Fitting negative binomial in python

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北海茫月
北海茫月 2021-02-20 14:34

In scipy there is no support for fitting a negative binomial distribution using data (maybe due to the fact that the negative binomial in scipy is only discrete).

For a

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  • 2021-02-20 14:42

    I know this thread is quite old, but current readers may want to look at this repo which is made for this purpose: https://github.com/gokceneraslan/fit_nbinom

    There's also an implementation here, though part of a larger package: https://github.com/ernstlab/ChromTime/blob/master/optimize.py

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  • 2021-02-20 14:48

    Not only because it is discrete, also because maximum likelihood fit to negative binomial can be quite involving, especially with an additional location parameter. That would be the reason why .fit() method is not provided for it (and other discrete distributions in Scipy), here is an example:

    In [163]:
    
    import scipy.stats as ss
    import scipy.optimize as so
    In [164]:
    #define a likelihood function
    def likelihood_f(P, x, neg=1):
        n=np.round(P[0]) #by definition, it should be an integer 
        p=P[1]
        loc=np.round(P[2])
        return neg*(np.log(ss.nbinom.pmf(x, n, p, loc))).sum()
    In [165]:
    #generate a random variable
    X=ss.nbinom.rvs(n=100, p=0.4, loc=0, size=1000)
    In [166]:
    #The likelihood
    likelihood_f([100,0.4,0], X)
    Out[166]:
    -4400.3696690513316
    In [167]:
    #A simple fit, the fit is not good and the parameter estimate is way off
    result=so.fmin(likelihood_f, [50, 1, 1], args=(X,-1), full_output=True, disp=False)
    P1=result[0]
    (result[1], result[0])
    Out[167]:
    (4418.599495886474, array([ 59.61196161,   0.28650831,   1.15141838]))
    In [168]:
    #Try a different set of start paramters, the fit is still not good and the parameter estimate is still way off
    result=so.fmin(likelihood_f, [50, 0.5, 0], args=(X,-1), full_output=True, disp=False)
    P1=result[0]
    (result[1], result[0])
    Out[168]:
    (4417.1495981801972,
     array([  6.24809397e+01,   2.91877405e-01,   6.63343536e-04]))
    In [169]:
    #In this case we need a loop to get it right
    result=[]
    for i in range(40, 120): #in fact (80, 120) should probably be enough
        _=so.fmin(likelihood_f, [i, 0.5, 0], args=(X,-1), full_output=True, disp=False)
        result.append((_[1], _[0]))
    In [170]:
    #get the MLE
    P2=sorted(result, key=lambda x: x[0])[0][1]
    sorted(result, key=lambda x: x[0])[0]
    Out[170]:
    (4399.780263084549,
     array([  9.37289361e+01,   3.84587087e-01,   3.36856705e-04]))
    In [171]:
    #Which one is visually better?
    plt.hist(X, bins=20, normed=True)
    plt.plot(range(260), ss.nbinom.pmf(range(260), np.round(P1[0]), P1[1], np.round(P1[2])), 'g-')
    plt.plot(range(260), ss.nbinom.pmf(range(260), np.round(P2[0]), P2[1], np.round(P2[2])), 'r-')
    Out[171]:
    [<matplotlib.lines.Line2D at 0x109776c10>]
    

    enter image description here

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  • 2021-02-20 15:07

    Statsmodels has discrete.discrete_model.NegativeBinomial.fit(), see here: https://www.statsmodels.org/dev/generated/statsmodels.discrete.discrete_model.NegativeBinomial.fit.html#statsmodels.discrete.discrete_model.NegativeBinomial.fit

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