content_image/308610.jpg content_image/308611.jpg content_image/308614.jpg
depending on y ∗ > 0 (i.e., y > µ ) or y ∗ ≤ 0 (i.e., y ≤ µ ). 

Case (i) : When α > 0 and y ∗ > 0 (i.e., y > µ ), we have the following three components, 

<img src='content_image/308610.jpg'>

and when α > 0 and y ∗ ≤ 0 (i.e., y ≤ µ ) we have, 

<img src='content_image/308611.jpg'>

We first consider M$_{1}$ , substitute z = y ∗ α − αp$_{α}$$_{−}$ , change the limits of integration and integrate- by-parts as follows: 

<img src='content_image/308614.jpg'>

