توزیع کاپا سه پارامتری و برازش آن به داده‌های مجموع بارش ماهانه ایستگاه آبعلی استان تهران

توزیع کاپا یکی از توزیع‌های چوله مثبت است که به‌منظور تجزیه و تحلیل داده‌های بارندگی، سرعت باد و جریان سیلاب استفاده می‌شود. در این مقاله ابتدا به بررسی توزیع کاپا سه پارامتری معرفی شده به‌وسیلۀ پارک و همکاران پرداخته و سپس چهار روش برآوردیابی شامل روش گشتاوری، گشتاورهای خطی بیشینۀ درست‌نمایی و بیشینۀ حاصل‌ضرب فاصله‌ها را برای برآوردیابی پارامترهای این توزیع ارائه داده و با استفاده از یک بررسی شبیه‌سازی، به مقایسۀ عملکرد آنها پرداخته و در پایان، این روش‌ها، برای داده‌های مربوط به مجموع بارش ماهانه ایستگاه آبعلی استان تهران به‌کار گرفته می‌شود.

Three-Parameter Kappa Distribution and its Fitting to the Whole Monthly Rainfall Data of Abali Station in Tehran Province

IntroductionThe kappa distribution was first introduced by Mielke (1973) and Mielke and Johnson (1973) for describing and analyzing precipitation data. This distribution is positively skewed and is widely applied when studying precipitation, wind speed and the stream flow data in hydrology. The kappa distribution has some advantages over gamma and lognormal distributions in fitting historical rainfall. Data It is because, unlike the latter two distributions, it has closed forms for the cumulative distribution function and quantile function. Due to this important feature, the kappa distribution attracts the attention of several researchers. Park et al. (2009) introduced the threeparameter kappa distribution and provided a description of the mathematical properties of the distribution and estimated the parameters by three methods. Also, they illustrated its applicability for rainfall data from Seoul, Korea. In this paper, we study the distribution and the estimation methods for the parameters considered by Park et al. (2009), and propose a new estimation method. Then, we will compare these estimation methods using a Monte Calro simulation study and a real dataset.Material and methodsIn this scheme, first we consider the threeparameter kappa distribution and study some of its properties and then estimate the parameters of the distribution by four methods. These methods are method of moment (MM), Lmoments (LM), maximum likelihood (ML) and maximum product of spacing method (MPS). Using a Monte Carlo simulation study and a real data set, performance of these methods are compared.Results and discussionComparing the performance of the proposed estimation methods in terms of bias and root of mean squares error (rmse), it can be concluded that the MPS method has a better performance due to its lower bias and rmse. The KolmogorovSmirnov test is applied for goodnessoffit test in the threeparameter kappa distribution to the whole monthly rainfall data of Abali station in Tehran province. The results demonstrate that the MPSE method leads to better results than other mentioned methods.ConclusionThe following conclusions were drawn from this research.The Monte Carlo simulation shows that the maximum product spacing method, which is proposed in this paper, is the best method for estimating the parameters of the threeparameter kappa distribution.The statistics and pvalue of the Kolmogorov -Smirnov test show that the threekappa distribution with the MPS method of estimation has better fit than the other methods.