fa تأثیر تغییر توزیع داده‌ها در آمیزه‌ای متناهی از مدل‌های خطی تعمیم‌یافته نیم پارامتری آمار stat مقاله استخراج شده از طرح پژوهشی Research Paper <p><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">انتخاب مدل آماری </span></span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">مناسب برای متغیر پاسخ </span></span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">یکی از مهم‌ترین مسایل در آمیزه&shy;ای متناهی از مدل&shy;های خطی تعمیم یافته است.</span></span></span> <span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">یکی از توزیع&shy;هایی که در آمیزه&shy;ای متناهی از مدل&shy;های </span></span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">خطی تعمیم یافته نیم پارامتری </span></span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">با مشکل روبه‌رو است، توزیع پواسون است. </span></span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">در این مقاله، </span></span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">برای غلبه بر بار محاسباتی و بیش پراکندگی، آمیزه&shy;ای متناهی </span></span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">از مدل&shy;های خطی تعمیم&shy;یافته نیم پارامتری </span></span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">با استفاده از توزیع دوجمله</span></span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">&shy;</span></span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">ای منفی (</span></span></span><span style="font-family:times new roman,serif;"><span style="font-size:9.0pt;">G</span></span><span style="font-family:times new roman,serif;"><span style="font-size:9.0pt;">FMMNB</span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">) به‌جای آمیزه&shy;ای متناهی </span></span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">از مدل&shy;های خطی تعمیم یافته نیم پارامتری </span></span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">با استفاده از توزیع پواسون (</span></span></span><span style="font-family:times new roman,serif;"><span style="font-size:9.0pt;">G</span></span><span style="font-family:times new roman,serif;"><span style="font-size:9.0pt;">FMMP</span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">) </span></span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">پیشنهاد می</span></span></span><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;">&shy;</span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">شود</span></span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">. کارایی مدل&shy;های آمیزه&shy;ای متناهی </span></span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">از مدل‌های خطی تعمیم یافته نیم پارامتری </span></span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">با استفاده از توزیع دوجمله&shy;ای منفی نسبت مدل&shy;های آمیزه&shy;ای متناهی </span></span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">از مدل&shy;های خطی تعمیم یافته نیم پارامتری </span></span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">با استفاده از توزیع پواسون برای داده&shy;های شبیه&shy;سازی شده و داده&shy;های واقعی </span></span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">و </span></span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">با استفاده از میانگین وزنی توان دوم انحرافات (</span></span></span><span style="font-family:times new roman,serif;"><span style="font-size:9.0pt;">WGMSE</span></span><span dir="RTL"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">) نشان داده شده است.&nbsp;</span></span></span></p> <p><strong>Introduction</strong><br> Selection the appropriate statistical model for the response variable is one of the most important problem in the finite mixture of generalized linear models. One of the distributions which it has a problem in a finite mixture of semi-parametric generalized statistical models, is the Poisson distribution. In this paper, to overcome over dispersion and computational burden, finite mixture of semi-parametric generalized linear models using the negative binomial (GFMMNB) distributions instead of finite mixture of semi-parametric generalized linear models using the Poisson distributions (GFMMP) has been proposed. Efficiency of GFMMNB to GFMMP using weighted generalized mean of square error (WGMSE) for both the simulation data and real data are shown.<br> &nbsp;<strong>Material and methods</strong><br> In this scheme, first we have introduced finite mixture of semi-parametric generalized linear models using the Poisson distributions (GFMMP). Then, we have introduced finite mixture of semi-parametric generalized linear models using the negative binomial (GFMMNB) instead of GFMMP. For estimating the parameters in the proposed model, the EM algorithm in two steps computed. We have used the efficiency method using weighted generalized mean of square error (WGMSE) for comparing between GFMMNB and GFMMP model in both the simulation and real data.<br> <strong>Results and discussion</strong><br> Results of real example and simulation study between GFMMNB and GFMMP model are shown that the proposed method is very competitive in terms of estimation accuracy and speed of computational estimation methods. The reported results demonstrate that there is a good agreement between simulation study and real data in the GFMMNB model.<br> Also, the numerical results reported in the tables indicate that the accuracy improve by increasing the <em>n </em>for GFMMNB model. Therefore, to get more accurate results, the larger <em>n </em>is recommended.<br> <strong>Conclusion</strong><br> The following conclusions were drawn from this research.</p> <ul> <li>Computation of estimators for proposed model using the EM algorithm are found very easily and therefore many calculations are reduced.</li> <li>Confidence intervals for parameters in GFMMNB model is more accurate than GFMMP model.</li> </ul> <p>&middot;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The main ch<a name="_GoBack"></a>aracteristic of proposed method is that it improves the finite mixture model and can be easily solved by using iterative method.<br> <a href="./files/site1/files/51/%D8%A7%D8%B3%DA%A9%D9%86%D8%AF%D8%B1%DB%8C.pdf">./files/site1/files/51/%D8%A7%D8%B3%DA%A9%D9%86%D8%AF%D8%B1%DB%8C.pdf</a></p> مدل های آمیزه, الگوریتم EM , تابع تاوان, هم‌ترازسازی Equating, EM Algorithm, Penalized Function, Mixture Models 9 28 http://mmr.khu.ac.ir/browse.php?a_code=A-10-175-1&slc_lang=fa&sid=1 Farzad Eskandari فرزاد اسکندری askandari@atu.ac.ir 10031947532846002699 10031947532846002699 Yes Faculty of Mathematical Science and Computer, Allameh Tabataba’i University, Tehran, Iran دانشگاه علامه طباطبائی، دانشکدۀ علوم ریاضی و رایانه