一种拓展的逆高斯分布的性质及其应用
发布时间：2018-12-18 18:20
【摘要】：随着时代的发展和科技的进步,人们对产品质量及可靠性的要求越来越高.很多新的分析可靠性的技术和数据处理的方法不断出现,使可靠性统计面临着许多新的问题.指数分布、Weibull分布、极值分布、Gamma分布等一些可靠性统计模型已经被很多专家学者研究并利用到实际生活中.但每一种可靠性统计模型并不是对所有类型的数据模拟效果都是好的,所以我们需要找到适应效果更好的分布对寿命数据进行模拟分析.本文针对上述问题展开讨论:第一,逆高斯分布和Weibull分布是可靠性理论中的两种重要的寿命分布模型,而T-X family方法是近年来拓展新分布中应用较广的一种方法.故而本文考虑由逆高斯分布与Weibull分布出发,利用T-X family的方法构建一个新的寿命分布,称之为拓展的逆高斯分布(EIG).我们讨论了它的一些基本性质,如密度曲线类型,危险率函数曲线、r阶中心距及矩母函数,偏度和峰度,随机序和剩余寿命等.第二,基于所产生的新分布,我们还研究了它的参数估计问题.讨论了新分布所含参数的极大似然估计和近似置信区间.针对已有数据,利用TTT转换分析数据危险率的形状,并对数据拟合的可行性作了分析.进而用EIG分布模拟真实数据,进行K-S拟合检验,分析讨论结果.第三,近年来,缺失和退化数据处理方面的应用研究大量出现,使得可靠性理论得到迅速发展.疲劳数据常常有限,尤其是从节约费用时间角度上,即使使用特殊的疲劳试验方法(加速寿命试验),也得不到完整的样本数据,得到的大多是截尾数据.因此有必要发展截尾数据下参数的统计推断问题.2009年Kundu提出一个自适应II型逐次截尾方案,较Ⅰ型和Ⅱ型逐次截尾方案,节省了总试验的时间和测试失效单元的成本,提高了统计分析的效率,解决了I、II型截尾方案的许多缺点.本文将基于自适应II型逐次截尾样本,对新分布的参数进行极大似然估计,并运用真实数据进行模拟研究.
[Abstract]:With the development of the times and the progress of science and technology, the demand of product quality and reliability is higher and higher. Many new techniques for reliability analysis and data processing are emerging, which make reliability statistics face many new problems. Some reliability statistical models, such as exponential distribution, Weibull distribution, extremum distribution, Gamma distribution and so on, have been studied by many experts and scholars and used in real life. However, each reliability statistical model is not good for all types of data simulation, so we need to find a better distribution of adaptive effect to simulate the life data. In this paper, the following problems are discussed: first, inverse Gao Si distribution and Weibull distribution are two important life distribution models in reliability theory, and T-X family method is a widely used method to expand new distribution in recent years. Therefore, in this paper, starting from the inverse Gao Si distribution and Weibull distribution, a new life distribution is constructed by using T-X family method, which is called the extended inverse Gao Si distribution (EIG). Some basic properties are discussed, such as density curve type, risk rate function curve, r order center distance and moment generating function, skewness and kurtosis, random order and residual life, etc. Secondly, based on the new distribution, we also study the parameter estimation problem. The maximum likelihood estimation and approximate confidence interval of the parameters contained in the new distribution are discussed. According to the existing data, the shape of data risk rate is analyzed by TTT transform, and the feasibility of data fitting is analyzed. EIG distribution is used to simulate the real data, K-S fitting test is carried out, and the results are analyzed. Thirdly, in recent years, applications of missing and degenerate data processing have emerged in large numbers, which makes the reliability theory develop rapidly. Fatigue data are often limited, especially from the point of view of saving cost and time. Even if special fatigue test method (accelerated life test) is used, the complete sample data can not be obtained, and most of the data obtained are truncated data. Therefore, it is necessary to develop the statistical inference of parameters under censored data. In 2009, Kundu proposed an adaptive II successive truncation scheme, which saves the total test time and the cost of the test failure unit compared with the successive truncation schemes of type 鈪，
本文编号：2386291
[Abstract]:With the development of the times and the progress of science and technology, the demand of product quality and reliability is higher and higher. Many new techniques for reliability analysis and data processing are emerging, which make reliability statistics face many new problems. Some reliability statistical models, such as exponential distribution, Weibull distribution, extremum distribution, Gamma distribution and so on, have been studied by many experts and scholars and used in real life. However, each reliability statistical model is not good for all types of data simulation, so we need to find a better distribution of adaptive effect to simulate the life data. In this paper, the following problems are discussed: first, inverse Gao Si distribution and Weibull distribution are two important life distribution models in reliability theory, and T-X family method is a widely used method to expand new distribution in recent years. Therefore, in this paper, starting from the inverse Gao Si distribution and Weibull distribution, a new life distribution is constructed by using T-X family method, which is called the extended inverse Gao Si distribution (EIG). Some basic properties are discussed, such as density curve type, risk rate function curve, r order center distance and moment generating function, skewness and kurtosis, random order and residual life, etc. Secondly, based on the new distribution, we also study the parameter estimation problem. The maximum likelihood estimation and approximate confidence interval of the parameters contained in the new distribution are discussed. According to the existing data, the shape of data risk rate is analyzed by TTT transform, and the feasibility of data fitting is analyzed. EIG distribution is used to simulate the real data, K-S fitting test is carried out, and the results are analyzed. Thirdly, in recent years, applications of missing and degenerate data processing have emerged in large numbers, which makes the reliability theory develop rapidly. Fatigue data are often limited, especially from the point of view of saving cost and time. Even if special fatigue test method (accelerated life test) is used, the complete sample data can not be obtained, and most of the data obtained are truncated data. Therefore, it is necessary to develop the statistical inference of parameters under censored data. In 2009, Kundu proposed an adaptive II successive truncation scheme, which saves the total test time and the cost of the test failure unit compared with the successive truncation schemes of type 鈪，
本文编号：2386291
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