Characterizations of some continuous distributions using partial moments

Inthis paper,we define partial moments for a univariate continuous random variable. A recurrence relationship for the Pearson curve using the partial moments is established. The interrelationship between the partial moments and other reliability measures such as failure rate, mean residual life function are proved. We also prove some characterization theorems using the partial moments in the context of length biased models and equilibrium distributions

The role of lower partial moments in stochastic modeling

Lower partial moments plays an important role in the analysis of risks and in income/poverty studies. In the present paper, we further investigate its importance in stochastic modeling and prove some characterization theorems arising out of it. We also identify its relationships with other important applied models such as weighted and equilibrium models. Finally, some applications of lower partial moments in poverty studies are also examined

Quantile based reliability aspects of partial moments

Partial moments are extensively used in literature for modeling and analysis of lifetime data. In this paper, we study properties of partial moments using quantile functions. The quantile based measure determines the underlying distribution uniquely. We then characterize certain lifetime quantile function models. The proposed measure provides alternate definitions for ageing criteria. Finally, we explore the utility of the measure to compare the characteristics of two lifetime distributions

Mn2þ-induced room-temperature ferromagnetism and spin-glass behavior in hydrothermally grown Mn-doped ZnO nanorods

The magnetic properties of Mn-doped ZnO (ZnO:Mn) nanorods grown by hydrothermal process at a temperature of 200 8C and a growth time of 3 h have been studied. The samples were characterized by using powder X-ray diffraction with Rietveld refinement, scanning electron microscopy, energy-dispersive X-ray analysis and SQUID magnetometry. Mn (3 wt%) and (5 wt%)-doped ZnO samples exhibit paramagnetic and ferromagnetic behavior, respectively, at room temperature. The spin-glass behavior is observed from the samples with respect to the decrease of temperature. At 10 K, both samples exhibit a hysteresis loop with relatively low coercivity. The room-temperature ferromagnetism in 5 wt% Mn-doped ZnO nanorods is attributed to the increase in the specific area of grain boundaries, interaction between dopant Mn2þ ions substituted at Zn2þ site and the interaction between Mn2þ ions and Zn2þ ions from the ZnO host lattice