code: def invgamma_pdf(x, a):
      if x > 0:
          return math.exp(
              -(a + 1.0) * math.log(x) - math.lgamma(a) - 1 / x
          )
      else:
          return 0 if a >= 1 else np.inf
  
imports: import math
  import numbers
  import numpy
  from scipy import stats
  from scipy import special
  from ._qmc import check_random_state, Halton, QMCEngine
  from ._unuran.unuran_wrapper import NumericalInversePolynomial
  from scipy._lib._util import check_random_state
label_desc: Use image node_id 7 for calling a global function with example usage: invgamma_pdf(x, a) and returns: math, unknown