我找到了一个小样本的Gamma分布参数。后来,我需要使用参数来预测未来的数据。但是,结果显示错误答案。
这是我从Excel得到的结果,这是正确的答案我正在寻找Alpha 0.458718895 Beta 96.76626573
import scipy.stats as stats
data=[0.0621,0.046,0.0324,0.0279]
fit_alpha, fit_loc, fit_beta=stats.gamma.fit(data,floc=0)
print(fit_alpha, fit_loc, fit_beta)
ll=[1,2,3,4,5,6,7,8,9,10]
plop=stats.gamma.pdf(ll,fit_alpha, fit_loc, fit_beta)
print(plop)
预期结果:6.29%4.28%3.40%2.88%2.53%2.27%2.06%1.90%1.76%1.65%
你正在以错误的方式使用fit
。您尝试拟合PDF,而scipy.stat
适合随机数据的最佳基础分布。看看这里:
import matplotlib.pyplot as plt
import numpy as np
import scipy.stats as stats
from scipy.optimize import leastsq
def my_res( params, yData ):
a, b = params
xList= range( 1, len(yData) + 1 )
th = np.fromiter( ( stats.gamma.pdf( x, a, loc=0, scale=b ) for x in xList ), np.float )
diff = th - np.array( yData )
return diff
data = [ 0.0621, 0.046, 0.0324, 0.0279 ]
### this does not work as data is supposed to be the random variate data and not the pdf
fit_alpha, fit_loc, fit_beta = stats.gamma.fit(data, floc=0 )
print 'data fitted the wrong way:'
print(fit_alpha, fit_loc, fit_beta)
#### but making a least square fit with the pdf works
sol, err = leastsq( my_res, [.4, 1 ], args=( data, ) )
print '...and the right way:'
print sol
datath = [ stats.gamma.pdf( x, sol[0], loc=0, scale=sol[1]) for x in range(1,5) ]
### the result gives the expected answer
ll=[1,2,3,4,5,6,7,8,9,10]
plop=stats.gamma.pdf(ll, sol[0], loc=0, scale=sol[1])
print 'expected values:'
print(plop)
### if we generate random numbers with gamma distribution
### the fit does what is should
testData = stats.gamma.rvs(sol[0], loc=0, scale=sol[1], size=5000 )
print 'using stats.gamma.fit the correct way:'
print stats.gamma.fit( testData, floc=0 )
fig = plt.figure()
ax = fig.add_subplot( 1, 1, 1 )
ax.plot( data , ls='', marker='x')
ax.plot( datath , ls='', marker='^')
plt.show()
提供
>> data fitted the wrong way:
>> (10.36700043818477, 0, 0.00406096249836482)
>> ...and the right way:
>> [ 0.45826569 96.8498341 ]
>> expected values:
>> [0.06298405 0.04282212 0.0340243 0.02881519 0.02527189 0.02265992 0.02063036 0.01899356 0.01763645 0.01648688]
>> using stats.gamma.fit the correct way:
>> (0.454884062189886, 0, 94.94258888249479)