Parameter σ Estimation of p-norm Distribution

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 n/pλ^p σ^p/σ^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.