input: Write a python function to perform Fisher-Snedecor distribution tests and calculations as provided in the code.
  assert distribution_info()['mean'] == 1.1666666666666667
  assert distribution_info()['standardDeviation'] == 0.5449882979325274
  assert distribution_info()['skewness'] == 2.290245601967879
  assert distribution_info()['kurtosis'] == 7.336315893815938
output: def distribution_info():
      from scipy.stats import f
      
      dfn = 3  # degrees of freedom numerator
      dfd = 2  # degrees of freedom denominator
      
      mean = dfd / (dfd - 2) if dfd > 2 else float('inf')
      variance = (2 * (dfd ** 2) * (dfn + dfd - 2)) / (dfn * (dfd - 2) ** 2 * (dfd - 4)) if dfd > 4 else float('inf')
      standard_deviation = variance ** 0.5 if variance != float('inf') else float('inf')
      skewness = (2 * (dfd + 2 * dfn - 2) * ((dfd - 2) ** 0.5)) / ((dfn * (dfd + dfn - 2)) ** 0.5 * (dfd - 4)) if dfd > 4 else float('inf')
      kurtosis = 12 * (dfn * (5 * dfd - 22) * (dfd - 2) + (dfd - 4) * (dfd - 4) * (dfd - 6) * (dfd - 8)) / (dfn * (dfd - 6) * (dfd - 8) * (dfd - 10)) + 3 if dfd > 8 else float('inf')
      
      return {
          'mean': mean,
          'standardDeviation': standard_deviation,
          'skewness': skewness,
          'kurtosis': kurtosis
  }