在MATLAB中估计直方图的偏度 [英] Estimating skewness of histogram in MATLAB

问题描述

我可以在MATLAB中进行哪些测试来测试直方图的扩展?例如，在给定的直方图中，我只对1,2,3,5和7(从左到右，从上到下)感兴趣，因为它们的分布较少.如何获得一个可以告诉我直方图是否正偏的值?

What test can I do in MATLAB to test the spread of a histogram? For example, in the given set of histograms, I am only interested in 1,2,3,5 and 7 (going from left to right, top to bottom) because they are less spread out. How can I obtain a value that will tell me if a histogram is positively skewed?

使用Chi-Squared测试可能是可行的，但是我不确定MATLAB代码将适用于什么.

It may be possible using Chi-Squared tests but I am not sure what the MATLAB code will be for that.

推荐答案

您可以使用标准偏度的定义.换句话说，您可以使用:

You can use the standard definition of skewness. In other words, you can use:

您可以计算数据的平均值，并使用上面的公式来计算偏斜度.正偏度和负偏度是这样的:

You compute the mean of your data and you use the above equation to calculate skewness. Positive and negative skewness are like so:

^{来源:维基百科}

因此，值越大，偏斜度就越大.值越负，则歪斜度越大.

As such, the larger the value, the more positively skewed it is. The more negative the value, the more negatively skewed it is.

现在要计算直方图数据的平均值，这非常简单.您只需对直方图条目进行加权总和，然后除以条目总数即可.假设您的直方图存储在h中，则直方图的bin中心存储在x中，您可以执行以下操作.我在这里要做的是假设您具有从0到N-1的bin，其中N是直方图中的bin总数...从您的图片来看:

Now to compute the mean of your histogram data, it's quite simple. You simply do a weighted sum of the histogram entries and divide by the total number of entries. Given that your histogram is stored in h, the bin centres of your histogram are stored in x, you would do the following. What I will do here is assume that you have bins from 0 up to N-1 where N is the total number of bins in the histogram... judging from your picture:

x = 0:numel(h)-1; %// Judging from your pictures
num_entries = sum(h(:));
mu = sum(h.*x) / num_entries;
skew = ((1/num_entries)*(sum((h.*x - mu).^3))) / ...
       ((1/(num_entries-1))*(sum((h.*x - mu).^2)))^(3/2);

skew将包含遵循该公式的直方图的偏度的数值度量.因此，通过问题陈述，您将需要寻找正数和较大的偏度数.我不能真正评论您应该看什么阈值，但是要寻找比您拥有的大多数直方图大得多的正数.

skew would contain the numerical measure of skewness for a histogram that follows that formula. Therefore, with your problem statement, you will want to look for skewness numbers that are positive and large. I can't really comment on what threshold you should look at, but look for positive numbers that are much larger than most of the histograms that you have.

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