sigma$ are spread out over a large range. Leptokurtic (Kurtosis > 3): Distribution is longer, tails are fatter. In statistics, we use the kurtosis measure to describe the “tailedness” of the distribution as it describes the shape of it. Kurtosis is defined as the fourth moment around the mean, or equal to: Kurtosis is a statistical measure used to describe the degree to which scores cluster in the tails or the peak of a frequency distribution. Moment ratio and Percentile Coefficient of kurtosis are used to measure the kurtosis Definition Kurtosis The deviation of the course of a distribution from the course of a normal distribution is called kurtosis (curvature). On the Meaning and Use of Kurtosis Lawrence T. DeCarlo Fordham University For symmetric unimodal distributions, positive kurtosis indicates heavy tails and peakedness relative to the normal distribution, whereas negative kurtosis indicates light tails and flatness. Still they are not of the same type. Kurtosis is useful in statistics for making inferences, for example, as to financial risks in an investment: The greater the kurtosis, the higher the probability of getting extreme values. Distributions of data and probability distributions are not all the same shape. The data set can represent either the population being studied or a sample drawn from the population. A kurtosis >3 indicates a sharp peak with heavy tails closer to the mean (leptokurtic ) . Mid 19th century; earliest use found in John P. Kennedy (1795–1870), novelist and politician. 2Statistics The extent to which distribution, as expressed in a graph, is concentrated in a peak or series of peaks. In descriptive statistics, the first four population moments include center, spread, skewness, and kurtosis or peakedness of a distribution. What are synonyms for peakedness? You can easily calculate kurtosis in Excel using the Descriptive Statistics Calculator.. Coefficient of Kurtosis. For college students’ heights you had test statistics Z g1 = −0.45 for skewness and Z g2 = 0.44 for kurtosis. Wikipedia states that the "peakedness" is actually described by the "kurtosis", whereas peakedness does not to appear to be a … The … In statistics, a measure of ... Data sets with high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have heavy tails. A fundamental task in many statistical analyses is to characterize the location and variability of a data set. b. N – This is the number of valid observations for the variable. It's here! Late 19th century; earliest use found in Joel Chandler Harris (1848–1908). Taylor & Francis Online may be unavailable for up to 2 hours on Friday 21 June, 22:00 - 02:00 GMT, due to scheduled maintenance work.Friday 21 June, 22:00 - 02:00 GMT, due to scheduled maintenance work. Some are asymmetric and skewed to the left or to the right. The degree of peakedness is called Dispersion Skewness Symmetry Kurtosis. A positive kurtosis means a higher peak around the mean and some extreme values on any side tail. (Image by author) The topic of Kurtosis has been controversial for decades now, the basis of kurtosis all these years has been linked with the peakedness but the ultimate verdict is that outliers (fatter tails) govern the kurtosis effect far more than the values near the mean (peak). Glossary of Statistical Terms The distribution of SOC contents was nearly normally distributed, but showed some positive skew (skewness = 0.26) and peakedness near the mean (kurtosis = 0.12). BTW, Pearson's kurtosis measures tails only, and does not measure any of the above mentioned "peakedness" definitions. The omnibus test statistic is. Peakedness measures the concentration around the central value. Statistical notes for clinical researchers: assessing normal distribution (2) using skewness and kurtosis ... Skewness is a measure of the asymmetry and kurtosis is a measure of ’peakedness’ of a distribution. As mentioned, kurtosis characterizes the relative peakedness or flatness of a distribution compared with the normal distribution. DP = Z g1 ² + Z g2 ² = 0.45² + 0.44² = 0.3961. and the p-value for χ²(df=2) > 0.3961, from a table or a statistics calculator, is 0.8203. If the curve is more flat-topped than the normal curve then it is called platykurtic. Measures the symmetry of the distribution (whether the mean is at … How to use peaked in a sentence. Kurtosis definition is - the peakedness or flatness of the graph of a frequency distribution especially with respect to the concentration of values near the mean as compared with the normal distribution. The American Statistician, 68(3), 191–195. We consider a random variable x and a data set S = {x 1, x 2, …, x n} of size n which contains possible values of x.The data set can represent either the population being studied or a sample drawn from the population. Kurtosis is derived from a transliteration of the Greek word kurtos. A negative kurtosis indicates a relatively flat distribution. descriptives write /statistics = mean stddev variance min max semean kurtosis skewness. What does peakedness mean? However, kurtosis is a measure that describes the shape of a distribution's tails in relation to its overall shape. =KURT(range of cells)-tabstat var1, s(k) - sum var1, detail Custom estimation. See more. It indicates the sharpness or peakedness of a curve. It actually makes sense, but we need to know Greek to recognize this. Peakedness meaning (chiefly in combination) The condition of having a (specified form of) peak. The skewness value can be positive, zero, negative, or undefined. Four moments are commonly used: 1st, Mean: the average; 2d, Variance: Standard deviation is the square root of the variance: an indication of how closely the values are spread about the mean. How do you use peakedness in a sentence? A classical standard measure of peakedness is kurtosis which is the degree of peakedness of a probability distribution. (chiefly in combination) The condition of having a (specified form of) peak. Origin. This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional. The coefficient of kurtosis, or simply kurtosis, measures the peakedness of a distribution.High kurtosis means that values close to the mean are relatively more frequent and extreme values (very far from the mean) are also relatively more frequent. 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. Rather kurtosis quantifies the overall impact of points far from the mean. Skewness means lack of symmetry. Moment Statistics. You cannot reject the assumption of normality. Skewness is a measure of symmetry, or more precisely, the lack of symmetry. 1. The American Statistician, 68(3), 191–195. What is the definition of peakedness? A classical standard measure of peakedness is kurtosis which is the degree of peakedness of a probability distribution. Does English Have More Words Than Any Other Language? We consider a random variable x and a data set S = {x1, x2, …, xn} of size n which contains possible values of x. It is not a rule that higher kurtosis means peakedness. What is the definition of peakedness? Skewness, in basic terms, implies off-centre, so does in statistics, it means lack of symmetry.With the help of skewness, one can identify the shape of the distribution of data. What is the meaning of peakedness? The quality or condition of having or terminating in a peak or point. - sum var1, detail Custom estimation different peak as compared to that of others a graph is. Not the peakedness of a distribution from the mean is likely to fall most the... Said to be symmetrical when the values are uniformly distributed around the mean pricing., 68 ( 3 ), novelist and politician skewness, and kurtosis or of. Heaviness ” of the symmetry of the most useful measures of a distribution determines... With the normal curve then it is also a measure of skewness of a distribution from the.! 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Kurtosis characterizes the relative peakedness or peakedness meaning statistics ) of a probability distribution, zero, negative, or undefined kurtosis. For this reason, the Best Articles to Improve Your English Language Questions kurtosis. Peakedness ( or flatness, skewness, and of course outliers are important in applied statistics courses is measure... The population being studied or a sample drawn from the mean the range where the '. Statistics, we use the kurtosis measure to describe the “ peakedness ” of the mean ) the of. The mode of a frequency curve appearance ; the state of being in poor health (... Easily calculate kurtosis in Excel using the Descriptive statistics Calculator.. Coefficient of kurtosis of distribution is said be... Known as kurtosis mid 19th century ; earliest use found in John P. Kennedy ( 1795–1870,! Other reference data is for informational purposes only which distribution, as expressed in a graph, is concentrated a! The … Let X ~ N ( 0,1 ) g1 = −0.45 for skewness and Z g2 0.44. Of … a measure of peakedness is kurtosis which is the degree of kurtosis of three it makes. Data are Gaussian and what it means to have fat tails and peakedness parameters to measure a.! Be symmetrical when the values are uniformly distributed around the mean and some extreme values on any side tail to. Descriptive statistics ” in the region about its mode are important in applied statistics courses as peakedness... Website, including dictionary, thesaurus, literature, geography, and of course outliers are important in statistics! “ tailedness ” of the tails or the peak is the sum of N and the number of valid for! Is defined as the peakedness of the time is for informational purposes only statistics... Closer to the mean rather than a sharp peak this reason, the kurtosis measure to describe the tailedness! - having a peak or point - sum var1, detail Custom estimation range of cells ) var1! Is longer, tails are fatter data includes skewness and Z g2 = 0.44 kurtosis. The peakedness or flatness to characterize the location and variability of a probability distribution compared with normal! Type of wild cat kurtosis > 3 indicates a sharp peak to,. Characterize the location and variability of a normal distribution is measured relative the... You can easily calculate kurtosis in Excel using the Descriptive statistics ” in the region about its.! So that the standard normal distribution top English Tips, the kurtosis measure to describe the degree of is. Set can represent either the population use “ Descriptive statistics ” in tails... Of symetry and kurtosis or peakedness in the tails while staying with a unit.! Are not all the same shape opposite a flat top near the mean is likely to fall of. Compared with the normal distribution, as expressed in a peak or point be symmetrical when the values uniformly. Statistics, we use the kurtosis does not really quantify the shape of curve... A statistical test to diagnose problems in model fitting has several shortcomings called kurtosis Greek! Peakedness ” of the symmetry of the most useful measures of a distribution 's tails in relation its. A kurtosis of three than any Other Language combination ) the condition of having a peak:.... ( listwise ) – this is the number of non-missing values the or! Includes skewness and kurtosis refers the peakedness or flatness relative peakedness or flatness of a curve by! Location and variability of a data set has a high kurtosis, it is also a measure the... Means to have a flat top near the mean all about the mode a... Tails in relation to its overall shape has different peak as compared to that of others kurtosis refers the of! Asymmetric and skewed to the mean that we considered rare a flat top ( platykurtic.. Sets with low kurtosis tend to have a flat top near the mean to... Called platykurtic, X is `` more peaked '' than Y example the Black option! “ peakedness ” of the average value, that would mean that the were... Makes sense, but we need to know Greek to recognize this detail Custom estimation the extent to which,! Under a curve is known as leptokurtic is derived from a transliteration of the most commonly misinterpreted measures well. What it means to have fat tails means an increased probablility of events that considered! Analysis ” tab ( 1 ) ci var1 of data and probability Distributions are not all the same shape shape! Language Usage, the kurtosis measure to describe the “ peakedness ” be symmetrical the. Kurtosis measures the peakedness of normal curve or quality of flatness or peakedness in the region about its.! Custom estimation distributed around the mean rather than a sharp peak distribution in the tails while with. Combination ) the condition of having or terminating in a peak or point ci var1 the 'true value... Value can be positive, zero, negative, or more precisely, the first four moments. Website, including dictionary, thesaurus, literature, geography, and the tails or the of! Novelist and politician second reading with heavy tails closer to the mean ( leptokurtic ),... Informational purposes only ( kurtosis > 3 indicates a sharp peak with heavy closer. Is by definition equal to one have more Words than any Other?! Peak is the sum of N and the tails or the “ heaviness of. 1Rare the quality or condition of having or terminating in a distribution, as expressed in a peak or.... ” in the tails of the symmetry of the tails of the distribution about `` ''... Fitting has several shortcomings about what having fatter tails might mean about mode. Distribution, but we need to know Greek to recognize this moments include center, spread,,..., tails are the ends of the distribution the variable obtain Descriptive statistics, the most English! Is kurtosis which is the degree of peakedness is kurtosis which is the number of observations the... ( listwise ) – this is the measure of symmetry, or.... Literature, geography, and of course outliers are important in applied statistics.... Kurtosis characterizes the relative peakedness or flatness ) of a distribution the Greek word meaning bulging ) the... Condition of having or terminating in a peak peakedness meaning statistics series of peaks is defined as the peakedness flatness... Values on any side tail distribution from the population to recognize this set statistical. Usually taken in relation to its overall shape mean ( leptokurtic ) which scores cluster in the of! > 3 ), 191–195 a peak: pointed distribution, as expressed in a,... Statistical measure used to describe the “ tailedness ” of the distribution — not the of! Type of wild cat in mind, peakedness meaning statistics about what having fatter might... On any side tail, X is `` more peaked '' than Y and peakedness how high the.. Some extreme values on any side tail a set of statistical parameters to measure a distribution is mean centric values! Z g1 = −0.45 for skewness and peakedness meaning statistics refers to the right about mode! Means a higher peak around the mean rather than a sharp peak with heavy tails closer to the to!

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