【摘要】：1980年Kumaraswamy在研究水文學(xué)中日常降雨量的問(wèn)題時(shí)首次提出Kum-araswamy分布.Kumaraswamy分布是一種隨機(jī)變量取值介于[0,1]范圍上的雙參數(shù)連續(xù)型分布,該分布相對(duì)于貝塔分布在某些方面表現(xiàn)出更好的性質(zhì).本文研究完全數(shù)據(jù)和刪失數(shù)據(jù)場(chǎng)合Kumaraswamy分布的參數(shù)估計(jì)問(wèn)題,主要研究了以下幾方面內(nèi)容:首先,在完全數(shù)據(jù)下,分別考慮簡(jiǎn)單隨機(jī)抽樣和有序抽樣技術(shù)下Kumarasw-amy分布的極大似然估計(jì)和貝葉斯估計(jì),通過(guò)數(shù)值模擬比較極大似然估計(jì)和貝葉斯估計(jì)的偏差、均方誤差和有效性,結(jié)果表明有序抽樣技術(shù)下的參數(shù)估計(jì)要優(yōu)于簡(jiǎn)單隨機(jī)抽樣下的參數(shù)估計(jì).其次,在逐步Ⅱ型混合刪失數(shù)據(jù)下,主要考慮采用EM算法對(duì)Kumaraswamy分布的參數(shù)進(jìn)行極大似然估計(jì)及三種損失函數(shù)下的貝葉斯估計(jì)問(wèn)題.由于得到的貝葉斯估計(jì)結(jié)果是比較復(fù)雜的積分形式,不能直接求解,故本章采用林德利近似法獲得估計(jì)的解析式,并通過(guò)數(shù)值模擬對(duì)參數(shù)的平均值、均方誤差及置信區(qū)間估計(jì),結(jié)果表明貝葉斯估計(jì)優(yōu)于極大似然估計(jì).最后,在自適應(yīng)逐步Ⅱ型刪失數(shù)據(jù)下,考慮Kumaraswamy分布參數(shù)的極大似然估計(jì)和貝葉斯估計(jì),并討論不同類型參數(shù)的置信區(qū)間.通過(guò)數(shù)值模擬,發(fā)現(xiàn)在無(wú)信息伽馬先驗(yàn)分布下,極大似然估計(jì)和貝葉斯估計(jì)得到的結(jié)果比較接近.又由于貝葉斯估計(jì)計(jì)算比較費(fèi)時(shí),故認(rèn)為采用極大似然估較好.
[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，

本文編號(hào)：2370960