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Skewness is a measure of the asymmetry of a probability distribution about its mean. A right-skewed distribution has a longer right tail and a mean that is skewed to the right of the median. See graphs, formulas, and counterexamples of skewness.
A normal probability plot is a graphical technique to identify departures from normality in data. It plots the sorted data vs. an approximation to the means or medians of the corresponding order statistics, and a straight line indicates normality.
The exponentially modified normal distribution is another 3-parameter distribution that is a generalization of the normal distribution to skewed cases. The skew normal still has a normal-like tail in the direction of the skew, with a shorter tail in the other direction; that is, its density is asymptotically proportional to for some positive .
A log-normal distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Learn about its definitions, properties, statistical inference, occurrence and applications, and related distributions.
A box plot or boxplot is a graphical representation of the quartiles, spread and skewness of a dataset. It can also show outliers, whiskers, notches and other variations to compare different groups or distributions.
The first is the square of the skewness: β 1 = γ 1 where γ 1 is the skewness, or third standardized moment. The second is the traditional kurtosis, or fourth standardized moment: β 2 = γ 2 + 3. (Modern treatments define kurtosis γ 2 in terms of cumulants instead of moments, so that for a normal distribution we have γ 2 = 0 and β 2 = 3.
Learn about the generalization of the univariate normal distribution to higher dimensions, also known as the multivariate normal or joint normal distribution. Find definitions, density functions, equivalent conditions, and examples of bivariate normal distributions.
Learn about the beta distribution, a continuous probability distribution with two shape parameters that describes the range of possible values for a random variable. Find out its properties, parameters, mean, variance, mode, and applications in Bayesian inference and statistics.