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For a sample of n values, a method of moments estimator of the population excess kurtosis can be defined as = = = (¯) [= (¯)] where m 4 is the fourth sample moment about the mean, m 2 is the second sample moment about the mean (that is, the sample variance), x i is the i th value, and ¯ is the sample mean.
In statistics, the Jarque–Bera test is a goodness-of-fit test of whether sample data have the skewness and kurtosis matching a normal distribution. The test is named after Carlos Jarque and Anil K. Bera. The test statistic is always nonnegative. If it is far from zero, it signals the data do not have a normal distribution.
In the following, { x i } denotes a sample of n observations, g 1 and g 2 are the sample skewness and kurtosis, m j ’s are the j-th sample central moments, and ¯ is the sample mean. Frequently in the literature related to normality testing, the skewness and kurtosis are denoted as √ β 1 and β 2 respectively.
So, in this sample of 66 observations, only 2 outliers cause the central limit theorem to be inapplicable. Robust statistical methods, of which the trimmed mean is a simple example, seek to outperform classical statistical methods in the presence of outliers, or, more generally, when underlying parametric assumptions are not quite correct.
To test if a distribution is other than unimodal, several additional tests have been devised: the bandwidth test, [48] the dip test, [49] the excess mass test, [50] the MAP test, [51] the mode existence test, [52] the runt test, [53] [54] the span test, [55] and the saddle test. An implementation of the dip test is available for the R ...
For the first seven weeks of the MLB offseason, the first-base market was frozen. Despite a wealth of intriguing candidates to change threads in both free agency and on the trade block, there was ...
Fantasy football analyst Scott Pianowski delivers the Week 17 traffic report with his green-light, yellow-light and red-light plays of the week.
A simple way to compute the sample partial correlation for some data is to solve the two associated linear regression problems and calculate the correlation between the residuals. Let X and Y be random variables taking real values, and let Z be the n-dimensional vector-valued random variable.