正态变差系数的经典限

Classical Limits for the Coefficient of Variation for the Normal Distribution

摘要: 本文推导了正态变差系数的经典精确限.为了满足工程实践的需要,利用Odeh和Owen的计算方法及Brent算法,给出了高精度的可手算的近似限.对不同的置信度γ及样本大小n=1(1)30,40,60,120,样本变差系数ε=0.01(0.01)0.20,计算了正态变差系数的经典精确限表.本文指出,当n≤8,ε≤0.20时,经典精确限C_u略大于Fiducial精确限C_u,F.当n>8.ε≤0.20时.C_u-C_u,F<5×10^-6.

Abstract: The exact classical limits for the coefficient of variation c for the normal distribution are derived.The hand-calculating approximated classical limits for c having high accuracy are given to meet practical engineering needs.Using Odeh and Owen's computational method and Brent's algorithm,the tables for the r-upper exact classical limits of coefficient of variation for normal distribution are calculated for the different confidence coefficient γ,the sample size n=1(1)30,40,60,120,the sample coefficient of variation ε=0.01(0.01)0.20.It is shown that if n<8,ε<0.20,then the γ-upper exact classical limits c_u for c are slightly higher than the exact fiducial limits c_u,F for c if.n>8,c<0.02,then c_u-c_u,F<5×10^-6.

[1]	周源泉,正态变差系数的Fiducial及Bapes限,机械工程学报,22,3(1986),67-74.
[2]	Mckay,A.T.,Distribution of the coefficient of variation and extended t-distribution,J.R.Statist.Soc.,95(1932),695-698.
[3]	Pearson,E.S.,Comparison of A.T.Mckay's approximation with experimental sampling results,J.R.Statist.Soc.,95(1932),703-704.
[4]	Fieller,E.C,A numerical test of the adequacy of A.T.Mckay's approximation,J.R.Statist.Soc.,95(1932),699-702.
[5]	Koopmans,L.H.,D.B.Owen and J.I.Rosenblatt,Confidence intervals for the coefficient of variation for the normal and lognormal distribution,Biometrika,51(1964),25-32.
[6]	Johnson,N.L.and B.L.Welch,Application of the noncentral t-distribution Biometrika,27(1940),362-381.
[7]	周源泉,正态可靠寿命的玩yes限、Fiducial限及经典限,电子学报,14,2(1986),46-52.
[8]	山内二郎,《统计数值表》,JSA(1972).
[9]	Odeh,R.E.and D.B.Owen,Tables for Normal Tolerance Limits,Sampling Plans and Screening,Dekker(1980).
[10]	Brent,R.P.,An algorithm with guaranteed convergence for finding a zero of a function,Comput.J.,14(1971),422-425.