矩量法：beta二项分布

Question

我正在尝试通过β二项分布的α和β矩估计方法。采取以下步骤： http://en.wikipedia.org/wiki/Beta-binomial_distribution#Maximum_likelihood_estimation

我认为我已经能够在python中准确编码：

import numpy as np

males = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], dtype=float)
fams = np.array([3, 24, 104, 286, 670, 1033, 1343, 1112, 829, 478, 181, 45, 7], dtype=float)
n = 12

k = 1
m_1 = (sum(fams*males**k))/(sum(fams)) 

k = 2
m_2 = (sum(fams*males**k))/(sum(fams)) 

alpha = (n*m_1-m_2)/(n*(m_2/m_1-m_1-1)+m_1)
beta = (n-m_1)*(n-m_2/m_1)/(n*(m_2/m_1-m_1-1)+m_1)

print "n =", n
print "m_1 =", m_1
print "m_2 =", m_2
print "alpha =", alpha
print "beta =", beta

输出：

n = 12
m_1 = 6.23058053966
m_2 = 42.3094031071
alpha = 34.135021177
beta = 31.6084920506

这与示例的结果相同。但是，如果我使用最大可能性的R包VGAM，则alpha和beta的估计值完全不同

x = c(0,1,2,3,4,5,6,7,8,9,10,11,12)
y = c(3,24,104,286,670,1033,1343,1112,829,478,181,45,7)
library("VGAM")
fit=vglm(cbind(x, y) ~ 1, betabinomialff, trace = TRUE)
Coef(fit)
  shape1    shape2 
0.4241806 4.9069560

我做错了吗？