从数据到无直方图的概率密度
From Data to Probability Densities without Histograms
摘要：
当处理从连续变量中提取的数据时，直方图通常不足以显示其概率密度。它对统计噪音的处理效率低下，并且二进制大小是自由参数。与此相反，经验累积分布函数（在对数据进行排序后获得）是无参数的。但它是一个阶跃函数，所以它的微分不能给出一个光滑的概率密度。基于傅里叶级数展开和柯尔莫哥洛夫检验，我们介绍了一种简单的方法，克服了这个问题。估计的概率密度的误差线使用刀切法计算。我们给出了几个例子，并提供计算机代码再现他们。您可能想先看看相应的图4至图9。
英文摘要：
When one deals with data drawn from continuous variables, a histogram is often inadequate to display their probability density. It deals inefficiently with statistical noise, and binsizes are free parameters. In contrast to that, the empirical cumulative distribution function (obtained after sorting the data) is parameter free. But it is a step function, so that its differentiation does not give a smooth probability density. Based on Fourier series expansion and Kolmogorov tests, we introduce a simple method, which overcomes this problem. Error bars on the estimated probability density are calculated using a jackknife method. We give several examples and provide computer code reproducing them. You may want to look at the corresponding figures 4 to 9 first.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
