On Conditional Lower Partial Moments and Its Applications

SYNOPTIC ABSTRACTLower partial moments (LPM) are predominantly used in portfolio theory and in areas involving financial risk, which addresses the problem of managing risky investment policies with the object of maximizing returns. LPM also plays an important role in the analysis of risks in income (poverty) studies. In this article, we extend the notion of LPM to the conditional set up and study its usefulness in the context of stochastic modeling. The relationship between various measures in reliability studies, income (poverty) studies, and risk analysis are also proved. Finally, a non-parametric estimator for conditional LPM is proposed and has been validated through simulated and real data sets.