پديد آورنده :
موسايي، زهرا
عنوان :
تقريب تابع توزيع جرم احتمال توسط تبديل معكوس فوريه گسسته
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
[ده]، ۷۱ص.: مصور
استاد راهنما :
فريد بهرامي، امير نادري
توصيفگر ها :
تقريب تابع توزيع , فوريه گسسته , محاسبه انتگرال , زنجير ماركف
استاد داور :
محمدتقي جهانديده، محمود منجگاني
تاريخ ورود اطلاعات :
1397/04/03
چكيده انگليسي :
Numerical Approximation of ProbabilityMass Functions Via the Inverse Discrete Fourier Transform Zahra Mousaei zahramousaei5@gmail com 2018 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Farid Bahrami fbahrami@cc iut ac ir Supervisor Dr Amir Naderi anaderi@cc iut ac ir 2017 MSC 65V45 65V10 Keywords characteristic function discrete Weibull rst passage distribution fast Fourier trans form semi Markov process statistical owgraph AbstractFirst passage distributions of semi Markov processes are of interest in elds such as reliability sur vival analysis and many others The problem of nding or computing rst passage distributions is in general quite challenging We take the approach of us ing characteristic functions or Fouriertransforms and inverting them to numerically calculate the rst passage distribution Numericalinversion of characteristic functions can be numerically unstable for a general probability measure however we show for lattice distributions they can be quickly calculated using the inverse discreteFourier transform Using the fast Fourier transform algorithm these computations can be ex tremelyfast In addition to the speed of this approach we are able to prove a few useful bounds for thenumerical inversion error of the characteristic functions These error bounds rely on the existence of a rst or second moment of the distribution or on an eventual monotonicity condition We demonstratethese techniques in an example and include R code Statistical literature abounds with proofs usingcharacteristic functions CFs Asymptotic results such as the central limit theorem rely heavily onthe properties of CFs However when it comes to applied statistics the reverse is true In generalstatisticians seem very uncomfortable using the CF or numeric approximations of it even though theyroutinely use numerical approximations and calculations for various other procedures This could bepartly due to the fact that CFs are complex functions but this is a deterrent based on fear of the
استاد راهنما :
فريد بهرامي، امير نادري
استاد داور :
محمدتقي جهانديده، محمود منجگاني
