Exact Distribution of Difference of Two Sample Proportions and Its Inferences

Comparing two population proportions using confidence interval could be misleading in many cases, such as the sample size being small and the test being based on normal approximation. In this case, the only one option that we have is to collect a large sample. Unfortunately, the large sample might not be possible. One example is a person suffering from a rare disease. The main purpose of this journal is to derive a closed formula for the exact distribution of the difference between two independent sample proportions, and use it to perform related inferences such as a confidence interval, regardless of the sample sizes and compare with the existing Wald, Agresti-Caffo and Score. In this journal, we have derived a closed formula for the exact distribution of the difference between two independent sample proportions. This distribution doesn’t need any requirements, and can be used to perform inferences such as: a hypothesis test for two population proportions, regardless of the nature of the distribution and the sample sizes. We claim that exact distribution has the least confidence width among Wald, Agresti-Caffo and Score, so it is suitable for inferences of the difference between the population proportion regardless of sample size.

Indentation size effect of germanium single crystal with different crystal orientations

In order to study the indentation size effect(ISE)of germanium single crystals,nano-indentation experiments were carried out on the(100),(110)and(111)plane-orientated germanium single crystals.The true hardness of each crystal plane of germanium single crystals was calculated based on the Meyer equation,proportional sample resistance(PSR)model and Nix-Gao model,and the indentation size effect(ISE)factor of each crystal plane was calculated.Results show that,the germanium single crystals experience elastic deformation,plastic deformation and brittle fracture during the loading process,and the three crystal planes all show obvious ISE phenomenon.All three models can effectively describe the ISE of germanium single crystals,and the calculated value of Nix-Gao model is the most accurate.Compared with the other two crystal planes,Ge(110)has the highest size effect factor m and the highest hardness,which indicates that Ge(110)has the worst plasticity.

Design and research of an LED driving circuit with accurate proportional current sampling mode

An LED driving circuit in accurate proportional current sampling mode is designed and fabricated based on CSMC 0.5 μm standard CMOS technology. It realizes accurate sensing of sampling current variation with output driving current. A better constant output current characteristic is achieved by using an amplifier to clamp the drain voltage of both the sampling MOSFET and power MOSFET to the same value with feedback control. Small signal equivalent circuit analysis shows that the small signal output resistance in the accurate proportional current sampling mode circuit is much larger than that in a traditional proportional current sampling mode circuit, and circuit stability could be assured. Circuit simulation and chip testing results show that when the LED driving current is 350 mA and the power supply is 6 V with ± 10% variation, the stability of the output constant current of the accurate proportional current sampling mode LED driving IC will show 41% improvement over that of a traditional proportional current sampling mode LED driving IC.