code: def LogNormal(x, a, mu, sigma):
      
      return a / np.sqrt(2 * np.pi * sigma ** 2 * x ** 2) *\
          np.exp(-(np.log(x) - mu) ** 2 / (2 * sigma ** 2))
docs: PDF of a log-normal distribution
  
      Inputs:
      -------
          ``x``: independent variable
          ``a``: amplitude
          ``mu``: center parameter
          ``sigma``: width parameter
  
      Formula:
      --------
          ``a/ (2*pi*sigma^2*x^2)^0.5 * exp(-(log(x)-mu)^2/(2*sigma^2))