毕业论文指数分布

【中文摘要】：本文由几何分布产品的统计分析和Weibull分布产品的统计分析两篇组成。 第一篇：几何分布产品的统计分析 几何分布是离散型分布中最重要的分布之一，它在信息工程、电子工程、控制论及经济学中有着重要的应用。例如一些接插件产品(如开关等)，其寿命就可以用几何分布来描述。在可靠性理论中，由于几何分布的无记忆性，使得其是离散型寿命分布中最为重要的寿命分布之一，其相当于指数分布在连续型寿命分布中的地位，这正如程侃研究员在文献[5]中所指出的“在离散寿命的情形，几何分布起着连续情形下指数分布所起的作用”一样。由此可见，对几何分布产品的研究有着重要的理论与应用价值。本文对几何分布作了比较全面系统的研究。涉及三个方面的工作，主要结果如下： 第一、几何分布产品的统计特征。 (1)研究离散型分布次序统计量的分布，给出一个、二个和三个次序统计量的概率分布。 (2)几何分布总体次序统计量性质与指数分布次序统计量性质的比较，着重说明其相似和差异性。 (3)在证明Arnold猜想方面取得了一些进展。 第二、几何分布产品的可靠性统计分析。 (1)给出求定数截尾数据埸合下参数的点估计的多种方法，比较了各种点估计的精度；构造了求参数近似区间估计的枢轴量，并通过模拟说明本文方法是可行的。 (2)定时截尾场合下参数的点估计和区间估计以及缺失数据和分组型数据埸合下参数的点估计。 (3)恒定应力、步进应力加速寿命试验下参数的点估计。 第三、离散寿命分布类与几何分布贴近性和统计贴近性。 (1)研究了几何分布的特征性质，首次提出统计封闭性和统计贴近性的概念。 (2)研究了离散的新比旧平均好的类(dNBUE类)与几何分布的贴近性，在附加一定条件下进一步缩小了贴近性的上界。 第二篇：Weibull分布产品的统计分析 Weibull分布已成为可靠性中应用最广泛的连续型寿命分布之一，它可用来描述不少产品的失效分布。例如金属材料的疲劳寿命等等。针对长寿命、高可靠的产品用通常的试验办法无法获得寿命数据，由此出现了加速寿命试验方法。此方法不仅对试验设备有较高的要求，而且还要对模型作出一定的假设。本文是针对损伤失效率模型(TFR)模型就Weibull分布产品在步进应力加速寿命试验下研究了参数的点估计。主要结果如下： (1)给出了参数的近似极大似然估计(AMLE)和逆矩估计，比较了AMLE、MLE和逆矩估计的精度，另外给出了求形状参数区间估计的方法。 (2)研究了逐次Ⅱ型截尾场合下参数的点估计。 (3)给出了求正常工作应力下参数点估计的方法。'【英文摘要】：This article is composed of two parts: the statistical analysis for geometric distribution and the statistical analysis for Weibull distribution as one: The statistical analysis for geometric distributionThe geometric distribution is one of the better known discrete probability distributions and has many useful applications. Its applications include in the fields of information engineering, electronics industry, theory of controls and economic, example, we use geometric distribution to describe the life distribution of runs of a species in transect surveys of plant populations and inventory demand distributions. In the theory of reliability, geometric distribution is one of the most important discrete probability distributions because of its loss of memory. This article gives the key results for geometric distribution with respect to the following three aspects:1. The statistical character for geometric distribution.(1) The distributions of the order statistics for discrete distribution are studied in this section. Therefore, the probability distributions of the 1st, 2nd and 3rd order statistics are derived, respectively.(2) We point out the similarity and difference between the properties of the order statistics from the geometric distribution population and exponential distribution population.(3) We make some progress in proving the Arnolds's . The statistical analysis of geometric distribution.(1) After giving the various methods for getting the point estimations of parameters based on the type-Ⅱ censored data. We do the comparison of the accuracy of all these point estimations. In the portion, the pivotal quantity used to get the approximate interval estimation of parameters is also derived. Afterwards, we show the feasibility of our method by using the Monte-Carlo simulation.(2) The point estimation and interval estimation of parameters under type-Ⅰ censored case and the point estimation of parameters based on the missing data and grouped data are obtained, respectively.(3) The point estimations of parameters under the constant stress and step-stress accelerated life testing are derived in this part, . The approach property and statistical approach property of discrete lifedistribution class and geometric distribution.(l)We carry out the research on the characteristic property of geometric distribution. Hence, we propose the two new concepts: statistical closed property and statistical approach property.(2) Make a detailed study of the discrete new better than used in expectation class and the approach property of geometric distribution. Furthermore, we narrow the upper bound by adding certain Two: The statistical analysis for Weibull distributionWeibull distribution is one of the widely used continuous life distributions, it can be used to describe the failure distribution of quite a lot product. For example, the weakness in metals etc. caused by repeated stress. This article gives the point estimation of parameters based on tampered failure rate model for Weibull distribution under step-stress accelerated life testing. The main results are listed as follows:(l)We present the inverse moment estimations and approximate maximum likelihood estimations of parameters, and then we examine the accuracy of the AMLE, MLE and interval estimations. Moreover we derive the method to get interval estimation of the shape parameter.(2)Focus on the point estimation of parameters under Type- Ⅱ life testing basedon step-increasing data.(3) Derive a way to get the point estimations of parameters under normal working condition stress.对不起，只能写这么多 可以看：【牛彪论文网】