我试图用Python实现以下功能:
和
r >= 0
.代码是:
import scipy.integrate as integrate
from scipy.stats import norm
import numpy as np
def integrand(n, u, r):
return norm.pdf(u, 0, 1) * ((norm.cdf(u + r, 0, 1) -
norm.cdf(u, 0, 1)) ** (n - 2)) * norm.pdf(u + r, 0, 1)
def fRn(n, r):
return n * (n - 1) * integrate.quad(integrand, -np.inf, np.inf, args=(n, r))[0]
但结果是
fRn(2, 1)
是:
__main__:14: RuntimeWarning: overflow encountered in double_scalars
__main__:17: IntegrationWarning: The occurrence of roundoff error is detected, which prevents
the requested tolerance from being achieved. The error may be
underestimated.
Out[56]: nan
我找不到如何处理这个错误。我将非常感谢您的帮助。
感谢
第二种方法
我试过以下方法:
from scipy.integrate import quad
import math
import numpy as np
def phi(x):
return (1/math.sqrt(2*np.pi)) * np.exp(-x**2/2)
def PHI(x):
return (1.0 + math.erf(x / math.sqrt(2.0))) / 2.0
def integrand(n, u, r):
return phi(u) * ((PHI(u+r) - PHI(u))**(n-2)) * phi(u+r)
def fRn(n, r):
return n * (n - 1) * quad(integrand, -np.inf, np.inf, args=(n, r))
我得到了以下错误:
Traceback (most recent call last):
File "C:\Users\AppData\Local\Temp/ipykernel_15576/4053151620.py", line 1, in <module>
fRn(2,0.1)
File "C:\Users\Desktop\Simulation\Task_2.py", line 24, in fRn
return quad(integrand, -np.inf, np.inf, args=(n, r))
File "C:\Users\Anaconda3\lib\site-packages\scipy\integrate\quadpack.py", line 352, in quad
points)
File "C:\Users\Anaconda3\lib\site-packages\scipy\integrate\quadpack.py", line 465, in _quad
return _quadpack._qagie(func,bound,infbounds,args,full_output,epsabs,epsrel,limit)
File "C:\Users\Desktop\Simulation\Task_2.py", line 20, in integrand
return phi(u) * ((PHI(u+r) - PHI(u))**(n-2)) * phi(u+r)
OverflowError: (34, 'Result too large')
