本研究針對數個天琴RR型變星的經驗週光-金屬豐度關係進行比較，藉以檢驗其在估算距離的可靠度與準確性。透過數組源於不同宿主系統──大麥哲倫星雲、天龍座矮星系、半人馬座$\omega$──之樣本，實際使用經驗週光-金屬豐度關係量測至宿主系統的距離模數，並與文獻提供之參考距離模數比較，評估各個週光-金屬豐度關係量測距離的表現。為深入了解不同經驗週光-金屬豐度關係的不一致與估算距離時的表現差異，並討論其本質原因，以統計學檢驗──二維度科摩哥洛夫-史密諾夫檢定、能量距離檢驗──比較各樣本的天琴RR型變星性質。此對於天琴RR變星週光關係的的綜合性測試，將提供對於在不同系統中該變星性質的了解，以避免未來校正新的週光-金屬豐度關係，或利用週光關係量測距離時產生系統性偏差。;We compared empirical period-luminosity-metallicity (PLZ) and period-Wesenheit index-metallicity (PWZ) relations of RR Lyrae stars to evaluate their validity and precision in distance estimation. Our analysis employs RR Lyrae samples from various host systems， including the Large Magellanic Cloud， Draco dwarf galaxy， and globular cluster $\omega$ Centauri. By comparing the inferred distances from different empirical relations with the independently established distance moduli of these systems， we evaluate the performance and consistency of empirical relations. To discuss the intrinsic factors that may contribute to discrepancies among the empirical relations and various behaviors in estimating distance， we compared the sampled population of RR Lyrae of each dataset using statistical tests， two dimensional Kolmogorov-Smirnov test and energy distance test. This comprehensive examination of RR Lyrae PLZ and PWZ relations provides insights that can help reduce systematic biases in future distance measurements obtained from surveys utilizing Sloan-like photometric filters.
