def __init__(self, p = 0.1, r = 10):

nbin_mpmath = lambda k, p, r: mpmath.gamma(k + r)/(mpmath.gamma(k+1)*mpmath.gamma(r))*np.power(1-p, r)*np.power(p, k)

self.nbin = np.frompyfunc(nbin_mpmath, 3, 1)

self.p = p

self.r = r

def mleFun(self, par, data, sm):

'''

Objective function for MLE estimate according to

https://en.wikipedia.org/wiki/Negative_binomial_distribution#Maximum_likelihood_estimation

Keywords:

data -- the points to be fit

sm -- \sum data / len(data)

'''

p = par[0]

r = par[1]

n = len(data)

f0 = sm/(r+sm)-p

f1 = np.sum(special.psi(data+r)) - n*special.psi(r) + n*np.log(r/(r+sm))

return np.array([f0, f1])

def fit(self, data, remove_lower, remove_upper):

p = None

r = None

data = [float(i) for i in data]

data.sort()

data_len = len(data)

data_selected = data[int(data_len*remove_lower):int(data_len*remove_upper)]

if p is None or r is None:

av = np.average(data_selected)

va = np.var(data_selected)

r = (av*av)/(va-av)

p = (va-av)/(va)

sm = np.sum(data_selected)/len(data_selected)

x = optimize.fsolve(self.mleFun, np.array([p, r]), args=(data_selected, sm))

self.p = x[0]

self.r = x[1]

mu = self.p*self.r/(1-self.p)

fi = 1/self.r

return np.array([mu,fi])

def gaussian_fit(self,data,remove_lower,remove_upper):

data = [float(i) for i in data]

data.sort()

data_len = len(data)

data_selected = data[int(data_len*remove_lower):int(data_len*remove_upper)]

mu = np.average(data_selected)

sd = np.std(data_selected)

return np.array([mu, sd])

def pdf(self, k):