کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1155096 958444 2008 7 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A class of weighted Poisson processes
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آمار و احتمال
پیش نمایش صفحه اول مقاله
A class of weighted Poisson processes
چکیده انگلیسی

Let NN have a Poisson distribution with parameter λ>0λ>0, and let U1,U2,…U1,U2,… be a sequence of independent standard uniform variables, independent of NN. Then the random sum N(t)=∑j=1NI[0,t](Uj), where IAIA is an indicator of the set AA, is a Poisson process on [0,1][0,1]. Replacing NN by its weighted version NwNw, we obtain another process with weighted Poisson marginal distributions. We then derive the basic properties of such processes, which include marginal and joint distributions, stationarity of the increments, moments, and the covariance function. In particular, we show that properties of overdispersion and underdispersion of N(t)N(t) are related to the correlation of the process increments, and are equivalent to the analogous properties of NwNw. Theoretical results are illustrated through examples, which include processes with geometric and negative binomial marginal distributions.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Statistics & Probability Letters - Volume 78, Issue 15, 15 October 2008, Pages 2346–2352
نویسندگان
, ,