基于完全数据和删失数据场合Kumaraswamy分布的参数估计
发布时间：2018-12-10 17:36
【摘要】：1980年Kumaraswamy在研究水文学中日常降雨量的问题时首次提出Kum-araswamy分布.Kumaraswamy分布是一种随机变量取值介于[0,1]范围上的双参数连续型分布,该分布相对于贝塔分布在某些方面表现出更好的性质.本文研究完全数据和删失数据场合Kumaraswamy分布的参数估计问题,主要研究了以下几方面内容:首先,在完全数据下,分别考虑简单随机抽样和有序抽样技术下Kumarasw-amy分布的极大似然估计和贝叶斯估计,通过数值模拟比较极大似然估计和贝叶斯估计的偏差、均方误差和有效性,结果表明有序抽样技术下的参数估计要优于简单随机抽样下的参数估计.其次,在逐步Ⅱ型混合删失数据下,主要考虑采用EM算法对Kumaraswamy分布的参数进行极大似然估计及三种损失函数下的贝叶斯估计问题.由于得到的贝叶斯估计结果是比较复杂的积分形式,不能直接求解,故本章采用林德利近似法获得估计的解析式,并通过数值模拟对参数的平均值、均方误差及置信区间估计,结果表明贝叶斯估计优于极大似然估计.最后,在自适应逐步Ⅱ型删失数据下,考虑Kumaraswamy分布参数的极大似然估计和贝叶斯估计,并讨论不同类型参数的置信区间.通过数值模拟,发现在无信息伽马先验分布下,极大似然估计和贝叶斯估计得到的结果比较接近.又由于贝叶斯估计计算比较费时,故认为采用极大似然估较好.
[Abstract]:In 1980, when Kumaraswamy studied the problem of daily rainfall in hydrology, the Kum-araswamy distribution was first put forward. The Kumaraswamy distribution is a two-parameter continuous distribution with the value of random variable in the range of [0 ~ 1]. This distribution shows better properties than Beta distribution in some aspects. In this paper, we study the parameter estimation of Kumaraswamy distribution in the case of complete data and censored data. The main contents are as follows: firstly, in the case of complete data, The maximum likelihood estimation and Bayesian estimation of Kumarasw-amy distribution under simple random sampling and ordered sampling are considered respectively. The deviation, mean square error and validity of maximum likelihood estimation and Bayesian estimation are compared by numerical simulation. The results show that the parameter estimation of ordered sampling is better than that of simple random sampling. Secondly, the EM algorithm is used to estimate the parameters of Kumaraswamy distribution with maximum likelihood and Bayesian estimation under three loss functions. Because the result of Bayesian estimation is a complex integral form, it can not be solved directly. In this chapter, the analytical formula of the estimation is obtained by using the Lindelli approximation method, and the mean value, mean square error and confidence interval of the parameters are estimated by numerical simulation. The results show that Bayesian estimation is superior to maximum likelihood estimation. Finally, the maximum likelihood estimation and Bayesian estimation of the parameters of Kumaraswamy distribution are considered, and the confidence intervals of different types of parameters are discussed under the condition of adaptive stepwise type 鈪，
本文编号：2370960
[Abstract]:In 1980, when Kumaraswamy studied the problem of daily rainfall in hydrology, the Kum-araswamy distribution was first put forward. The Kumaraswamy distribution is a two-parameter continuous distribution with the value of random variable in the range of [0 ~ 1]. This distribution shows better properties than Beta distribution in some aspects. In this paper, we study the parameter estimation of Kumaraswamy distribution in the case of complete data and censored data. The main contents are as follows: firstly, in the case of complete data, The maximum likelihood estimation and Bayesian estimation of Kumarasw-amy distribution under simple random sampling and ordered sampling are considered respectively. The deviation, mean square error and validity of maximum likelihood estimation and Bayesian estimation are compared by numerical simulation. The results show that the parameter estimation of ordered sampling is better than that of simple random sampling. Secondly, the EM algorithm is used to estimate the parameters of Kumaraswamy distribution with maximum likelihood and Bayesian estimation under three loss functions. Because the result of Bayesian estimation is a complex integral form, it can not be solved directly. In this chapter, the analytical formula of the estimation is obtained by using the Lindelli approximation method, and the mean value, mean square error and confidence interval of the parameters are estimated by numerical simulation. The results show that Bayesian estimation is superior to maximum likelihood estimation. Finally, the maximum likelihood estimation and Bayesian estimation of the parameters of Kumaraswamy distribution are considered, and the confidence intervals of different types of parameters are discussed under the condition of adaptive stepwise type 鈪，
本文编号：2370960
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