Determination of System Dimensionality from Observing Near-Normal Distributions
المؤلفون المشاركون
المصدر
العدد
المجلد 2015، العدد 2015 (31 ديسمبر/كانون الأول 2015)، ص ص. 1-17، 17ص.
الناشر
Hindawi Publishing Corporation
تاريخ النشر
2015-08-31
دولة النشر
مصر
عدد الصفحات
17
التخصصات الرئيسية
الملخص EN
This paper identifies a previously undiscovered behavior of uniformly distributed data points or vectors in high dimensional ellipsoidal models.
Such models give near normal distributions for each of its dimensions.
Converse of this may also be true; that is, for a normal-like distribution of an observed variable, it is possible that the distribution is a result of uniform distribution of data points in a high dimensional ellipsoidal model, to which the observed variable belongs.
Given the currently held notion of normal distributions, this new behavior raises many interesting questions.
This paper also attempts to answer some of those questions.
We cover both volume based (filled) and surface based (shell) ellipsoidal models.
The phenomenon is demonstrated using statistical as well as mathematical approaches.
We also show that the dimensionality of the latent model, that is, the number of hidden variables in a system, can be calculated from the observed distribution.
We call the new distribution “Tanazur” and show through experiments that it is at least observed in one real world scenario, that of the motion of particles in an ideal gas.
We show that the Maxwell-Boltzmann distribution of particle speeds can be explained on the basis of Tanazur distributions.
نمط استشهاد جمعية علماء النفس الأمريكية (APA)
Razzaq, Shahid& Khalid, Shehzad. 2015. Determination of System Dimensionality from Observing Near-Normal Distributions. Abstract and Applied Analysis،Vol. 2015, no. 2015, pp.1-17.
https://search.emarefa.net/detail/BIM-1052051
نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)
Razzaq, Shahid& Khalid, Shehzad. Determination of System Dimensionality from Observing Near-Normal Distributions. Abstract and Applied Analysis No. 2015 (2015), pp.1-17.
https://search.emarefa.net/detail/BIM-1052051
نمط استشهاد الجمعية الطبية الأمريكية (AMA)
Razzaq, Shahid& Khalid, Shehzad. Determination of System Dimensionality from Observing Near-Normal Distributions. Abstract and Applied Analysis. 2015. Vol. 2015, no. 2015, pp.1-17.
https://search.emarefa.net/detail/BIM-1052051
نوع البيانات
مقالات
لغة النص
الإنجليزية
الملاحظات
Includes bibliographical references
رقم السجل
BIM-1052051
قاعدة معامل التأثير والاستشهادات المرجعية العربي "ارسيف Arcif"
أضخم قاعدة بيانات عربية للاستشهادات المرجعية للمجلات العلمية المحكمة الصادرة في العالم العربي
تقوم هذه الخدمة بالتحقق من التشابه أو الانتحال في الأبحاث والمقالات العلمية والأطروحات الجامعية والكتب والأبحاث باللغة العربية، وتحديد درجة التشابه أو أصالة الأعمال البحثية وحماية ملكيتها الفكرية. تعرف اكثر