Abstract
The (Cauchy) principal value is a method for assigning values to certain improper integrals which would otherwise be undefined. Using the principal value sense, this study derives an explicit expression of the first negative moment of skew-tand generalized Student'st-distributions for practical applications. Some applications obtained from the FNM of skew-tand generalized Student'st-distributions are also discussed.
Highlights
The first negative moment (FNM) of a continuous density function defined on the real axis has important applications that can arise in many practical situations
The primary objective considered in this study is to derive the exact form of the PV-FNM of a skew-t distribution
In addition to our attempt, the exact form of the PV-FNM of other distributions will be of great interest
Summary
The first negative moment (FNM) of a continuous density function defined on the real axis has important applications that can arise in many practical situations. The mean lifetime of the products turns out to be the FNM of a prior distribution defined on the real line. Existence of the FNM for a distribution defined on the real line and the corresponding evaluation are practical issues in fundamental statistics. By the result in Piegorsch and Casella [10], the FNM of a skew-t distribution does not exist in the usual sense since the value of the density function at origin is larger than zero. Based on the principal value sense, Peng [1] gave alternative sufficient conditions for the existence and finiteness of the FNM in which the mild conditions are easy to hold for the most commonly used distributions defined on the real line.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
