考试成绩标准化处理数学方法初探

利用概率统计学原理处理考试成绩，用两个处理方法，构造两个函数，使得考试 成绩分布在较合理的范围内。     

Probability distributions,trading strategies and leverage: an application of Gaussian mixture models

The purpose of this paper is twofold. Firstly, to assess the merit of estimating probability density functions rather than level or classification estimations on a one‐day‐ahead forecasting task of the EUR/USD time series. This is implemented using a Gaussian mixture model neural network, benchmarking the results against standard forecasting models, namely a naïve model, a moving average convergence divergence technical model (MACD), an autoregressive moving average model (ARMA), a logistic regression model (LOGIT) and a multi‐layer perceptron network (MLP). Secondly, to examine the possibilities of improving the trading performance of those models with confirmation filters and leverage. While the benchmark models perform best without confirmation filters and leverage, the Gaussian mixture model outperforms all of the benchmarks when taking advantage of the possibilities offered by a combination of more sophisticated trading strategies and leverage. This might be due to the ability of the Gaussian mixture model to identify successfully trades with a high Sharpe ratio. Copyright © 2004 John Wiley & Sons, Ltd.     

排队模型中状态概率方程的简化

提出排队模型中的稳态下状态概率方程的简化形式，用数学归纳法给以证明并进行了进一步讨论．计算实例表明，使用简化的状态概率方程求解结果与传统算法完全一致，而前者计算过程更为简捷方便．     

维恩位移定律公式的讨论

本文指出了一本教科书中关于维恩位移定律公式推导的一个错误,并分析了产生错误的原因。     

川西平原农田啮齿动物群落变量的模拟研究

利用Monte Carlo方法，模拟了川西平原农田啮齿动物群落变量的总和、年间和月间变动情况及统计学特征，其变量是：物种数、生物量、物种多样性和均匀性。真实群落4个变量的所有值均在模拟群落变量的95％置信区间内。物种数和物种多样性显示出了相似的变动规律。真实群落4个变量与模拟群落4个变量也显示出了相似的变动规律。当零假设为这些变量服从正态分布时，用单样本Kolmogorov-Smirnov方法检验，得到的结果与偏度和峭度显示的结果并不完全一致。结果说明，要估计一个变量的置信区间，需要有足够大的样本含量。     

古典概型中摸球模型的解法探讨

通过对古典概型中摸球模型的探讨,提供了一些有用的解题思路和方法,并试图以明确的公式形式表达特定问题的解.     

THE TRANSITION PROBABILITY MATRIX OF A MARKOV CHAIN MODEL IN AN ATM NETWORK

In this paper we consider a Markov chain model in an ATM network, which has been studied by Dag and Stavrakakis. On the basis of the iterative formulas obtained by Dag and Stavrakakis, we obtain the explicit analytical expression of the transition probability matrix. It is very simple to calculate the transition probabilities of the Markov chain by these expressions. In addition, we obtain some results about the structure of the transition probability matrix, which are helpful in numerical calculation and theoretical analysis.     

一类连续型随机数学模型的参数估计

讨论一类连续型随机数学模型的参数估计问题，分析解过程的概率特性，构造解过程的密度函数，借助极大似然法给出了未知参数的估计公式，证明了参数估计依概率1收敛到参数的真值。     

无穷伯努利试验中的一个连贯问题

利用概率的下连续性,我们定义了无穷伯努利试验中一个连贯问题的概率,进而我们用一个比较简单但在一般场合也可以应用的方法导出了这个概率的计算公式。     

关于数据不完整情形下的参数估计问题

本文针对数理统计中,在数据不完整(例如缺数值小的数据)情形下,如何进行参数估计问题,提出了求解方法,并进行了实例验证.