正态分布会计英语题

其详细过程可以是，∵X~N(0,1)，∴其密度函数f(x)=[1/√(2π)]e^(-x²/2)【设A=1/√(2π)】。∴Φ(x)=∫(-∞,x)f(x)dx=A∫(-∞,x)e^(-x²/2)dx。∴Φ(-x)=A∫(-∞,-x)e^(-x²/2)dx。对∫(-∞,-x)e^(-x²/2)dx。令x=-t，∴∫(-∞,-x)e^(-x²/2)dx=∫(t,∞)e^(-t²/2)dt=∫(x,∞)e^(-x²/2)dx，∴Φ(x)+Φ(-x)=A[∫(-∞,x)e^(-x²/2)dx+∫(x,)e^(-x²/2)dx]=A[∫(-∞,∞)e^(-x²/2)dx=1。∴ Φ(-x)=1-Φ(x)。供参考。

任选一名同学考试成绩与总体是同分布的，记总体x服从正态分布n(120,100)，则y=(x-120)/10~n(0,1)因此，“任选一名同学考试成绩在110分到130分之间的概率”为p(110评论018加载更多

THEORETICAL BACKGROUND理论背景A wide range of prediction models can be found in literature review. These models use different approaches to evaluate company's performance and predict its failure. A brief chronological and methodological overview of the most important papers is presented below, describing researches that were pioneering (at least for the applied methodology) only at the time and those that are either still widely used or left a mark and provided incentives for other scientists.在文献查阅中，可以查到各式各样的预测模型。这些模型使用不同的方法评估公司绩效并预测其破产。以下按照年代顺序和分析方法分类，简要介绍一些最主要的理论。这些研究有的在当时是开拓性的（至少应用方法如此），但仅领一时风骚；一些仍在被广泛使用，或者转瞬即逝，但激发了其他的科学家。The financial statements analysis dates to the 1920s, when F. Donaldson Brown joined Du Pont Company and in period from 1920 to 1924 developed a model for financial performance measurement. This deductive ratio, known as Du Pont Model analyzes the profitability of a company using traditional financial ratios. It integrates company's profitability and asset management, measuring its liquidity, leverage and efficiency. Return on investment is calculated by interacting different financial ratios from the aforementioned areas. The main strengths of Du Pont model are its simplicity and its linkage to compensation schemes. On the other hand, its main disadvantage is that is based on accounting numbers from balance sheet and income statement which are not reliable because of accrual concept. Du Pont Model remained the dominant form of financial analysis until the 1970s.财务决算分析始于20世纪20年代，F.Donaldson Brown入主杜邦公司之后，在1920年到1924年之间建立了一个用于财务状况评估的模型。这个被称作“杜邦模型”的演绎比率，利用传统的财务比率分析了公司的盈利性。它综合了公司的盈利性和资产管理，测量它的流动性、杠杆和效率。并通过交叉引用以上领域的相关财务比率计算出投资回报率。杜邦模型最大的优点是它的简单和它与薪资规划的联结。另一方面，它最大的缺点是它是基于资产负债表和损益表中的会计数字的。而这些数字，由于利息观念的存在，是不可靠的。杜邦模型直到20世纪70年代仍是财务分析的主流。One of the first researches in the area of ratio analysis and bankruptcy prediction, applying statistical methods was conducted by Beaver (1967) in 1966. He applied univariate analysis, using each of 14 accounting ratios separately, and found the difference in financial ratios structure between failed and non-failed companies for as long as five years prior to failure. He concluded that the cash flow to debt ratio was the best single ratio predictor, with a 78% accuracy in predicting bankruptcy. Discussants criticized his model because of the statistical methods used. 最早涉足比率分析和破产预测领域的一位研究者，用的是统计方法。由Beaver（1967）在1966年实施。他应用了单变量分析，分别使用14个会计比率，从而至少在破产的五年之前，就找出了破产与未破产公司之间财务比率结构的差别。他总结出，现金流与负债比率是最好的单比率预测器——在破产预测中有78%的正确率。而评论者则因为他使用的统计方法而批评他的模型。Altaian (Altaian and Hotchkiss, 2006) precluded this statistical limitation and applied multivariate discriminant analysis to construct his Z-score in 1968, probably the most famous model to the present day. The Zscore model claimed to predict bankruptcy correctly in 95% of the cases one year prior to defaulting, and in 83% of the cases two years in advance and rapidly decreased for longer time observations. However, in the 1980s the theorists, mainly econometricians, began to stress the statistical methodology applied as a major deficiency of the Zscore model. They claimed that linear discriminant analysis follows a normal distribution of financial ratios and equal structure of variance and covariance between paired good and bad companies, which is often not the case in practice. Altaian阿勒坦恩（Altaian阿勒坦恩和Hotchkiss霍奇基斯, 2006）排除了这种统计上的局限，应用多变量判别分析，在1968年建立起他的Z-score理论——也许是现今最有名的模型。Z-score模型宣称，其提前一年预知破产的准确率在95%，提前两年预知的正确率为83%，但在更长时间观测中，正确率会急剧下降。但是，在20世纪80年代，理论家们——主要是经济学家，将Z-score模型中的统计方法视为其重大缺陷。他们认为在分析成对的优秀与不良公司时，线性判别分析遵从财务比率的正态分布，以及方差和协方差的平衡结构。但现实往往不是如此。

标准正态分布又称为u分布，是以0为均数、以1为标准差的正态分布，记为N（0，1）。正态分布（Normal distribution）又名高斯分布（Gaussian distribution），是一个在数学、物理及工程等领域都非常重要的概率分布，在统计学的许多方面有着重大的影响力。期望值μ=0，即曲线图象对称轴为Y轴，标准差σ=1条件下的正态分布，记为N(0，1)。