Python scipy rv_连续实现的问题

Question

我正在尝试创建一个带有自定义分布的rv_continuous子类，我可以通过许多函数计算pdf

这是我到目前为止所做的

import numpy as np
from scipy.stats import rv_continuous

辅助功能

def func1(xx, a_, b_, rho, m, sigma):
    return a_ + b_*(rho*(xx-m) + np.sqrt((xx-m)*(xx-m) + sigma*sigma))

def func2(xx, a_, b_, rho, m, sigma):
    sig2 = sigma*sigma
    return b_*(rho*np.sqrt((xx-m)*(xx-m)+sig2)+xx-m)/(np.sqrt((xx-m)*(xx-m)+sig2))

def func3(xx, a_, b_, rho, m, sigma):
    sig2 = sigma*sigma
    return b_*sig2/(np.sqrt((xx-m)*(xx-m)+sig2)*((xx-m)*(xx-m)+sig2))

def func4(xx, a_, b_, rho, m, sigma):
    w = func1(xx, a_, b_, rho, m, sigma)
    w1 = func2(xx, a_, b_, rho, m, sigma)
    w2 = func3(xx, a_, b_, rho, m, sigma)
    return (1.-0.5*xx*w1/w)*(1.0-0.5*xx*w1/w) - 0.25*w1*w1*(0.25 + 1./w) + 0.5*w2

def func5(xx, a_, b_, rho, m, sigma):
    vsqrt = np.sqrt(func1(xx, a_, b_, rho, m, sigma))
    return -xx/vsqrt - 0.5*vsqrt

密度函数

def density(xx, a_, b_, rho, m, sigma):
    dm = func5(xx, a_, b_, rho, m, sigma)
    return func4(xx, a_, b_, rho, m, sigma)*np.exp(-0.5*dm*dm)/np.sqrt(2.*np.pi*func1(xx, a_, b_, rho, m, sigma))

一组参数

Params = 1.0073, 0.3401026, -0.8, 0.000830, 0.5109564

从函数中检查pdf

xmin, xmax, nbPoints = -10., 10., 2000
x_real = np.linspace(xmin, xmax, nbPoints)

den_from_func = density(x_real, *Params)

现在构造我的分发类

class density_gen(rv_continuous):
    def _pdf(self, x, a_hat, b_hat, rho, m, sigma):
        return density(x, a_hat, b_hat, rho, m, sigma)

实例化

my_density = density_gen(name='density_gen')

my_density.a, my_density.b, my_density.numargs

正如我指定的pdf，我应该有一个工作的分发实例

这很有效

pdf = my_density._pdf(x_real, *Params)

cdf工作得太慢，尽管速度非常慢

cdf = my_density._cdf(x_real, *Params)
my_density._cdf(0.1, *Params)

但对于所有其他方法，例如，我得到了NaN

my_density.mean(*Params)    
my_density.ppf(0.01, *Params)

我做错了什么

Answer 1

似乎需要将^{}方法添加到density_gen，因为您的发行版使用自定义参数：

class density_gen(rv_continuous):

    def _argcheck(self, *Params):
        return True

    def _pdf(self, x, a_hat, b_hat, rho, m, sigma):
        return density(x, a_hat, b_hat, rho, m, sigma)

my_density = density_gen(name='density_gen')
pdf = my_density._pdf(x_real, *Params)
print(my_density.rvs(size=5, *Params))
print(my_density.mean(*Params))  
print(my_density.ppf(0.01, *Params))

但是，rvs、mean等等都会非常慢，这可能是因为该方法每次需要生成随机数或计算统计数据时都需要对PDF进行积分。如果速度很高，那么您将需要向density_gen添加一个使用自己的采样器的_rvs方法。这方面的一个例子是我自己的^{}，当只给出PDF和采样域时，它通过数值反转生成随机数