Positive Skewed If the frequency curve of distribution has a longer tail to the right of the central maximum than to the left, the distribution is said to be skewed to the right or to have positively skewed. Making statements based on opinion; back them up with references or personal experience. \operatorname E\big(X(X-1)(X-2)\big) = {} & \sum_{x=0}^\infty x(x-1)(x-2) \cdot \frac{\lambda^x e^{-\lambda}}{x!} The skewness of a random variable X is often measured by the standardized third central moment Y1=83/03. Looks like youve clipped this slide to already. vbscript global variable; best way to apply roof coating; orangina citrus beverage. Why do American universities have so many gen-eds? If the data includes multiple modes or a weak mode, Pearsons median skewness is used. By whitelisting SlideShare on your ad-blocker, you are supporting our community of content creators. \\ Free access to premium services like Tuneln, Mubi and more. Skewness in statistics can be divided into two categories. Science Advisor. Should teachers encourage good students to help weaker ones? Instant access to millions of ebooks, audiobooks, magazines, podcasts and more. Skewness of a difference of random variables? You can learn more about Excel modeling from the following articles: , Your email address will not be published. By the Variance of Poisson Distribution: Var(X) = E[X2] (E[X])2 = E[X2] 2 = . Use MathJax to format equations. Thanks for contributing an answer to Mathematics Stack Exchange! Now, one can calculate the mean of the distribution as, Mean= ($25 * 2 + $75 * 3 + $125 * 5 + $175 * 6 + $225 * 4) / 20. By the Variance of Poisson Distribution: $Var(X)=\lambda \Rightarrow E[X^2]-(E[X])^2=\lambda\Rightarrow E[X^2]-\lambda^2=\lambda\Rightarrow E[X^2]=\lambda+\lambda^2$. Skewness is a measure of symmetry, or more precisely, the lack of symmetry. How did muzzle-loaded rifled artillery solve the problems of the hand-held rifle? You should be able to calculate the third and fourth moments and thus the quantities you want. & \text{where $y=x-3,$ so $x=y+3$} \\[10pt] did anything serious ever run on the speccy? &= \sum_{x=0}^\infty e^{tx} e^{-\lambda} \frac{\lambda^x}{x!} It is inherited from the of generic methods as an instance of the rv_continuous class. 1 Answer. \\[10pt] Well, the normal distribution is the probability distribution without any skewness. As the name suggests, a positively skewed distribution assumes a skewness value of more than zero. Uncertainty and randomness are two basic types of indeterminacy, where uncertain variable is used to represent quantities with human uncertainty and random variable is applied for modeling quantities with objective randomness. If the reverse is true, it has positive skewness. = {} & \lambda^3 \sum_{y=0}^\infty \frac{\lambda^y e^{-\lambda}}{y!} coskewness is a measure of how much three random variables change together It then says If two random variables exhibit positive coskewness they will tend to undergo extreme positive deviations at the same time. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company. Negative skew commonly indicates that the tail is on the left side of the distribution, and positive skew indicates that the tail is on the right. Variable \\ y = skewness (X,flag,dim) returns the skewness along the operating dimension dim of X. example. By accepting, you agree to the updated privacy policy. 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Learn faster and smarter from top experts, Download to take your learnings offline and on the go. Making statements based on opinion; back them up with references or personal experience. Skewness - Key takeaways. Clipping is a handy way to collect important slides you want to go back to later. If skewness is between and +, the distribution is approximately symmetric. The term "skewness" refers to the statistical metric used to measure the asymmetry of a probability distribution of random variables about its mean. Are squares of independent random variables independent? If your data hold a simple random sample from some population, use. Skewness is the degree of asymmetry or departure from the symmetry of the distribution of a real-valued random variable.. \operatorname{E}[X^3] = M_X'''(0) = \lambda(1 + 3\lambda + \lambda^2). Skewness Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable. This expression is the expected value: E [ (X - ) 3 / 3] = (E [X 3] - 3 E [X 2] + 3 2 E [X] - 3 )/ 3 = (E [X 3] - 3 ( 2 - 3 )/ 3 . Thank you for reading CFIs guide to Skewness. Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. Skewness of Random Variable Antonio F. Balatar Jr. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. where variable X consists of all possible values and P consist of respective probabilities. Variance of Random Variable: The variance tells how much is the spread of random variable X around the mean value. A further characterization of the data includes skewness and kurtosis. Skewness can be measured using several methods; however, Pearson mode skewness and Pearson median skewness are the two frequently used methods. Skewness - the measurement of symmetry or asymmetry of the probability distribution of a random variable. Skewness is a measure of asymmetry or distortion of symmetric distribution. Definition 1: We use skewness as a measure of symmetry. A positively skewed distribution has the mean of the distribution larger than the median, and a longer tail on the right side of the graph. The exponential random variable is defined by the density function [see Fig.1-2b] (1.4-5)P (x) = {a exp (-ax), if x0,0, if x>0,where a is any positive real number. f SK = Take Note: If the skewness is less than -1 or greater than +1, the distribution is highly skewed. (a) Show that Skew [X] = 31 (E[X 3]32 3). Asking for help, clarification, or responding to other answers. Calculate the skewness of a random variable that is Poisson distributed with the parameter $\lambda> 0$. CFA And Chartered Financial Analyst Are Registered Trademarks Owned By CFA Institute. Define the skewness of a random variable X as Skew [X] =E[( X )3]. = {} & \sum_{x=3}^\infty x(x-1)(x-2) \cdot \frac{\lambda^x e^{-\lambda}}{x!} When reporting the skewness and kurtosis of a given distribution in a formal write-up, we generally use the following format: The skewness of [variable name] was found to be -.89, indicating that the distribution was left-skewed. Typesetting Malayalam in xelatex & lualatex gives error, Obtain closed paths using Tikz random decoration on circles. = {} & \lambda^3. On the other hand, a negative skew indicates that the extreme variables are smaller, bringing down the mean value and resulting in a median larger than the meanMeanMean refers to the mathematical average calculated for two or more values. &= e^{\lambda (e^t - 1)}. The final dexpression for the skewness of the sum of independent random variables is: skewness(X+Y)=(3(X)+3(Y))/(2(X)+2(Y))^3/2, $$\text{skewness}(Z) = \frac{\mu _3}{\mu _2^{3/2}}$$. However, skewed data will increase the accuracy of the financial model. So to review, is the set of outcomes, F the collection of events, and P the probability measure on the sample space ( , F). Suppose that X is a real-valued random variable for the experiment. If a return distribution shows a positive skew, investors can expect recurrent small losses and few large returns from investment. It only takes a minute to sign up. Skewness can come in the form of negative skewness or positive skewness . If you know $\lambda^3 = \operatorname E(X(X-1)(X-2)) = \operatorname E(X^3) - 3\operatorname E(X^2) + {}2\operatorname E(X)$ and you know $\operatorname E(X^2)$ and $\operatorname E(X),$ then you can find $\operatorname E(X^3).$, It will follow that $\operatorname E\big((X-\lambda)^3\big) = \lambda.$. Probability with discrete random variables Get 3 of 4 questions to level up! You already have the centered second moment (variance). Estimate and interpret the skewness and kurtosis of a random variable. We've updated our privacy policy. Show that the random variables \ ( X \) and \ ( a X+b \) have the same coeflicients of skewness. One can calculate the squares of the deviations of each variable as below. Mathematically, the skewness formula represents, You are free to use this image on your website, templates, etc., Please provide us with an attribution linkHow to Provide Attribution?Article Link to be HyperlinkedFor eg:Source: Skewness Formula (wallstreetmojo.com), .free_excel_div{background:#d9d9d9;font-size:16px;border-radius:7px;position:relative;margin:30px;padding:25px 25px 25px 45px}.free_excel_div:before{content:"";background:url(https://www.wallstreetmojo.com/assets/excel_icon.png) center center no-repeat #207245;width:70px;height:70px;position:absolute;top:50%;margin-top:-35px;left:-35px;border:5px solid #fff;border-radius:50%}. The right and the left side may not be mirror images. The skewness value can be positive or negative, or even undefined. The two potential problems are (1) if your data set is small, you may not represent the distribution well, and (2) you will not generate a value larger than the largest one in your existing data set. Cookies help us provide, protect and improve our products and services. Are the S&P 500 and Dow Jones Industrial Average securities? In other words, skewness tells you the amount and direction of skew (departure from horizontal symmetry). Then $Std(X)=\sqrt{Var(X)}=\sqrt{\lambda}$. 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. 48.2K subscribers In this Video you will learn discrete and continuous random variable in hindi. we obtain the first three moments through differentiation: $$M_X'(t) = M_X(t) \frac{d}{dt}[\lambda (e^t - 1)] = \lambda e^t M_X(t),$$ using the fact that $\frac{d}{dt}[e^{f(t)}] = f'(t) e^{f(t)}$. Explanation Of Normal Distribution Formula. From the definition of the continuous uniform distribution, X has probability density function : f X ( x) = 1 b a. This article has been a guide to Skewness Formula. Connect and share knowledge within a single location that is structured and easy to search. The skewness value of any distribution showing a negative skew is always less than zero. How about the features? The SlideShare family just got bigger. The skewness is a measure of symmetry or asymmetry of data distribution, and kurtosis measures whether data is heavy-tailed or light-tailed in a normal distribution. In this article( http://www.diva-portal.org/smash/get/diva2:302313/FULLTEXT01.pdf )page 28 explains how to derive the skewness of a sum of random variables; I haven't been able to derive this expression in case of dealing with a difference of random variables. How to smoothen the round border of a created buffer to make it look more natural? A tail is referred to as the tapering of the curve differently from the data points on the other side. MathJax reference. S a m p l e s k e w n e s s = N ( X i X ) 3 S 3 ( N 1) ( N 2) where. Therefore, the calculation of the skewness of the distribution will be as follows, = (-1622234.4 * 2 + -307546.9 * 3 + -5359.4 * 5 + 34328.1 * 6 + 561515.6 * 4) /[ (20 1) * (61.80)3]. How to say "patience" in latin in the modern sense of "virtue of waiting or being able to wait"? Skewness of the logarithm of a gamma random variable - Cross Validated Skewness of the logarithm of a gamma random variable Ask Question Asked 5 years ago Modified 5 years ago Viewed 2k times 16 Consider gamma random variable . Let us calculate the midpoint of each of the intervals. read more. Asking for help, clarification, or responding to other answers. If skewness is less than 1 or greater than +1, the distribution is highly skewed. The optional parameter oversample can be used to modify the number of skewed-uniformly-distributed variables to be added. So, skewness ascertains the lack of symmetry or the extent of asymmetry. As this article shows, one may use skewness to describe or estimate the symmetry of data distribution. If the given distribution is shifted to the right and with its tail on the left side, it is a negatively skewed distribution. The rubber protection cover does not pass through the hole in the rim. Expected Value of Square Root of Poisson Random Variable, Distribution of Poisson random variable with scale parameter distributed as Negative Binomial. Follow Advertisement Recommended January 5, 2015 khyps13 683 views 15 slides A comparatative study on maggi&top ramen Rishi vyas 1.8k views 22 slides January 22, 2016 khyps13 267 views 12 slides Math lesson 69 fraction Rainiel Victor Crisologo 1.7k views 17 slides Activate your 30 day free trialto continue reading. A probability distribution does not need to be a perfect bell shaped curve. The Landau distribution is a skewed distribution with a long tail at the high-energy side (Figure 2.5.4 ). Standard deviation (SD) is a popular statistical tool represented by the Greek letter '' to measure the variation or dispersion of a set of data values relative to its mean (average), thus interpreting the data's reliability. How does legislative oversight work in Switzerland when there is technically no "opposition" in parliament? Let us take the example of a summer camp in which 20 students assign certain jobs that they performed to earn money to raise funds for a school picnic. To learn more, see our tips on writing great answers. For the Pareto distribution with density f(x)=O/x9+1, for x:1, 0>0 the Appealing a verdict due to the lawyers being incompetent and or failing to follow instructions? What is Skewness? Continuous random variables, PDF CDF Expectation Mean, mode, median Common random variables Uniform Exponential Gaussian Transformation of random variables How to generate random numbers Today's lecture: Definition of Gaussian Mean and variance Skewness and kurtosis Origin of Gaussian 2/22 Abstract. We often denote the expected value as X or . X = E (X) is also referred to as the mean of the random variable X, Use MathJax to format equations. If the given distribution is shifted to the left and with its tail on the right side, it is a positively skewed distribution. The skewness value can be positive, zero, negative, or undefined. Several types of skewness are defined, the . A negative skew indicates that the tail on the left side of the probability density function is longer than the right side. If the skewness is between -1 and - or between + and +1, the distribution is moderately skewed. 8. If the skewness of S is zero then the distribution represented by S is perfectly symmetric. find parallel line with equation and given point calculator; where are aeolus tires made; littlebits steam+ coding kit How to interpret "a Poisson distributed random variable approximates a binomial distributed one"? Similarly, if two random variables exhibit negative coskewness they will tend to undergo extreme negative deviations at the same time. The skewness in statistics is a measure of asymmetry or the deviation of a given random variable's distribution from a symmetric distribution (like normal Distribution).. How to set a newcommand to be incompressible by justification? Skewness. In symbols, Var ( X) = ( x - ) 2 P ( X = x) Skewness risk occurs when a symmetric distribution is applied to the skewed data. With a skewness of 0.1098, the sample data for student heights are If $Z = X - Y$ and given independence, the formula becomes: $$\text{skewness}(X-Y) = \frac{\mu _3(X) - \mu _3(Y)}{\big(\mu _2(X) + \mu _2(Y)\big)^{3/2}}$$, The denominator does not change since $\text{Var}(X-Y) = \text{Var}(X+Y) = \text{Var}(X) + \text{Var}(Y)$. Save my name, email, and website in this browser for the next time I comment. Why is this usage of "I've to work" so awkward? Skewness is defined by an expression related to the third moment about the mean. It appears that you have an ad-blocker running. The best answers are voted up and rise to the top, Not the answer you're looking for? Statistics and Probability questions and answers. Table of contents Skewness Meaning Types of Skewness Formula 1. concept of Random Variable, 2. definition of random variable 3. example 4. types of. Where does the idea of selling dragon parts come from? (TA) Is it appropriate to ignore emails from a student asking obvious questions? The financial models seeking to estimate an assets future performance consider a normal distribution. 13.7. \begin{align} do you know how to use a Moment Generating Function? Thanks for contributing an answer to Mathematics Stack Exchange! Why is apparent power not measured in Watts? \operatorname E\big(X(X-1)(X-2)\big) = {} & \sum_{x=0}^\infty x(x-1)(x-2) \cdot \frac{\lambda^x e^{-\lambda}}{x!} Its shape depends on the shape of X and a skewness parameter . gamma and exponential distribution; tools of thinking definition; balfour beatty sustainability report 2021; the ranch saloon age requirement. Based on the information given below, determine the skewness in the income distribution among the students during the summer camp. It has two tails one is known as the right tail and the other one is known as the left tail. \\[10pt] Two possible alternatives are: I. Connect and share knowledge within a single location that is structured and easy to search. The mean is used by researchers as a measure of central tendency. Skewness noun (statistics) A measure of the asymmetry of the probability distribution of a real-valued random variable; is the third standardized moment, defined as \scriptstyle\gamma_1 = \frac{\mu_3}{\sigma^3}, \! where $\mu_k$ denotes the $k^{th}$ central moment of $Z$. Activate your 30 day free trialto unlock unlimited reading. There are neat formulas for the mean, variance, and skewness: Consider now a log-transformed random variable . By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Its value can be positive, negative, or undefined. & \text{where $y=x-3,$ so $x=y+3$} \\[10pt] Enjoy access to millions of ebooks, audiobooks, magazines, and more from Scribd. If $Z = X + Y$ and given independence, the formula becomes: $$\text{skewness}(X+Y) = \frac{\mu _3(X) + \mu _3(Y)}{\big(\mu _2(X) + \mu _2(Y)\big)^{3/2}}$$. Skewness is a measure of asymmetry or distortion of symmetric distribution. The following is the data for the calculation of skewness. The value of this measure may become arbitrarily large, however, and thus difficult to interpret. Sample Skewness - Formula and Calculation. For example, if X is a 2-by-3-by-4 array, then skewness (X,1, [1 2]) returns a 1-by-1-by-4 array. Appropriate translation of "puer territus pedes nudos aspicit"? It measures the deviation of the given distribution of a random variable from a symmetric distribution, such as normal distribution. It may be because they prefer frequent small wins and a few. Skewness Example distribution with non-negative (positive) skewness. The formula for the variance of a random variable is given by; Var (X) = 2 = E (X 2) - [E (X)] 2. To keep advancing your career, the additional CFI resources below will be useful: Get Certified for Business Intelligence (BIDA). Skewness is a central moment, because the random variable's value is centralized by subtracting it from the mean. Skewness measures this extent of asymmetry. \end{align} Example 34 Skewness for a log-Normal random variable Let Y = eX,where X N(X, 2X), be a log-normally distributed random variable . 1 22e 1 22X (xX)2 dx = 0. Skewness is a term in statistics used to describes asymmetry from the normal distribution in a set of statistical data. The shape of the distribution changes as the parameter values change. Does a 120cc engine burn 120cc of fuel a minute? So far we have $$\eta(X)=\frac{E[X^3]-3E[X]E[X^2]+2(E[X])^3}{(Std(X))^3}=\frac{E[X^3]-3\cdot \lambda \cdot \left (\lambda+\lambda^2\right )+2\lambda^3}{\sqrt{\lambda}^3}=\frac{E[X^3]-3\lambda^2-3\lambda^3+2\lambda^3}{\sqrt{\lambda}^3}=\frac{E[X^3]-3\lambda^2-\lambda^3}{\sqrt{\lambda}^3}$$ How can we calculate $E[X^3]$ ? Add a new light switch in line with another switch? Skewness is a measure of the extent to which the probability distribution of a real-valued random variable leans on any side of the mean of the variable. \begin{align} By the Expectation of Poisson Distribution we have that E(X) = . \end{align}, $\lambda^3 = \operatorname E(X(X-1)(X-2)) = \operatorname E(X^3) - 3\operatorname E(X^2) + {}2\operatorname E(X)$, $\operatorname E\big((X-\lambda)^3\big) = \lambda.$, $$\operatorname{E}[X^k] = \left[\frac{d^k M_X}{dt^k}\right]_{t=0}$$, $$M_X'(t) = M_X(t) \frac{d}{dt}[\lambda (e^t - 1)] = \lambda e^t M_X(t),$$, $\frac{d}{dt}[e^{f(t)}] = f'(t) e^{f(t)}$, $$M_X''(t) = \lambda \left(\frac{d}{dt}[e^t] M_X(t) + e^t M_X'(t)\right) = \lambda \left(e^t + \lambda e^{2t}\right) M_X(t),$$, $$M_X'''(t) = \lambda \left(\frac{d}{dt}[e^t + \lambda e^{2t}] M_X(t) + (e^t + \lambda e^{2t}) M_X'(t)\right) \\ = \lambda (e^t + 2\lambda e^{2t} + \lambda (e^{2t} + \lambda e^{3t})) M_X(t) \\ Of the three statistics, the mean is the largest, while the mode is the smallest. Mean () = XP. = {} & \sum_{y=0}^\infty (y+3)(y+2)(y+1)\cdot \frac{\lambda^{y+3}e^{-\lambda}}{(y+3)!} Normal distribution is a distribution that is symmetric i.e. Skewness is defined by: skewness ( Z) = 3 2 3 / 2 where k denotes the k t h central moment of Z. The numerator of Y is equal to E [ ( Y E [ Y]) 3] = E [ ( Y ( a E [ X] + b)) 3], any help with calculating this expectation is appreciated. rev2022.12.9.43105. Structured Query Language (SQL) is a specialized programming language designed for interacting with a database. Excel Fundamentals - Formulas for Finance, Certified Banking & Credit Analyst (CBCA), Business Intelligence & Data Analyst (BIDA), Commercial Real Estate Finance Specialization, Environmental, Social & Governance Specialization, Financial Planning & Wealth Management Professional (FPWM). Fortunately, many of the skewed random variables that arise in applications are lognormal. 1. Each element of the output array is the biased . How to say "patience" in latin in the modern sense of "virtue of waiting or being able to wait"? The degree of its skewness increases with the decrease in the thickness of the material. It is skewed to the right. Why is the federal judiciary of the United States divided into circuits? Mean refers to the mathematical average calculated for two or more values. #2. mathman. The parameters determine the shape and probabilities of the distribution. It is crucial in risk management, portfolio management, trading, and option pricingOption PricingOption pricing refers to the process of determining the theoretical value of an options contract. Connecting three parallel LED strips to the same power supply. This distribution is used for random variables that have some skewness and is not symmetrical, like the Normal Distribution. Skewness and Kurtosis As usual, our starting point is a random experiment, modeled by a probability space ( , F, P). To subscribe to this RSS feed, copy and paste this URL into your RSS reader. $$M_X'''(t) = \lambda \left(\frac{d}{dt}[e^t + \lambda e^{2t}] M_X(t) + (e^t + \lambda e^{2t}) M_X'(t)\right) \\ = \lambda (e^t + 2\lambda e^{2t} + \lambda (e^{2t} + \lambda e^{3t})) M_X(t) \\ So, from Expectation of Function of Continuous Random Variable : What's the densitiy of the product of two independent Gaussian random variables? These are normality tests to check the irregularity and asymmetry of the distribution. SUBJECT INSTRUCTOR. The histogram for the data: 67777888910, is also not symmetrical. = {} & \sum_{y=0}^\infty (y+3)(y+2)(y+1)\cdot \frac{\lambda^{y+3}e^{-\lambda}}{(y+3)!} document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); Copyright 2022 . It is also called the right-skewed distribution. In simple words, skewness is the measure of how much the probability distribution of a random variable deviates from the normal distribution. It completes the methods with details specific for this particular distribution. Since the skewness of the given distribution is on the right, the mean value is greater than the median and moves towards the right, and the mode occurs at the highest frequency of the distribution. This result is expected since the normal distribution is symmetric about it's mean value X. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Therefore, extremes need to be looked at when investors seek short-term and medium-term security positions. You can read the details below. 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