This paper investigates the moments of the surplus before ruin and the deficit at ruin in the Erlang(2) risk process. Using the integro-differential equation that we establish, we obtain some explicit expressions for the moments. Furthermore, when the claim size is exponentially and subexponentially distributed, asymptotic relationships for the moments are derived as the initial capital tends to infinity. Also, we show the joint probability density function of the surplus before ruin and the deficit at ruin.

No abstract

α-NiS and β-NiS hollow spheres were successfully synthesized via the Kirkendall effect under different hydrothermal conditions. The obtained α-NiS and β-NiS hollow spheres were evaluated as electrode materials for supercapacitors. Importantly, the α-NiS hollow sphere electrode has a large specific capacitance (562.3 F g(-1) at 0.60 A g(-1)) and good cycling property (maintaining about 97.5% at 2.4 A g(-1) after 1000 cycles). Furthermore, the as-prepared α-NiS and β-NiS hollow spheres were successfully applied to construct electrochemical glucose sensors. Especially, the α-NiS hollow spheres exhibit a good sensitivity (155 μA mM(-1)  cm(-2)), low detection limit (0.125 μM), and a wide linear range.

When testing a large number of hypotheses, estimating the proportion of true nulls, denoted by π(0), becomes increasingly important. This quantity has many applications in practice. For instance, a reliable estimate of π(0) can eliminate the conservative bias of the Benjamini-Hochberg procedure on controlling the false discovery rate. It is known that most methods in the literature for estimating π(0) are conservative. Recently, some attempts have been paid to reduce such estimation bias. Nevertheless, they are either over bias corrected or suffering from an unacceptably large estimation variance. In this paper, we propose a new method for estimating π(0) that aims to reduce the bias and variance of the estimation simultaneously. To achieve this, we first utilize the probability density functions of false-null p-values and then propose a novel algorithm to estimate the quantity of π(0). The statistical behavior of the proposed estimator is also investigated. Finally, we carry out extensive simulation studies and several real data analysis to evaluate the performance of the proposed estimator. Both simulated and real data demonstrate that the proposed method may improve the existing literature significantly.

No abstract