Rounding of continuous random variables and oscillatory asymptotics
نویسندگان
چکیده
منابع مشابه
Rounding of Continuous Random Variables and Oscillatory Asymptotics
We study the characteristic function and moments of the integer-valued random variable bX+αc, whereX is a continuous random variable. The results can be regarded as exact versions of Sheppard’s correction. Rounded variables of this type often occur as subsequence limits of sequences of integer-valued random variable. This leads to oscillatory terms in asymptotics for these variables, something ...
متن کاملRounding of Continuous Random Variables and Oscillatory Asymptotics by Svante Janson
We study the characteristic function and moments of the integer-valued random variable X+α , where X is a continuous random variables. The results can be regarded as exact versions of Sheppard’s correction. Rounded variables of this type often occur as subsequence limits of sequences of integer-valued random variables. This leads to oscillatory terms in asymptotics for these variables, somethin...
متن کاملContinuous Random Variables
Math 394 1 (Almost bullet-proof) Definition of Expectation Assume we have a sample space Ω, with a σ−algebra of subsets F , and a probability P , satisfying our axioms. Define a random variable as a a function X : Ω → R, such that all subsets of Ω of the form {ω |a < X(ω) ≤ b}, for any real a ≤ b are events (belong to F). Assume at first that the range of X is bounded, say it is contained in th...
متن کاملNotes on Continuous Random Variables
Continuous random variables are random quantities that are measured on a continuous scale. They can usually take on any value over some interval, which distinguishes them from discrete random variables, which can take on only a sequence of values, usually integers. Typically random variables that represent, for example, time or distance will be continuous rather than discrete. Just as we descri...
متن کاملTotal variation asymptotics for sums of independent integer random variables
Let Wn := ∑n j=1 Zj be a sum of independent integer valued random variables. In this paper, we derive an asymptotic expansion for the probability IP[Wn ∈ A] of an arbitrary subset A ∈ Z+. Our approximation improves upon the classical expansions by including an explicit, uniform error estimate, involving only easily computable properties of the distributions of the Zj : an appropriate number of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2006
ISSN: 0091-1798
DOI: 10.1214/009117906000000232