Are there any build-in functions like Gaussian or Epanechnikov functions in field calculator? Or I have to write that by myself?
First, you should note that field calculator applies only row by row (except if you use a static variable).
So you will need to precompute the mean and the standard deviation of your Gaussian distribution. Then run the equation in Python
def Gaussian(field, mean, std): return math.exp(-(field-mean)**2/(2*std**2))/(math.sqrt(math.pi()*2)*std)
Gaussian(!field!, mean, std)
def Epan(field, size): if math.fabs(field) >= size: return 0 else: return 3*(1-(field/size)**2)/4