Quick list of statistics Functions :
import numpy as np
class stats():
"""
Calculate the deviations in a sample.
"""
@staticmethod
def dev(xs): return xs - np.mean(xs)
"""
Calculate the covariance between two data sets.
sample=True : sample covarince
sample=False: population covariance
"""
@staticmethod
def cov(xs,ys,sample=True):
dec = 1 if sample else 0 #if sample-cov decrement len by 1
#sum of products of deviations
return np.dot( stats.dev(xs), stats.dev(ys) ) / (len(xs) - dec)
@staticmethod
def var(xs,sample=True):
dec = 1 if sample else 0 #if sample-cov decrement len by 1
return np.sum(stats.dev(xs)**2) / (len(xs) - dec)
@staticmethod
def std_dev(xs,sample=True):
return np.sqrt( stats.var(xs, sample) )
"""
Calculate Pearson correlation.
"""
@staticmethod
def corr(xs,ys,sample=True) :
varx = stats.var(xs)
vary = stats.var(ys)
corr = stats.cov(xs,ys,sample)/ np.sqrt(varx * vary)
return corr
@staticmethod
def rank(xs): return np.argsort(np.argsort(xs))
@staticmethod
def spearman_corr(xs,ys,sample=True):
xranks = stats.rank(xs)
yranks = stats.rank(ys)
return stats.corr(xranks,yranks,sample)
@staticmethod
def r2(ys,residuals): #coef of determination
return ( 1 - stats.var(residuals) ) / stats.var(ys)
"""
Calculate auto correlation coefficients for a time series or list of values.
lag : specifies up to how many lagging coef will be calculated.
!! The lag should be at most the lenght of the data minus 2, we skip lag-zero.
"""
@staticmethod
def auto_corr(xs,lag=1,sample=True):
if lag > len(xs) - 2 : raise Exception("Lag(%s) is bigger than the data-len(%s) - 2" % (lag,len(xs)))
ac = np.zeros(lag)
for i in range(1, lag+1) :
ac[i-1] = stats.corr(xs[:-i], xs[i:], sample)
return ac
