子类化 scipy 的连续分布 [英] Subclassing scipy's continuous distributions

问题描述

我正在研究如何创建一个新的 scipy.stats.rv_continuous 子类.我的分布取决于位置"和形状"参数，但是 scipy.stats.distributions 中 _pdf 的每个示例都假定形状 &位置参数可以简单地应用于 X 轴，但某些分布并非如此.

I'm trying to figure out how to create a new scipy.stats.rv_continuous subclass. My distribution depends on "location" and "shape" parameters, but every example of a _pdf in scipy.stats.distributions assumes that the shape & location parameters can simply be applied to the X-axis, which is not the case for some distributions.

例如，我正在使用的一个分布是对数正态分布的修改版本，其中 X 轴位置明确取决于分布的宽度，即:

For example, one distribution I'm working with is a modified version of the lognormal in which the X-axis location explicitly depends on the width of the distribution, i.e.:

def _pdf(self, x, x0, s):
    Px = exp(-(log(x/x0)+s**2/2.)**2 / (2*s**2))
    return Px / (s*x0*sqrt(2*pi))

我希望能够对 x0 使用 loc，对 s 使用 scale.有没有办法做到这一点，或者有没有更好的方法来子类rv_continuous?

I'd like to be able to use loc for x0 and scale for s. Is there any way to do this, or is there a better way to subclass rv_continuous?

(请注意，简单地使用我定义的 PDF 会导致其他 rv_continuous 方法出现问题，例如 .fit，因为 loc> 和 scale 仍然被视为自由参数"，即使它们不应该)

(note that simply using the PDF as I've defined it leads to problems in other rv_continuous methods, e.g. .fit, since loc and scale are still treated as "free parameters" even though they should not be)

推荐答案

你真的不应该试图改变 loc 和 scale 的含义.它们是标准的、定义明确的位置和比例参数，例如在 scipy.stats 教程，在维基百科这里和这里，还有这里.

You really shouldn't try to change the meaning of loc and scale. They are the standard, well-defined location and scale parameters as explained, for example, in the scipy.stats tutorial, on wikipedia here and here, and also here.

正如我在评论中提到的，您的公式中似乎缺少一个 1/x0 因子.没有它，PDF 从 0 到无穷大的积分是 x0，而不是 1.

As I mentioned in a comment, it looks like you are missing a factor of 1/x0 in your formula. Without it, the integral from 0 to infinity of your PDF is x0, not 1.

经过修正，很明显x0实际上是比例参数.s 是一个形状参数.像许多其他仅定义在正实轴上的分布(例如伽马或对数正态分布)一样，您可以简单地忽略位置参数——其默认值为 0.(如果您使用 fit 方法，请务必使用参数 floc=0，以防止该方法将 loc 视为自由参数.)但是，我不确定您所说的"X 轴位置明确取决于分布的宽度"--what 的 X 轴位置?

With the correction, it is clear that x0 is actually the scale parameter. s is a shape parameter. Like many other distributions only defined on the positive real axis (e.g. gamma or log-normal), you can simply ignore the location parameter--its default value is 0. (If you use the fit method, be sure to use the argument floc=0, to prevent the method from treating loc as a free parameter.) However, I'm not sure what you mean by "the X-axis location explicitly depends on the width of the distribution"--the X-axis location of what?

这篇关于子类化 scipy 的连续分布的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！