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Skewness and kurtosis interpretation

How to Interpret Excess Kurtosis and Skewness SmartPL

A general guideline for skewness is that if the number is greater than +1 or lower than -1, this is an indication of a substantially skewed distribution. For kurtosis, the general guideline is that if the number is greater than +1, the distribution is too peaked. Likewise, a kurtosis of less than -1 indicates a distribution that is too flat. Distributions exhibiting skewness and/or kurtosis that exceed these guidelines are considered nonnormal. (Hair et al., 2017, p. 61) Most commonly a distribution is described by its mean and variance which are the first and second moments respectively. Another less common measures are the skewness (third moment) and the kurtosis (fourth moment). Today, we will try to give a brief explanation of these measures and we will show how we can calculate them in R If the coefficient of kurtosis is larger than 3 then it means that the return distribution is inconsistent with the assumption of normality in other words large magnitude returns occur more frequently than a normal distribution. Skewness. The frequency of occurrence of large returns in a particular direction is measured by skewness of shape give a more precise evaluation: skewness tells you the amount and direction of skew(departure from horizontal symmetry), and kurtosis tells you how tall and sharp the central peak is, relative to a standard bell curve

If skewness is between −1 and −½ or between +½ and +1, the distribution is moderately skewed. If skewness is between −½ and +½, the distribution is approximately symmetric. With a skewness of −0.1098, the sample data for student heights are approximately symmetric. Caution: This is an interpretation of the data you actually have. Whe Kurtosis is a measure of how differently shaped are the tails of a distribution as compared to the tails of the normal distribution. While skewness focuses on the overall shape, Kurtosis focuses on the tail shape. Kurtosis is defined as follows Die Kurtosis gibt an, wie weit die Randbereiche einer Verteilung von der Normalverteilung abweichen. Durch die Kurtosis können Sie ein erstes Verständnis der allgemeinen Merkmale der Verteilung Ihrer Daten erlangen. Basislinie: Kurtosis-Wert 0. Daten, die perfekt einer Normalverteilung folgen, weisen den Kurtosis-Wert 0 auf. Normalverteilte Daten bilden die Basislinie für die Kurtosis. Wenn die Kurtosis einer Stichprobe wesentlich von 0 abweicht, kann dies darauf hinweisen, dass die Daten.

Skewness and Kurtosis in Statistics R-blogger

Skewness, Kurtosis, and the Normal Curve. Copyright 2019, Karl L. Wuensch - All rights reserved. Jump to Table 1. Skewness. In everyday language, the terms skewed and askew are used to refer to something that is out of line or distorted on one side. When referring to the shape of frequency or probability distributions, skewness refers to asymmetry of the distribution. A distribution with an asymmetric tail extending out to the right is referred to as positively skewed. The equation for kurtosis is pretty similar in spirit to the formulas we've seen already for the variance and the skewness. Except that where the variance involved squared deviations and the skewness involved cubed deviations, the kurtosis involves raising the deviations to the fourth power Skewness and Kurtosis A fundamental task in many statistical analyses is to characterize the location and variability of a data set. A further characterization of the data includes skewness and kurtosis. Skewness is a measure of symmetry, or more precisely, the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the center point So we can conclude from the above discussions that the horizontal push or pull distortion of a normal distribution curve gets captured by the Skewness measure and the vertical push or pull distortion gets captured by the Kurtosis measure. Also, it is the impact of outliers that dominate the kurtosis effect which has its roots of proof sitting in the fourth-order moment-based formula. I hope.

Kurtosis tells you virtually nothing about the shape of the peak - its only unambiguous interpretation is in terms of tail extremity. Dr. Westfall includes numerous examples of why you cannot relate the peakedness of the distribution to the kurtosis. Dr. Donald Wheeler also discussed this in his two-part series on skewness and kurtosis. He said: Kurtosis was originally thought to be. Verstehen, was Schiefe und Kurtosis ist. In diesem Artikel werden wir zwei der wichtigen Konzepte in der deskriptiven Statistik durchgehen - Skewness und Kurtosis. Am Ende des Artikels finden Sie Antworten auf Fragen wie Schiefe und Kurtosis, rechte / linke Schiefe, wie Schiefe und Kurtosis gemessen werden, wie nützlich sie ist usw Use skewness and kurtosis to help you establish an initial understanding of your data. In This Topic. Skewness; Kurtosis; Skewness. Skewness is the extent to which the data are not symmetrical. Whether the skewness value is 0, positive, or negative reveals information about the shape of the data. Figure A. Figure B. Symmetrical or non-skewed distributions. As data becomes more symmetrical, its. When you google Kurtosis, you encounter many formulas to help you calculate it, talk about how this measure is used to evaluate the peakedness of your data, maybe some other measures to help you do so, maybe all of a sudden a side step towards Skewness, and how both Skewness and Kurtosis are higher moments of the distribution Interprétation de Kurtosis. Kurtosis est la moyenne des données standardisées élevées à la quatrième puissance. Toutes les valeurs standardisées inférieures à 1 (c'est-à-dire les données à un écart-type de la moyenne, où serait le «pic»), ne contribuent pratiquement rien à l'aplatissement, car le fait d'élever un nombre inférieur à 1 à la quatrième puissance le rend plus proche de zéro. Les seules valeurs de données (observées ou observables) qui contribuent à l.

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. Kurtosis, on the other hand, refers to the pointedness of a peak in the distribution curve.The main difference between skewness and kurtosis is that the former talks of the degree of symmetry, whereas the latter talks. Skewness is a measure of asymmetry or distortion of symmetric distribution. It measures the deviation of the given distribution of a random variable. Random Variable A random variable (stochastic variable) is a type of variable in statistics whose possible values depend on the outcomes of a certain random phenomenon In probability theory and statistics, kurtosis (from Greek: κυρτός, kyrtos or kurtos, meaning curved, arching) is a measure of the tailedness of the probability distribution of a real-valued random variable. Like skewness, kurtosis describes the shape of a probability distribution and there are different ways of quantifying it for a theoretical distribution and corresponding ways of estimating it from a sample from a population. Different measures of kurtosis may have. In this blog, we have seen how kurtosis/excess kurtosis captures the 'shape' aspect of distribution, which can be easily missed by the mean, variance and skewness. Furthermore, we discussed some common errors and misconceptions in the interpretation of kurtosis. Kurtosis is a very useful metric to quantify the tail-risk in finance. Ignoring tail-risk can potentially lead to the overestimation of alphas, and hence tail-risk/kurtosis-risk evaluation should be a part of the overall.

Interpretation of Skewness, Kurtosis, CoSkewness

  1. Along with skewness Poisson Distribution The Poisson Distribution is a tool used in probability theory statistics to predict the amount of variation from a known average rate of occurrence, within, kurtosis is an important descriptive statistic of data distribution. However, the two concepts must not be confused with each other. Skewness essentially measures the symmetry of the distribution.
  2. Sample skewness and kurtosis are limited by functions of sample size. The limits, or approximations to them, have repeatedly been rediscovered over the last several decades, but nevertheless seem to remain only poorly known. The limits impart bias to estimation and, in extreme cases, imply that no sample could bear exact witness to its parent distribution. The main results are explained in a.
  3. Measures of Skewness And Kurtosis Chapter 9. Measures of Skewness and Kurtosis Symmetric vs Skewed Distribution (page 260) Definition 9.1 If it is possible to divide the histogram at the center into two identical halves, wherein each half is a mirror image of the other, then it is called a symmetric distribution. Otherwise, it is called a skewed distribution. Examples of Symmetric.
  4. Die Wölbung oder Kurtosis einer Häufigkeitsverteilung liefert Dir ein Maß für ihre Spitzheit oder Flachheit. In den Häufigkeitsverteilungen werden 810 bzw. 602 Personen auf 7 Größenklassen aufgeteilt. Im linken Fall sind alle Größenklassen deutlich mit Personen belegt, entfernt von der Mitte sinken die Häufigkeiten dagegen, wenn auch langsam
  5. sktest— Skewness and kurtosis test for normality 3 Methods and formulas sktest implements the test described byD'Agostino, Belanger, and D'Agostino(1990) with the empirical correction developed byRoyston(1991c). Let g 1 denote the coefficient of skewness and b 2 denote the coefficient of kurtosis as calculate

The measure of kurtosis is defined as the ratio of fourth central moment to the square of the second central moment. The measure is a pure number and is always positive. Base on the value of kurtosis, we can classify a distribution as, If kurtosis>3, the distribution is leptokurtic. If kurtosis<3, the distribution is platykurtic Interpretation: A positive value indicates positive skewness. A 'zero' value indicates the data is not skewed. Lastly, a negative value indicates negative skewness or rather a negatively skewed distribution. Sample Kurtosis. Sample kurtosis is always measured relative to the kurtosis of a normal distribution, which is 3. Therefore, we are. To resolve the problem, another method of assessing normality using skewness and kurtosis of the distribution may be used, which may be relatively correct in both small samples and large samples. 1) Skewness and kurtosis. Skewness is a measure of the asymmetry and kurtosis is a measure of 'peakedness' of a distribution. Most statistical packages give you values of skewness and kurtosis as well.

Skewness - Skewness measures the degree and direction of asymmetry. A symmetric distribution such as a normal distribution has a skewness of 0, and a distribution that is skewed to the left, e.g., when the mean is less than the median, has a negative skewness. n. Kurtosis - Kurtosis is a measure of the heaviness of the tails of a distribution. A normal distribution has a kurtosis of 3. The skewness and kurtosis are higher-order statistical attributes of a time series. Skewness indicates the symmetry of the probability density function (PDF) of the amplitude of a time series. A time series with an equal number of large and small amplitude values has a skewness of zero. A time series with many small values and few large values is positively skewed (right tail), and the. A symmetric distribution such as a normal distribution has a skewness of 0, and a distribution that is skewed to the left, e.g. when the mean is less than the median, has a negative skewness. i. Kurtosis - Kurtosis is a measure of tail extremity reflecting either the presence of outliers in a distribution or a distribution's propensity for producing outliers (Westfall,2014 Mithilfe von Skewness- und Kurtosis-Statistiken können Sie bestimmte Arten von Abweichungen von der Normalität Ihres Datengenerierungsprozesses beurteilen. Es handelt sich jedoch um sehr variable Statistiken. Die oben angegebenen Standardfehler sind nicht nützlich, da sie nur unter Normalität gültig sind, was bedeutet, dass sie nur als Test für Normalität nützlich sind, eine im.

Measures of Shape: Skewness and Kurtosi

Skewness Kurtosis test for normality. Skewness is a measure of the asymmetry of the probability distribution of a random variable about its mean. It represents the amount and direction of skew. On the other hand, Kurtosis represents the height and sharpness of the central peak relative to that of a standard bell curve. The figure below shows. L'analyse de la statistique descriptive consiste à évaluer le Skewness qui est un indicateur d'asymétrie, calculer le Kurtosis qui présente un coefficient d'aplatissement et d'effectuer l'essai de Jarque-Bera qui présente un test de normalité. 3.2.1.1. Le Skewness : C'est un outil statistique qui mesure le degré d'asymétrie de la distribution soit le moment d'ordre 3. Along with skewness Poisson Distribution The Poisson Distribution is a tool used in probability theory statistics to predict the amount of variation from a known average rate of occurrence, within, kurtosis is an important descriptive statistic of data distribution. However, the two concepts must not be confused with each other. Skewness essentially measures the symmetry of the distribution. The Effect of Skewness and Kurtosis on Mean and Covariance Structure Analysis: The Univariate Case and Its Multivariate Implication. Ke Yuan. Related Papers. Structural Equation Modeling with Small Samples: Test Statistics. By ke yuan. 10 Structural Equation Modeling. By ke yuan. Mean Comparison: Manifest Variable Versus Latent Variable. By Ke-Hai Yuan. Finite Normal Mixture Sem Analysis by. Ajili (2004) in a study on the French Stock Market found co-skewness and co-kurtosis don't subsume the SMB and HML factors. Chung, Johnson and Schill (2004) found it is conceivable that the SMB and HML loadings are such good proxies for the higher-order co-moments that, given problems of estimating higher-order co-moments, the Fama-French factors could be superior in actual use

Skewness and Kurtosis: A Definitive Guide. While dealing with data distribution, Skewness and Kurtosis are the two vital concepts that you need to be aware of. Today, we will be discussing both the concepts to help your gain new perspective. Skewness gives an idea about the shape of the distribution of your data Skewness, Kurtosis, Discreteness, and Ceiling Effects . Abstract . Many statistical analyses benefit from the assumption that unconditional or conditional distributions are continuous and normal. Over fifty years ago in this journal, Lord (1955) and Cook (1959) chronicled departures from normality in educational tests, and Micerri (1989) similarly showed that the normality assumption is met. This article shows how to compute Hogg's robust measures of skewness and kurtosis. The article was inspired by Bono et al. (2020), who explore the bias and accuracy of Hogg's measures of skewness and kurtosis as compared to the usual moment-based skewness and kurtosis. They conclude that Hogg's estimators are less biased and more accurate. Bono et al. provide a SAS macro that computes Hogg's. Mean-Variance-Skewness-Kurtosis Portfolio Optimization with Return and Liquidity Xiaoxin W. Beardsley1, Brian Field2 and Mingqing Xiao3 Abstract In this paper, we extend Markowitz Portfolio Theory by incorporating the mean, variance, skewness, and kurtosis of both return and liquidity into an investor's objective function. Recent studies reveal that in addition to return, liquidity is also a.

Skewness and Kurtosis in Statistics - Predictive Hack

In statistics, skewness and kurtosis are the measures which tell about the shape of the data distribution or simply, both are numerical methods to analyze the shape of data set unlike, plotting graphs and histograms which are graphical methods. These are normality tests to check the irregularity and asymmetry of the distribution. To calculate skewness and kurtosis in R language, moments. Skewness and Kurtosis indicator. This indicator shows the skewness and kurtosis of a title. For all the statistic lovers . 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. The skewness value can be positive or negative, or undefined

Testing for Normality using Skewness and Kurtosis by

  1. Die Schiefe (englisch skewness bzw. skew) ist eine statistische Kennzahl, die die Art und Stärke der Asymmetrie einer Wahrscheinlichkeitsverteilung beschreibt. Sie zeigt an, ob und wie stark die Verteilung nach rechts (rechtssteil, linksschief, negative Schiefe) oder nach links (linkssteil, rechtsschief, positive Schiefe) geneigt ist
  2. Example 1: Use the skewness and kurtosis statistics to gain more evidence as to whether the data in Example 1 of Graphical Tests for Normality and Symmetry is normally distributed. As we can see from Figure 4 of Graphical Tests for Normality and Symmetry (cells D13 and D14), the skewness for the data in Example 1 is .23 and the kurtosis is -1.53
  3. Skewness and kurtosis explained using examples and case studies based on climatic changes to explain these concepts. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising
  4. Like skewness, kurtosis is a statistical measure that is used to describe distribution. Whereas skewness differentiates extreme values in one versus the other tail, kurtosis measures extreme.
  5. Skewness and kurtosis provide quantitative measures of deviation from a theoretical distribution. Here we will be concerned with deviation from a normal distribution. Skewness. In everyday English, skewness describes the lack of symmetry in a frequency distribution. A distribution is right (or positively) skewed if the tail extends out to the right - towards the higher numbers. A distribution.

So wirken sich Schiefe und Kurtosis auf eine Verteilung

  1. One last point I would like to make: the skewness and kurtosis statistics, like all the descriptive statistics, are designed to help us think about the distributions of scores that our tests create. Unfortunately, I can give you no hard-and-fast rules about these or any other descriptive statistics because interpreting them depends heavily on the type and purpose of the test being analyzed.
  2. For test 5, the test scores have skewness = 2.0. A histogram of these scores is shown below. The histogram shows a very asymmetrical frequency distribution. Most people score 20 points or lower but the right tail stretches out to 90 or so. This distribution is right skewed. If we move to the right along the x-axis, we go from 0 to 20 to 40 points and so on. So towards the right of the graph.
  3. taan sebab warisan budaya semakin dilupakan. The.
  4. Further, I took a look on the skewness and kurtosis of my distribution. Shapiro- Wilk-Test Skewness Kurtosis W p Statistic SE Z Statistic SE Z 0.92 0.41 0.39 0.66 0.59 -0.99 1.27 -0.78 As -1.96 < Z < 1.96 I reject the H1 for skewness as well for kurtosis

Skewness and Kurtosis P Subhash Chandra Bose1*, R Nagaraju2, Damineni Saritha2, K Deepthy1 and B Supraja1 1Department of Pharmaceutics, MNR College of Pharmacy, Sangareddy, Telangana, India 2Department of Pharmaceutics, Sultan ul Uloom College of Pharmacy, Hyderabad, Telangana, India _____ ABSTRACT For pharmaceutical powders it is unusual to be completely monosized as they are frequently. The paper considers some properties of measures of asymmetry and peakedness of one dimensional distributions. It points to some misconceptions of the first and the second Pearson coefficients, the measures of asymetry and shape, that frequently occur in introductory textbooks. Also it presents different ways for obtaining the estimated values for the coefficients of skewness and kurtosis and. Skewness and Kurtosis Assignments & Project are generally puzzle and complex, and needs a deep understanding of the subject understanding. Specialists at Spsshelponline work hard to lead students in the Skewness and Kurtosis help in lucid, specific & understandable method. We wish to share couple of subjects where our Experts have actually shown themselves to be the very best in their. Kurtosis is a characteristic of the shape of the density function related to both the center and the tails. Distributions with density functions that have significantly more mass toward the center and in the tails than the normal distribution are said to have high kurtosis. Kurtosis is invariant under changes in location and scale; thus, kurtosis remains the same after a change in units or the.

Video: Skew and kurtosis — Learning statistics with jamov

1.3.5.11. Measures of Skewness and Kurtosi

Kurtosis wordt eigenlijk alleen maar gebruikt ter beschrijving van de variabele. Variabelen met een hoge score op kurtosis (zeg meer dan 5) zullen nauwelijks enige relatie vertonen met andere variabelen omdat de scores van die variabele allemaal op een kluitje liggen. Een negatieve waarde voor de kurtosis wijst op een vrij platte verdeling. Dat is niet erg omdat er dan een goede spreiding is. An R tutorial on computing the kurtosis of an observation variable in statistics. The excess kurtosis of a univariate population is defined by the following formula, where μ 2 and μ 4 are respectively the second and fourth central moments.. Intuitively, the excess kurtosis describes the tail shape of the data distribution. The normal distribution has zero excess kurtosis and thus the.

Skewness & Kurtosis Simplified

Testing normality including skewness and kurtosis. High levels of skewness (symmetry) and kurtosis (peakedness) of regression/ANOVA model residuals (which may be saved in SPSS) are not desirable and can undermine these analyses. SPSS gives these values (see CBSU Stats methods talk on exploratory data analysis). Steve Simon (see here) gives some sound advice on checking normality assumptions. In Monte Carlo simulations, the most successful of these methods relied on the (Vale & Maurelli, 1983, Psychometrika, 48, 465) family to approximate a distribution via the marginal skewness and kurtosis of the sample data. In Simulation 1, this method provided more accurate confidence intervals of the correlation in non-normal data, at least as compared to no adjustment of the Fisher z. skewness or kurtosis for the distribution is not outside the range of normality, so the distribution can be considered normal. If the values are greater than ± 1.0, then the skewness or kurtosis for the distribution is outside the range of normality, so the distribution cannot be considered normal. This column tells you the number of cases with . These two columns tell you the minimum and.

Are the Skewness and Kurtosis Useful Statistics? BPI

Kurtosis is a statistical measure used to describe the degree to which scores cluster in the tails or the peak of a frequency distribution. The peak is the tallest part of the distribution, and the tails are the ends of the distribution. There are three types of kurtosis: mesokurtic, leptokurtic, and platykurtic. Mesokurtic: Distributions that are moderate in breadth and curves with a medium. Like skewness, kurtosis describes the shape of a probability distribution and there are different ways of quantifying it for a theoretical distribution and corresponding ways of estimating it from a sample from a population. Different measures of kurtosis may have different interpretations. The standard measure of a distribution's kurtosis, originating with Karl Pearson, is a scaled version of. Is there an interpretation of the hyper skewness? Let X be a random variable. The standardized n th moment of X is defined as. E [ ( X − E [ X]) n] Var [ X] n / 2. Special cases are the skewness ( k = 3) and the kurtosis k = 4. The skewness is a measure for the asymmetry of a distribution while the kurtosis measures how peaked the. To calculate the skewness and kurtosis of this dataset, we can use skewness () and kurtosis () functions from the moments library in R: The skewness turns out to be -1.391777 and the kurtosis turns out to be 4.177865. Since the skewness is negative, this indicates that the distribution is left-skewed. This confirms what we saw in the histogram

Skewness & Kurtosis

Was sind Schiefe und Kurtosis? - ICHI

  1. Horizontal Skew: The difference in implied volatility (IV) across options with different expiration dates. Horizontal skew refers to the situation where at a given strike price, IV will either.
  2. acy are presented. The basic measures to evaluate the nature of the wind speed in the presence of neutrosophic numbers are given. The importance of the proposed measures of skewness and kurtosis under neutrosophic statistics is discussed over the existing measures of skewness and kurtosis under classical.
  3. Problems based on Skewness and concepts. We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads

How skewness and kurtosis affect your distribution

non-normally distributed, with skewness of 1.87 (SE = 0.05) and kurtosis of 3.93 (SE = 0.10) Participants were 98 men and 132 women aged 17 to 25 years (men: M = 19.2, SD = 2.32; women: M = 19.6, SD = 2.54). Non-parametric tests Do not report means and standard deviations for non-parametric tests. Report the median and range in the text or in a table. The statistics U and Z should be. Die Wölbung oder Kurtosis einer Häufigkeitsverteilung liefert Dir ein Maß für ihre Spitzheit oder Flachheit. In den Häufigkeitsverteilungen werden 810 bzw. 602 Personen auf 7 Größenklassen aufgeteilt. Im linken Fall sind alle Größenklassen deutlich mit Personen belegt, entfernt von der Mitte sinken die Häufigkeiten dagegen, wenn auch langsam Skewness and Kurtosis: A Definitive Guide. While dealing with data distribution, Skewness and Kurtosis are the two vital concepts that you need to be aware of. Today, we will be discussing both the concepts to help your gain new perspective. Skewness gives an idea about the shape of the distribution of your data

Kurtosis Interpretation - Eran Ravi

  1. Worse, skewness and kurtosis statistics and formulas are opaque to the average student, and lack concrete reference points. Cobb and Moore (1997, p. 803) note that In data analysis, context provides meaning. Realizing this, over the past several decades, more and more instructors are using sample data arising from real (or realistic) scenarios. One result is that students are learning.
  2. ology, modified from Krumbein and Pettijohn (1938) and Folk and Ward (1957) (f is the frequency in per cent; m is the mid-point of each class interval in metric (m m) or.
  3. 123 Skewness and kurtosis 489 Distributions with kurtosis depending of their parameters are for example: gamma, beta, chi, Frechet, inverse normal, lognormal, Weibull, etc. There are also distributions that have not kurtosis as for example Cauchy distribution. If the coefficient of kurtosis is less than −1.2 (the value for the coefficient of kurtosis for the uniform distribution), then the.

Skewness et Kurtosis dans les statistiques - ICHI

We ended 2017 by tackling skewness, and we will begin 2018 by tackling kurtosis. R Views Home About Contributors. Home: About: Contributors: R Views An R community blog edited by Boston, MA. 320 Posts. 313 Tags Introduction to Kurtosis 2018-01-04. by Jonathan Regenstein. Happy 2018 and welcome to our first reproducible finance post of the year! What better way to ring in a new beginning than. The Skewness-Kurtosis All test for normality is one of three general normality tests designed to detect all departures from normality. It is comparable in power to the other two tests. The normal distribution has a skewness of zero and kurtosis of three. The test is based on the difference between the data's skewness and zero and the data's kurtosis and three. The test rejects the hypothesis.

Skewness and Kurtosis of Each ItemKurtosis

Interpretation: The skewness here is -0.01565162. This value implies that the distribution of the data is slightly skewed to the left or negatively skewed. It is skewed to the left because the computed value is negative, and is slightly, because the value is close to zero. For the kurtosis, we have 2.301051 implying that the distribution of the. In this article I'll briefly review six well-known normality tests: (1) the test based on skewness, (2) the test based on kurtosis, (3) the D'Agostino-Pearson omnibus test, (4) the Shapiro-Wilk test, (5) the Shapiro-Francia test, and (6) the Jarque-Bera test. In a subsequent article, I'll analyse the analytical p-value approximations for these tests, and in a third article, I'll. Increasing skewness from −0.72 to 0.72 only increases the mean return of the best month in 20 from 3.50 to 4.87%. In this particular distribution and for this range of skewness and kurtosis, an increase in 1.00 of skewness translates to a 94 bp increase in 95th percentile mean monthly returns

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