Version Of Central Limit Theorem Research Articles

Intuitionistic fuzzy probability and convergence of intuitionistic fuzzy observables

The aim of this contribution is to define a convergence in distribution, a convergence in measure and an almost everywhere convergence with respect to an intuitionistic fuzzy probability. We prove a version of Central limit theorem, a version of Weak law of large numbers and a version of Strong law of large numbers for intuitionistic fuzzy observables with respect to the intuitionistic fuzzy probability. We study a connection between convergence of intuitionistic fuzzy observables with respect to the intuitionistic fuzzy probability and a convergence of random variables, too.

Sensitivity Analysis of Calibration Methods and Factors Effecting the Statistical Nature of Radiation Measurement

The scintillator detectors are recalibrated against the datasheet given by the manufacturer. Optimal and mutual dependent values of (a) high voltage at PMT (Photomultiplier Tube), (b) amplifier gain, (c) average time to count the radiation particles (set by operator), and (d) number of instances/sample number are estimated. Total 5: two versions of Central Limit Theorem (CLT), (3) industry preferred Pulse Width Saturation, (4) calibration based on MPPC coupled Gamma-ray detector, and (5) gross method are used. It is shown that the CLT method is the most optimal method to calibrate the detector and its respective electronics couple. An inverse modeling-based Computerized Tomography method is used for verification. It is shown that statistically averaging results are more accurate and precise data than mode and median if the data is not skewed and a random number of samples are used during the calibration process. It is also shown that the average time to count the radiation particle is the most important parameter affecting the optimal calibration setting for precision and accurate measurements of gamma radiation.

On the Asymptotic Behavior in Random Fields: The Central Limit Theorem

The aim of this paper is to provide an applicable version of Central Limit Theorem for strictly stationary m-dependent random fields on a lattice. The type of sampling is considered increasing domain sampling.

Further research on limit theorems for self-normalized sums

In this paper, we show that self-normalized versions of central limit theorem and almost sure central limit theorem hold with more general weight sequence both for i.i.d. random sequence and mixing sequence. Our conclusions generalize and improve the known results from the logarithmic averages which used traditionally in almost sure central limit theorem to some general averages.

L evy Ornstein-Uhlenbeck Processes - An Approximating Density

The objective of this paper is to approximate the probability density functions for Ornstein-Uhlenbeck processes that are driven by Levy processes. This is achieved by considering a truncated set of cumulants relating to the Levy measure and expressing these as moments of Gaussian random variables. This can be thought of as a weaker version of Central Limit Theorem. We illustrate the use of these densities via Brownian motion (a benchmark) and Meixner process.

The uniform central limit theorem for the tent map

This paper considers the asymptotic behaviors of the processes generated by the classical ergodic tent map that is defined on the unit interval. We get the uniform version of central limit theorem for the tent map by using the method of uniformly integrable entropy. An application to Kolmogorov–Smirnov type result is provided.

퍼지 랜덤 집합에 대한 중심극한정리

이 논문에서는 서로 독립이고 동일한 분포를 갖는 집합치 랜덤 변수의 합에 대한 중심극한정리의 일반화로서, 수준연속인 퍼지 집합치 랜덤 변수의 합에 대한 중심극한정리를 연구하였다. The present paper establishes the improved version of central limit theorem for sums of level-continuous fuzzy set-valued random variables as a generalization of central limit theorem for sums of independent and identically distributed set-valued random variables.