New maximal inequalities for N-demimartingales with scan statistic applications

2017 ◽  
Vol 54 (2) ◽  
pp. 363-378 ◽  
Author(s):  
Markos V. Koutras ◽  
Demetrios P. Lyberopoulos
Keyword(s):  
Distribution Function ◽  
Waiting Time ◽  
Cumulative Distribution Function ◽  
Numerical Study ◽  
Cumulative Distribution ◽  
Scan Statistic ◽  
Maximal Inequalities ◽  
Binary Trials ◽  
First Occurrence ◽  
Independent And Identically Distributed

Abstract In the present work, some new maximal inequalities for nonnegative N-demi(super)martingales are first developed. As an application, new bounds for the cumulative distribution function of the waiting time for the first occurrence of a scan statistic in a sequence of independent and identically distributed (i.i.d.) binary trials are obtained. A numerical study is also carried out for investigating the behavior of the new bounds.

scholarly journals BOUNDS FOR THE DISTRIBUTION OF TWO-DIMENSIONAL BINARY SCAN STATISTICS

2003 ◽  
Vol 17 (4) ◽  
pp. 509-525 ◽  
Author(s):  
Michael V. Boutsikas ◽  
Markos V. Koutras
Keyword(s):  
Distribution Function ◽  
Present Article ◽  
Numerical Study ◽  
Double Sequence ◽  
Reliability Theory ◽  
Scan Statistics ◽  
Asymptotic Result ◽  
Two Dimensional ◽  
Scan Statistic ◽  
Binary Trials

In the present article, we develop some efficient bounds for the distribution function of a two-dimensional scan statistic defined on a (double) sequence of independent and identically distributed (i.i.d.) binary trials. The methodology employed here takes advantage of the connection between the scan statistic problem and an equivalent reliability structure and exploits appropriate techniques of reliability theory to establish tractable bounds for the distribution of the statistic of interest. An asymptotic result is established and a numerical study is carried out to investigate the efficiency of the suggested bounds.

DISSONANCE — A MEASURE OF VARIABILITY FOR ORDINAL RANDOM VARIABLES

2001 ◽  
Vol 09 (01) ◽  
pp. 39-53 ◽  
Author(s):  
RONALD R. YAGER
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Random Variables ◽  
Cumulative Distribution ◽  
General Properties

We look at the issue of obtaining a variance like measure associated with probability distributions over ordinal sets. We call these dissonance measures. We specify some general properties desired in these dissonance measures. The centrality of the cumulative distribution function in formulating the concept of dissonance is pointed out. We introduce some specific examples of measures of dissonance.

Estimating the cumulative distribution function for the linear combination of gamma random variables

2017 ◽  
Vol 20 (5) ◽  
pp. 939-951
Author(s):  
Amal Almarwani ◽  
Bashair Aljohani ◽  
Rasha Almutairi ◽  
Nada Albalawi ◽  
Alya O. Al Mutairi
Keyword(s):  
Distribution Function ◽  
Linear Combination ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Cumulative Distribution
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