二維聯合分配下條件常態分配相容性之探討

Abstract

根據Arnold and Press (1989) 提出檢驗兩個條件分配是否滿足相容條件的理論內容，本研究推論出，當給定二個條件機率密度函數的形式為常態（normal）時，如何判斷這兩個條件常態分配是否相容的充要條件，並進而推論出這兩個條件常態分配對應的聯合機率密度函數亦為常態分配的條件。我們更進一步透過電腦模擬方法，提供兩個不同聯合常態分配下所分別得到的兩組不同條件分配樣本，據以推得當對應的母數相差到何種程度時，可判定這兩組樣本其原始母體不同。

Arnold and Press (1989) provide the theory about the compatibility of two conditional densities. In this research, we use their results to find the sufficient conditions of the compatibility of two conditional densities, which have the normal form. New sufficient conditions are also given if we further assume that corresponding joint density is normal. In addition, we use computer to generate two different samples from two different conditional normal distributions, which are from two different joint normal distributions. With the repeated samples, we provide the ranges of one population parameter when the other population parameters are fixed so that the samples are almost always incompatible.