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Bayesian Inference for the Mean and Standard Deviation of a Normal Population when only the Sample Size, Mean and Range are Observed

机译:当仅观察样本大小,均值和范围时,贝叶斯推断正态总体的均值和标准差

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摘要

Consider a random sample X_1, X_2,..., X_n, from a normal population with unknown mean and standard deviation. Only the sample size, mean and range are recorded and it is necessary to estimate the unknown population mean and standard deviation. In this paper the estimation of the mean and standard deviation is made from a Bayesian perspective by using a Markov Chain Monte Carlo (MCMC) algorithm to simulate samples from the intractable joint posterior distribution of the mean and standard deviation. The proposed methodology is applied to simulated and real data. The real data refers to the sugar content (°BRIX level) of orange juice produced in different countries.
机译:考虑来自均值和标准差未知的正常总体的随机样本X_1,X_2,...,X_n。仅记录样本大小,均值和范围,有必要估计未知总体的均值和标准差。在本文中,均值和标准差的估计是从贝叶斯角度出发,使用马尔可夫链蒙特卡洛(MCMC)算法从均值和标准差的难处理的联合后验分布模拟样本。所提出的方法应用于模拟和真实数据。实际数据是指不同国家/地区生产的橙汁的糖含量(°BRIX水平)。

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