fa توزیع کاپا سه پارامتری و برازش آن به داده‌های مجموع بارش ماهانه ایستگاه آبعلی استان تهران آمار stat علمی پژوهشی کاربردی S <span style="font-family:B Nazanin;"><span style="font-size:10.0pt;">توزیع کاپا یکی از توزیع‌های چوله مثبت است که به‌منظور</span></span> <span style="font-family:B Nazanin;"><span style="font-size:10.0pt;">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 [1]&nbsp; پرداخته و سپس چهار روش برآوردیابی شامل روش گشتاوری، گشتاورهای خطی</span>&nbsp;بیشینۀ درست‌نمایی و بیشینۀ حاصل‌ضرب فاصله‌ها را برای برآوردیابی پارامترهای این توزیع ارائه</span> 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.<br> <strong><span style="font-family:B Nazanin;"><span style="font-size:10.0pt;"></span></span></strong> <div>&nbsp; <hr align="left" size="1" width="33%" ><div id="ftn1"></div></div> <strong>Introduction</strong><br> The 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 log-normal 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 three-parameter 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.<br> <strong>Material and methods</strong><br> In this scheme, first we consider the three-parameter 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), L-moments (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.<br> <strong>Results and discussion</strong><br> Comparing 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 Kolmogorov-Smirnov test is applied for goodness-of-fit test in the three-parameter 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.<br> <strong>Conclusion</strong><br> The following conclusions were drawn from this research. <ul> <li>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 three-parameter kappa distribution.</li> <li>The statistics and p-value of the Kolmogorov&ndash;Smirnov test show that the three-kappa distribution with the MPS method of estimation has better fit than the other methods.&nbsp;</li> </ul> توزیع کاپا سه پارامتری, برآوردگر بیشینۀ درست‌نمایی, برآوردگر گشتاورهای خطی, برآوردگر بیشینۀ حاصل‌ضرب فاصله‌ها. Three-parameter kappa distribution, Maximum likelihood estimator, L-Moments estimator, Maximum product of spacings estimator. 405 416 http://mmr.khu.ac.ir/browse.php?a_code=A-10-664-1&slc_lang=fa&sid=1 Maryam Sharafi مریم شرفی msharafi@shirazu.ac.ir 10031947532846003963 10031947532846003963 Yes Shiraz University دانشگاه شیراز، دانشکدۀ علوم، گروه آمار Farideh Tavangar فریده توانگر f.tavangar@gmail.com 10031947532846003964 10031947532846003964 No دانشگاه یورک، کانادا، گروه آمار و ریاضی Shohre Enami شهره انعامی enami1387@yahoo.com 10031947532846003965 10031947532846003965 No دانشگاه پیام نور بوشهر حسین نادب honadeb@yahoo.com 10031947532846003966 10031947532846003966 No دانشگاه یزد، گروه آمار