We quantify the elementary Borel–Cantelli Lemma by higher moments of overlap count statistic in terms weighted summability probabilities. Applications include mean deviation frequencies Strong Law and Iterated Logarithm.

Research Online is the open access institutional repository for the University of Wollongong. For further information contact the UOW (2013). On the weighting of the mean-absolute-deviation cost minimization model. Abstract The mean-absolute-deviation cost minimization model, which aims to minimize sum of the mean value and the absolute deviation (AD) of the total cost multiplied by a given non...

independence of observations is a fundamental assumption in designing an x chart for individual observations. but unfortunately, the assumption of existence of independent data is not even approximately satisfied. in fact, there is one kind of autocorrelation in the data. this paper demonstrates, through simulating an ar(1) process, that the autocorrelation in the data has deep effect on x char...

The asymptotic relative efficiency of the mean deviation with respect to the standard deviation is 88% at the normal distribution. In his seminal 1960 paper A survey of sampling from contaminated distributions, J. W. Tukey points out that, if the normal distribution is contaminated by a small -fraction of a normal distribution with three times the standard deviation, the mean deviation is more ...

This article presents deviation based exponentially weighted moving average control charts to monitor type-I censored data. Due practical applications, this study considers Weibull distribution assess the performance of proposed memory-type charts. The observations are replaced with conditional expected value (CEV), median (CM), and standard (CSD) Various shifts, smoothing weights, censoring ra...

Faculty members from the Department of Pathology at The University of Arizona College of Medicine-Tucson have offered a 4-credit course on enhanced general pathology for graduate students since 1996. The course is titled, "Mechanisms of Human Disease." Between 1997 and 2016, 270 graduate students completed Mechanisms of Human Disease. The students came from 21 programs of study. Analysis of Var...

We developed a deductive database system PACADE for analyzing three dimensional and secondary structures of protein. PACADE is equipped with a function to search for similar structures in proteins. Unlike other approaches based on calculation of the inter-atomic root mean square distance, this function is based on logic programming and source level rule rewriting techniques. We describe herein ...