where (2 -1)!! is the term of double factorial notation, which can be simplified by
Mathematica Software, Wolfram Research [22]. We use L(σ|x) to derive predictive
inference for future response. Khan [4] considered a predictive inference problem by
making use of the Bayesian approach with an inverted gamma prior. In the present study,
we consider the same inverted gamma prior for σ with hyperparameters (η and δ). For
more information about hyperparameters, the reader is referred to Berger [14]. Thus, the
predictive density for a single future response (z) is given by