def tansey_linear_regression(points):
"""
to be commented.
@param points is a list of tuples (x,y) of float values.
@return intercept,slope
"""
if len(points)==0:
return 0.
sumOfXSq = 0.
sumCodeviates = 0.
n = len(points)
for x,y in points:
sumCodeviates += (x*y)
sumOfXSq += (x*x)
sum_x = central.fsum( [x for x,y in points] )
sum_y = central.fsum( [y for x,y in points] )
mean_x = central.fmean( [x for x,y in points] )
mean_y = central.fmean( [y for x,y in points] )
ssx = sumOfXSq - ((sum_x*sum_x) / n)
sco = sumCodeviates - ((sum_x * sum_y) / n)
b = mean_y - ((sco / ssx) * mean_x)
m = sco / ssx
return b, m
def tga_linear_regression(points):
"""
to be commented.
@param points is a list of tuples (x,y) of float values.
@return intercept,slope
"""
if len(points)==0:
return 0.
# Fix means
mean_x = central.fmean( [x for x,y in points] )
mean_y = central.fmean( [y for x,y in points] )
xysum = 0.
xsqsum = 0.
for x,y in points:
dx = x - mean_x
dy = y - mean_y
xysum += (dx*dy)
xsqsum += (dx*dx)
# Intercept
if xsqsum == 0:
m = xysum
else:
m = xysum / xsqsum
# Slope
b = mean_y - m * mean_x
return b,m
def lvariation(items):
"""
Calculates the coefficient of variation of data values.
It shows the extent of variability in relation to the mean.
It's a standardized measure of dispersion: stdev / mean and returned as a percentage.
@param items (list) list of data values
@return (float)
"""
return variability.lstdev(items) / float(central.fmean(items)) * 100.0
def lmoment(items, moment=1):
"""
Calculates the r-th moment about the mean for a sample:
1/n * SUM((items(i)-mean)**r)
@param items (list) list of data values
@return (float)
"""
if moment == 1:
return 0.0
mn = central.fmean(items)
momentlist = [(i - mn) ** moment for i in items]
return sum(momentlist) / float(len(items))
def lvariance(items):
"""
Calculates the variance of the data values,
using N for the denominator.
The variance is a measure of dispersion near the mean.
@param items (list) list of data values
@return (float)
"""
if len(items) < 2:
return 0.0
mn = central.fmean(items)
return central.fsum(pow(i - mn, 2) for i in items) / (len(items))
def lz(items, score):
"""
Calculates the z-score for a given input score, given that score and the
data values from which that score came.
The z-score determines the relative location of a data value.
@param items (list) list of data values
@param score (float) a score of any items
@return (float)
"""
if len(items) < 2:
return 0.0
return (score - central.fmean(items)) / lstdev(items)
@param items (list) list of data values
@return (float)
"""
if len(items) < 2:
return 0.0
n = len(items) - 1
sumd = 0.0
for i in range(n):
d1 = items[i]
d2 = items[i + 1]
delta = math.fabs(d1 - d2)
meand = (d1 + d2) / 2.0
sumd += delta / meand
return 100.0 * sumd / n
# ----------------------------------------------------------------------------
if __name__ == "__main__":
l = [x * x for x in range(1, 11)]
print l
print "mean:", central.fmean(l)
print "median:", central.fmedian(l)
print "variance:", lvariance(l)
print "standard deviation:", lstdev(l)
print "rPVI:", rPVI(l)
print "nPVI:", nPVI(l)
a high kurtosis distribution has a sharper peak and fatter tails,
while a low kurtosis distribution has a more rounded peak and thinner
tails.
@param items (list) list of data values
@return (float)
"""
return lmoment(items, 4) / pow(lmoment(items, 2), 2.0)
# ----------------------------------------------------------------------------
if __name__ == "__main__":
import datetime
l = [x * x for x in range(1, 500)]
print "moment:"
print datetime.datetime.now().isoformat()
moment = 10
mn = central.fmean(l)
s = 0
for x in l:
s = s + (x - mn) ** moment
print s / float(len(l))
print datetime.datetime.now().isoformat()
print lmoment(l, moment)
print datetime.datetime.now().isoformat()
print