p-范分布中参数的置信区间

The confidence intervals of parameters in p-norm distribution

在观测值服从p-范分布时,通过矩估计,极大似然估计和中心极限定理等工具确定了合适的枢轴量,得到了不同情况下各参数的(近似)置信区间。在单总体情况下,对于参数μ分别讨论了方差参数σ已知和未知两种情况下的近似置信区间,对于参数σ亦讨论了参数μ已知和未知两种情况,而参数p在理论中只讨论了h(p)的近似置信区间,在模拟算例中可求出p的近似置信区间。在双总体情况下,对于μ1-μ2分别讨论了方差参数σ1,σ2已知和未知两种情况下的近似置信区间,对于σ1p/σ2p亦讨论了参数μ1,μ2已知和未知两种情况,在理论中只讨论了h(p1)-h(p2)的近似置信区间,在模拟算例中通过中值定理等可求出p1-p2的近似置信区间。几个模拟算例均可说明得出的(近似)置信区间相关结论是可行的。

When the observed values obey the p-norm distribution,the appropriate pivotal quantity is determined by methods of moment estimation,maximum likelihood estimation(MLE)and central limit theorem(CLT).The(approximate)confidence intervals of each parameter under different conditions are obtained.In single population,the author discussed the approximate confidence interval of the parameterμ,when the variance parameterσis known and unknown.The author also discusses the parameterσwith known and unknown the parameterμ.For the parameter p,only the approximate confidence interval of h(p)is discussed,and the approximate confidence interval of p can be obtained in the simulation example.In double populations,the author discussed the approximate confidence interval ofμ1-μ2,whenσ1 andσ2 are known and unknown respectively.The author also discussed the approximate confidence interval ofσp1/σp2,under the parameterμ1、μ2 known and unknown.In theory,only the approximate confidence interval of h(p1)-h(p2)is discussed.In the simulation example,the approximate confidence interval of p1-p2 can be obtained by the mean value theorem.Several numerical examples demonstrate the feasibility of the(approximate)confidence intervals.