hsmode.py

def discrete_mode(zs):
  return sorted(
      [(x, len([y for y in xs if y == x])) \
       for x in set(zs)],
      key=lambda x:x[1],reverse=True)[0][0]
def _hsmode(zs, tol):

  if len(zs)==1: 
    return zs[0]
  elif len(zs)==2:
    return (zs[0]+zs[1])/2
  elif len(zs)==3:
    if (zs[1]-zs[0]) < (zs[2]-zs[1]):
      return (zs[0]+zs[1])/2
    else:
      return (zs[1]+zs[2])/2
  elif abs(zs[-1] - zs[0]) <= tol:

    return (zs[0]+zs[-1])/2
  else:
    h = math.floor(len(zs)/2)
    if (zs[h]-zs[0]) <  (zs[-1]-zs[h+1]):
      return hsmode(zs[:h],tol)
    else:
      return hsmode(zs[h:],tol)

def hsmode(xs,tol=1e-4):
    return _hsmode(sorted(xs),tol)


# Source and references:

# https://stats.stackexchange.com/questions/189379/finding-the-peak-of-a-kernel-density-estimator

# Bickel, D.R. 2002. Robust estimators of the mode and skewness of continuous data. Computational Statistics & Data Analysis 39: 153-163.

# Bickel, D.R. and R. Frühwirth. 2006. On a fast, robust estimator of the mode: comparisons to other estimators with applications. Computational Statistics & Data Analysis 50: 3500-3530.

# Dalenius, T. 1965. The mode - A neglected statistical parameter.
# Journal, Royal Statistical Society A 128: 110-117.

# Robertson, T. and J.D. Cryer. 1974. An iterative procedure for estimating the mode. Journal, American Statistical Association 69: 1012-1016.