【摘要】：心理狀態(tài)數(shù)可以反映實際工作者在在工作要求下的操作技術(shù)水平。在評價一個工作者的技術(shù)水平時,一般通過衡量其結(jié)果與要求標(biāo)準(zhǔn)之間的差異大小來進行判斷,如果差異值過大或者超過某一值時,則認(rèn)定該結(jié)果效果較差或判為不合格。在偏差自然地服從正態(tài)分布的基礎(chǔ)上,出于對結(jié)果的需求,即某種心理狀態(tài)作用,偏差的分布更傾向于工工作者的需要而不再服從正態(tài)分布,進而形成一種偏態(tài)分布。在人為因素影響的工作環(huán)境,該分布相對于正態(tài)分布更具有應(yīng)用價值。本文首先對心理狀態(tài)數(shù)以及偏態(tài)分布的產(chǎn)生背景及其發(fā)展進行了闡述。參考前人的研究成果,對兩參數(shù)偏態(tài)分布的分布性質(zhì)及數(shù)字特征進行了考察。結(jié)合其性質(zhì),運用了幾種矩估計和極大似然估計方法對參數(shù)進行了估計,同時列出了前人的一些Bayes估計方法。通過Monte Carlo模擬對所有的方法進行了比較。由此得出:本人給出的兩種矩估計方法在不同情況下均有更好的效果。隨后給出了參數(shù)的區(qū)間估計,討論了卡方分布與中心極限定理下的在不同環(huán)境狀況下對于區(qū)間長度的影響。其次提出了三參數(shù)偏態(tài)分布下的統(tǒng)計分析方法,給出了極大似然估計與兩種矩估計得出的結(jié)果及其比較,極大似然估計在給出的樣本數(shù)量較大時效果更好。在考慮到兩參數(shù)偏態(tài)分布的正負(fù)偏差的方差其實并不是相等的情況下,引入了參數(shù)θ,表示為正負(fù)偏差的標(biāo)準(zhǔn)差的比值,給出三參數(shù)廣義偏態(tài)分布,運用了矩估計和極大似然估計對參數(shù)進行了估計,控制變量在Monte Carlo模擬下得到,極大似然估計對參數(shù)θ,c的擬合效果較好,矩估計對參數(shù)σ的擬合效果較好。進一步,引入位置參數(shù)μ,給出四參數(shù)廣義偏態(tài)分布下的統(tǒng)計分析方法,運用極大似然估計的方法對參數(shù)進行了估計,并通過Monte Carlo模擬得出該方法對參數(shù)的擬合效果。給出了兩參數(shù)偏態(tài)分布SN(σ12,σ22)的統(tǒng)計分析方法,區(qū)別于三參數(shù)廣義偏態(tài)分布,此處將給出正值偏差與負(fù)值偏差的方差值替代心理狀態(tài)數(shù)c進行考察。結(jié)合現(xiàn)有文獻中的研究方法,給出了一種新的矩估計方法(方法三),通過Monte Carlo模擬比較,該方法參數(shù)的擬合效果更好。在上述基礎(chǔ)上再次引入位置參數(shù)μ,給出三參數(shù)偏態(tài)分布SN(σ12,σ22,μ)下的統(tǒng)計分析方法,運用了矩估計以及極大似然估計的方法對參數(shù)進行了估計,由于求解過程過于復(fù)雜未能得出模擬結(jié)果。最后,通過實例對文章中的方法進行了比較。
[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.
【學(xué)位授予單位】：上海師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O212.1

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