p-范分布参数σ的估计

Parameter σ Estimation of p-norm Distribution

用极大似然法估计一元 p_范分布参数σ。在 μ、p已知的条件下 ,得出 ^σp 是σp 的无偏估计及 npλp·^σpσp服从 χp 分布 ,进而给出方差的假设检验方法。

In surveying data processing,when the distribution of observational errors is symmetry and has only one peak value,we may assume that it is p _norm distribution.By choosing a specific value of p ,the p _norm distribution can be closer to the real distribution of the errors than a normal one.Equations about parameters of p _norm distribution could not be directly solved using average method,so the estimations of the parameters could not be obtained directly.In this paper,we try to discuss them under the conditions that the values of the parameter μ and p are known.The following results are derived. First,the estimator of parameter σ is given by the method of maximum likelihood.Second,because the expectancy and variance are very important to depict the statistical property of a random variance,we give the calculating formulas of the expectancy and variance of estimator p ,and prove that p is a unbiased estimator.Third,we derive that the estimate of npλ p pσ p is χ p distributed.Lastly,by using the above results,hypothesis testing about p is discussed.The testing method of hypothesis to the variance is concluded when the hypothetical universe is a p _norm distribution.