使分布适合数据-MATLAB [英] Fitting a distribution to data - MATLAB
问题描述
我正在尝试根据我从显微镜图像中收集到的一些数据来分配分布.我们知道，大约152处的峰值是由于泊松过程造成的.我想使分布适合于图像中心的大密度，而忽略了高强度数据.我知道如何将正态分布拟合到数据(红色曲线)，但是在捕获右边的粗尾时做得不好.尽管泊松分布应该能够对右边的尾巴进行建模，但是它也不是很好(绿色曲线)，因为分布的模式为152.
I am trying to fit a distribution to some data I've collected from microscopy images. We know that the peak at about 152 is due to a Poisson process. I'd like to fit a distribution to the large density in the center of the image, while ignoring the high intensity data. I know how to fit a Normal distribution to the data (red curve), but it doesn't do a good job of capturing the heavy tail on the right. Although the Poisson distribution should be able to model the tail to the right, it doesn't do a very good job either (green curve), because the mode of the distribution is at 152.
PD = fitdist(data, 'poisson');
λ= 152的泊松分布看起来很像高斯型.
The Poisson distribution with lambda = 152 looks very Gaussian-like.
有没有人知道如何适合可以很好地捕获数据右尾的分布?
Does anyone have an idea how to fit a distribution that will do a good job of capturing the right-tail of the data?
推荐答案
分布看上去有点像 Ex -Gaussian (请参见第一个Wikipedia图中的绿线)，即正态和指数随机变量的混合模型.
The distribution looks a bit like an Ex-Gaussian (see the green line in the first wikipedia figure), that is, a mixture model of a normal and an exponential random variable.
在旁注中，您是否知道，尽管泊松过程的事件是泊松分布的，但事件之间的等待时间却呈指数分布?考虑到您的测量中增加了高斯噪声，理论上可能会出现高斯分布. (当然，这并不意味着这也是合理的.)
On a side note, are you aware that, although the events of a poisson process are poisson distributed, the waiting times between the events are exponentially distributed? Given that a gaussian noise added to your measurement, an ex-gaussian distribution could be theoretically possible. (Of course this does not mean that this is also plausible.)
有关使用MatLab使前高斯拟合的教程可以在
A tutorial on fitting the ex-gaussian with MatLab can be found in
库苏尼奥(Cosineau D.)的Lacouture Y(2008) 如何使用MATLAB将前高斯函数和其他概率函数拟合为响应时间分布. 心理学定量方法教程4(1)，p. 35‐45. http://www.tqmp.org/Content/vol04-1/p035 /p035.pdf
Lacouture Y, Cousineau D. (2008) How to use MATLAB to fit the ex‐Gaussian and other probability functions to a distribution of response times. Tutorials in Quantitative Methods for Psychology 4 (1), p. 35‐45. http://www.tqmp.org/Content/vol04-1/p035/p035.pdf
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