我正在尝试在看起来像这样的泊松分布的直方图上拟合一条曲线
I am trying to fit a curve over the histogram of a Poisson distribution that looks like this
我修改了拟合函数，使其类似于泊松分布，其中参数t为变量.但是curve_fit函数无法绘制，我不确定为什么.
I have modified the fit function so that it resembles a Poisson distribution, with the parameter t as a variable. But the curve_fit function can not be plotted and I am not sure why.
def histo(bsize): N = bsize #binwidth bw = (dt.max()-dt.min())/(N-1.) bin1 = dt.min()+ bw*np.arange(N) #define the array to hold the occurrence count bincount= np.array([]) for bin in bin1: count = np.where((dt>=bin)&(dt<bin+bw))[0].size bincount = np.append(bincount,count) #bin center binc = bin1+0.5*bw plt.figure() plt.plot(binc,bincount,drawstyle= 'steps-mid') plt.xlabel("Interval[ticks]") plt.ylabel("Frequency") histo(30) plt.xlim(0,.5e8) plt.ylim(0,25000) import numpy as np from scipy.optimize import curve_fit delta_t = 1.42e7 def func(x, t): return t * np.exp(- delta_t/t) popt, pcov = curve_fit(func, np.arange(0,.5e8),histo(30)) plt.plot(popt)推荐答案
您的代码存在的问题是您不知道curve_fit的返回值是什么.它是拟合函数及其协方差矩阵的参数-不能直接绘制.
The problem with your code is that you do not know what the return values of curve_fit are. It is the parameters for the fit-function and their covariance matrix - not something you can plot directly.
通常，您可以轻松得多地获得所有东西:
In general you can get everything much, much more easily:
import numpy as np import matplotlib.pyplot as plt from scipy.optimize import curve_fit from scipy.special import factorial from scipy.stats import poisson # get poisson deviated random numbers data = np.random.poisson(2, 1000) # the bins should be of integer width, because poisson is an integer distribution bins = np.arange(11) - 0.5 entries, bin_edges, patches = plt.hist(data, bins=bins, density=True, label='Data') # calculate bin centres bin_middles = 0.5 * (bin_edges[1:] + bin_edges[:-1]) def fit_function(k, lamb): '''poisson function, parameter lamb is the fit parameter''' return poisson.pmf(k, lamb) # fit with curve_fit parameters, cov_matrix = curve_fit(fit_function, bin_middles, entries) # plot poisson-deviation with fitted parameter x_plot = np.arange(0, 15) plt.plot( x_plot, fit_function(x_plot, *parameters), marker='o', linestyle='', label='Fit result', ) plt.legend() plt.show()这是结果:
一个更好的可能性是根本不使用直方图 而是进行最大似然拟合.
An even better possibility would be to not use a histogram at all and instead to carry out a maximum-likelihood fit.
但是通过仔细检查，这甚至是不必要的，因为 泊松分布参数的最大似然估计是算术平均值.
But by closer examination even this is unnecessary, because the maximum-likelihood estimator for the parameter of the poissonian distribution is the arithmetic mean.
但是，如果您还有其他更复杂的PDF，可以使用以下示例:
However, if you have other, more complicated PDFs, you can use this as example:
import numpy as np import matplotlib.pyplot as plt from scipy.optimize import minimize from scipy.special import factorial from scipy import stats def poisson(k, lamb): """poisson pdf, parameter lamb is the fit parameter""" return (lamb**k/factorial(k)) * np.exp(-lamb) def negative_log_likelihood(params, data): """ The negative log-Likelihood-Function """ lnl = - np.sum(np.log(poisson(data, params[0]))) return lnl def negative_log_likelihood(params, data): ''' better alternative using scipy ''' return -stats.poisson.logpmf(data, params[0]).sum() # get poisson deviated random numbers data = np.random.poisson(2, 1000) # minimize the negative log-Likelihood result = minimize(negative_log_likelihood, # function to minimize x0=np.ones(1), # start value args=(data,), # additional arguments for function method='Powell', # minimization method, see docs ) # result is a scipy optimize result object, the fit parameters # are stored in result.x print(result) # plot poisson-distribution with fitted parameter x_plot = np.arange(0, 15) plt.plot( x_plot, stats.poisson.pmf(x_plot, *parameters), marker='o', linestyle='', label='Fit result', ) plt.legend() plt.show()