心理状态数的统计分析方法

发布时间：2019-01-09 12:24

【摘要】：心理状态数可以反映实际工作者在在工作要求下的操作技术水平。在评价一个工作者的技术水平时,一般通过衡量其结果与要求标准之间的差异大小来进行判断,如果差异值过大或者超过某一值时,则认定该结果效果较差或判为不合格。在偏差自然地服从正态分布的基础上,出于对结果的需求,即某种心理状态作用,偏差的分布更倾向于工工作者的需要而不再服从正态分布,进而形成一种偏态分布。在人为因素影响的工作环境,该分布相对于正态分布更具有应用价值。本文首先对心理状态数以及偏态分布的产生背景及其发展进行了阐述。参考前人的研究成果,对两参数偏态分布的分布性质及数字特征进行了考察。结合其性质,运用了几种矩估计和极大似然估计方法对参数进行了估计,同时列出了前人的一些Bayes估计方法。通过Monte Carlo模拟对所有的方法进行了比较。由此得出:本人给出的两种矩估计方法在不同情况下均有更好的效果。随后给出了参数的区间估计,讨论了卡方分布与中心极限定理下的在不同环境状况下对于区间长度的影响。其次提出了三参数偏态分布下的统计分析方法,给出了极大似然估计与两种矩估计得出的结果及其比较,极大似然估计在给出的样本数量较大时效果更好。在考虑到两参数偏态分布的正负偏差的方差其实并不是相等的情况下,引入了参数θ,表示为正负偏差的标准差的比值,给出三参数广义偏态分布,运用了矩估计和极大似然估计对参数进行了估计,控制变量在Monte Carlo模拟下得到,极大似然估计对参数θ,c的拟合效果较好,矩估计对参数σ的拟合效果较好。进一步,引入位置参数μ,给出四参数广义偏态分布下的统计分析方法,运用极大似然估计的方法对参数进行了估计,并通过Monte Carlo模拟得出该方法对参数的拟合效果。给出了两参数偏态分布SN(σ12,σ22)的统计分析方法,区别于三参数广义偏态分布,此处将给出正值偏差与负值偏差的方差值替代心理状态数c进行考察。结合现有文献中的研究方法,给出了一种新的矩估计方法(方法三),通过Monte Carlo模拟比较,该方法参数的拟合效果更好。在上述基础上再次引入位置参数μ,给出三参数偏态分布SN(σ12,σ22,μ)下的统计分析方法,运用了矩估计以及极大似然估计的方法对参数进行了估计,由于求解过程过于复杂未能得出模拟结果。最后,通过实例对文章中的方法进行了比较。
[Abstract]:The number of mental state can reflect the operation skill level of the actual worker under the work request. When evaluating the technical level of a worker, it is generally judged by measuring the difference between the result and the required standard. If the difference value is too large or exceeds a certain value, the result is considered to be poor or unqualified. On the basis of the normal distribution of deviation naturally, out of the demand for the result, that is, the effect of some psychological state, the distribution of deviation is more inclined to the needs of the workers than to the normal distribution, and then forms a skewness distribution. In the working environment affected by human factors, this distribution is more valuable than normal distribution. In this paper, the background and development of the number of mental states and the distribution of skewness are discussed. Referring to the previous research results, the distribution properties and numerical characteristics of two-parameter skewness distribution are investigated. Combined with its properties, several methods of moment estimation and maximum likelihood estimation are used to estimate the parameters, and some previous Bayes estimation methods are listed. All the methods are compared by Monte Carlo simulation. It is concluded that the two moment estimation methods proposed by me have better results under different conditions. Then, the interval estimation of parameters is given, and the effects of chi-square distribution and central limit theorem on interval length under different environmental conditions are discussed. Secondly, a statistical analysis method with three parameter skewness distribution is proposed. The results of maximum likelihood estimation and two moment estimations are given and compared. The maximum likelihood estimation is more effective when the number of samples given is larger. Considering that the variance of the positive and negative deviations of the biasing distribution of two parameters is not actually equal, the parameter 胃 is introduced, which is expressed as the ratio of the standard deviation of the positive and negative deviations, and the generalized skewness distribution with three parameters is given. Moment estimation and maximum likelihood estimation are used to estimate the parameters. The control variables are obtained by Monte Carlo simulation. The maximum likelihood estimation has a better fitting effect on parameters 胃, c, and moment estimation has a better fitting effect on parameter 蟽. Furthermore, by introducing the position parameter 渭, the statistical analysis method under the generalized skewness distribution with four parameters is given. The maximum likelihood estimation method is used to estimate the parameters, and the fitting effect of the method is obtained by Monte Carlo simulation. The statistical analysis method of two-parameter skewness distribution SN (蟽 12, 蟽 22) is given, which is different from the general skewness distribution with three parameters. Here, the square difference between positive deviation and negative deviation is given to replace the number of mental state c. A new method of moment estimation (method 3) is proposed based on the existing research methods in the literature. Compared with the Monte Carlo simulation, the method has better fitting effect. On the basis of the above, the position parameter 渭 is introduced again, and the statistical analysis method under SN (蟽 12, 蟽 22, 渭) is given. The moment estimation and maximum likelihood estimation are used to estimate the parameters. Due to the complexity of the solution process, the simulation results can not be obtained. Finally, the method in this paper is compared with an example.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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