Nonparametric Statistical Inference And Application In Homogeneity Test Of Climatic Data Of Γ-distribution With Change-point

Change-point frequently occurs not only in industry automation, but also in many fields such as economy, finance, climatology and computer. This dissertation briefly introduces the development, the research status, the main method and the application in statistical analysis of change-point. Then, it studies the nonparametric statistical inference and the application in climatology ofΓ-distribution with change-point.In this dissertation, the change-point of parameter in distribution is considered. Suppose that X₁,...,X_[nt₀],X_[nt0]+1...,X_n are independent random variables, X₁,...,X_[nt₀]i.i.d～Γ(x;v₁,λ₁) and X_[nt0]+1...,X_ni.i.d～Γ(x;v₂,λ₂), t₀ is unknown, call t₀ as change-point. This dissertation discusses the detection of t₀ by CUSUM when the variance is known and the detection of t₀ by the thinking of self-normalization when the variance is unknown, and the strong consistency and rate of convergence of (t|^) which is the estimation of t₀. Next it extends the way to the case of many change-points. Finally, it proves the feasibility of the method by a mount of stochastic modeling.In the fourth chapter, a newΓ-test based onΓ-distribution is established for inhomogeneity tests of climatic data. This dissertation uses it to check up the average of month temperature series and the average of annual atmospheric pressure series in Anhui province. Furthermore, the concrete test and analysis are given by taking Hefei, Shouxian and Tongcheng as examples. After comparing the result ofΓ-test with SNHT, this method, which can verify a majority of temperature and atmospheric pressure series, is superior to SNHT in scope and accuracy. It also shows the reliability of the data quality of the month's average temperature series in Anhui province. The significance inhomogeneity of the month's average temperature series is mainly caused by station transfer and the significance inhomogeneity of the atmospheric pressure series is mostly attributed to the change of barometer altitude and the station transfer .The atmospheric pressure series must be used carefully because of the excessive change-points.