我有一个这样的数据框架:
Category Frequency
1 30000
2 45000
3 32400
4 42200
5 56300
6 98200
如何计算类别的平均值、中位数和偏度?
我已经试过了:
df['cum_freq'] = [df["Category"]]*df["Frequnecy"]
mean = df['cum_freq'].mean()
median = df['cum_freq'].median()
skew = df['cum_freq'].skew()
如果总频率足够小,可以装入内存,则使用repeat
来生成数据,然后您可以轻松地调用这些方法。
s = df['Category'].repeat(df['Frequency']).reset_index(drop=True)
print(s.mean(), s.var(ddof=1), s.skew(), s.kurtosis())
# 4.13252219664584 3.045585008424625 -0.4512924988072343 -1.1923306818513022
否则,你将需要更复杂的代数来计算矩,这可以用k统计量来完成,一些较低的矩可以用其他库来完成,如numpy
或statsmodels
。但是对于像偏度和峰度这样的东西,这是手动从去均值值的总和中完成的(从计数中计算)。因为这些总和会溢出numpy,所以我们需要使用普通python。
def moments_from_counts(vals, weights):
"""
Returns tuple (mean, N-1 variance, skewness, kurtosis) from count data
"""
vals = [float(x) for x in vals]
weights = [float(x) for x in weights]
n = sum(weights)
mu = sum([x*y for x,y in zip(vals,weights)])/n
S1 = sum([(x-mu)**1*y for x,y in zip(vals,weights)])
S2 = sum([(x-mu)**2*y for x,y in zip(vals,weights)])
S3 = sum([(x-mu)**3*y for x,y in zip(vals,weights)])
S4 = sum([(x-mu)**4*y for x,y in zip(vals,weights)])
k1 = S1/n
k2 = (n*S2-S1**2)/(n*(n-1))
k3 = (2*S1**3 - 3*n*S1*S2 + n**2*S3)/(n*(n-1)*(n-2))
k4 = (-6*S1**4 + 12*n*S1**2*S2 - 3*n*(n-1)*S2**2 -4*n*(n+1)*S1*S3 + n**2*(n+1)*S4)/(n*(n-1)*(n-2)*(n-3))
return mu, k2, k3/k2**1.5, k4/k2**2
moments_from_counts(df['Category'], df['Frequency'])
#(4.13252219664584, 3.045585008418879, -0.4512924988072345, -1.1923306818513018)
statmodels有一个很好的类,可以处理较低的矩,以及分位数。
from statsmodels.stats.weightstats import DescrStatsW
d = DescrStatsW(df['Category'], weights=df['Frequency'])
d.mean
#4.13252219664584
d.var_ddof(1)
#3.045585008418879
如果调用d.asrepeats()