有界线性指数损失函数下样本容量的确定
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摘要
文章研究线性指数损失函数和有界线性指数损失函数下的样本容量问题。在线性指数损失函数和正态分布假设下,给出了最优样本容量的解析解。对于有界线性指数损失函数,则给出了得到最优样本容量的算法,并且以正态分布与泊松分布为例求出了最优样本容量。由于有界线性指数函数在现实中的广泛应用,本文所给出的算法具有一定的应用价值。
This paper deals with the sample size problem under the linex loss function and blinex loss function. Firstly the paper gives the analytic solution of optimal sample size under the assumption of the linex loss function and the normal distribution.And for the blinex loss function, the paper gives an algorithm of obtaining the optimal sample size, and then takes the normal distribution and the Poisson distribution as an example to obtain the optimal sample size. Due to the wide application of blinex function in reality, the algorithm proposed in the paper has a certain application value.
This paper deals with the sample size problem under the linex loss function and blinex loss function. Firstly the paper gives the analytic solution of optimal sample size under the assumption of the linex loss function and the normal distribution.And for the blinex loss function, the paper gives an algorithm of obtaining the optimal sample size, and then takes the normal distribution and the Poisson distribution as an example to obtain the optimal sample size. Due to the wide application of blinex function in reality, the algorithm proposed in the paper has a certain application value.
引文
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[8]Wen D, Levy S. BLINEX:A Bounded Asymmetric Loss Function[J].Comm. Statist. Theory Methods 2001,(30).
[9]Wen D, Levy S. Algorithm of Fitting BLINEX Loss Parameters[J].Comm. Statist. Simulation Comput, 2004,(33).
[10]Afms I, L. P Bayesian Sample Size Determination Using Linex Loss and Linear Cost[J]. Comm. Stat. Theory Methods,2012,(41).
[11]Afms I, Li P. Bayesian Sample Size Determination for the Bounded Linex Loss Function[J].Journal of Statistical Computation and Simulation,2014,84(8).
[2]Joseph L, Wolfson D B,Berger, R. Sample Size Calculations for Binomial Proportions via Height Posterior Density Intervals[J].Statistician,1995,(44).
[3]Lindley D V. Bayesian Statistics, A Review[J].Society for Industrial and Applied Mathematics,1972.
[4]Lindley D V. The Choice of Sample Size[J].Statistician,1997,(46).
[5]Zellner A. Bayesian Estimation and Prediction Using Asymmetric Loss Functions[J].J. Amer. Statist. Assoc,1986,(81).
[6]Lindley D V. A Class of Utility Functions[J]. Ann. Statist,1976,(4).
[7]Smith J Q. Bayes Estimates Under Bounded Loss[J].Biometrika,1980,(67).
[8]Wen D, Levy S. BLINEX:A Bounded Asymmetric Loss Function[J].Comm. Statist. Theory Methods 2001,(30).
[9]Wen D, Levy S. Algorithm of Fitting BLINEX Loss Parameters[J].Comm. Statist. Simulation Comput, 2004,(33).
[10]Afms I, L. P Bayesian Sample Size Determination Using Linex Loss and Linear Cost[J]. Comm. Stat. Theory Methods,2012,(41).
[11]Afms I, Li P. Bayesian Sample Size Determination for the Bounded Linex Loss Function[J].Journal of Statistical Computation and Simulation,2014,84(8).