On The Prediction Limits for Rayleigh Life Distribution

1990 ◽  
Vol 39 (1-2) ◽  
pp. 105-110 ◽  
Author(s):  
S. K. Sinha
1983 ◽  
Vol 20 (03) ◽  
pp. 529-536
Author(s):  
W. J. R. Eplett

A natural requirement to impose upon the life distribution of a component is that after inspection at some randomly chosen time to check whether it is still functioning, its life distribution from the time of checking should be bounded below by some specified distribution which may be defined by external considerations. Furthermore, the life distribution should ideally be minimal in the partial ordering obtained from the conditional probabilities. We prove that these specifications provide an apparently new characterization of the DFRA class of life distributions with a corresponding result for IFRA distributions. These results may be transferred, using Slepian's lemma, to obtain bounds for the boundary crossing probabilities of a stationary Gaussian process.


2017 ◽  
Vol 4 (2) ◽  
pp. 160900 ◽  
Author(s):  
Dániel Kondor ◽  
Sebastian Grauwin ◽  
Zsófia Kallus ◽  
István Gódor ◽  
Stanislav Sobolevsky ◽  
...  

Thanks to their widespread usage, mobile devices have become one of the main sensors of human behaviour and digital traces left behind can be used as a proxy to study urban environments. Exploring the nature of the spatio-temporal patterns of mobile phone activity could thus be a crucial step towards understanding the full spectrum of human activities. Using 10 months of mobile phone records from Greater London resolved in both space and time, we investigate the regularity of human telecommunication activity on urban scales. We evaluate several options for decomposing activity timelines into typical and residual patterns, accounting for the strong periodic and seasonal components. We carry out our analysis on various spatial scales, showing that regularity increases as we look at aggregated activity in larger spatial units with more activity in them. We examine the statistical properties of the residuals and show that it can be explained by noise and specific outliers. Also, we look at sources of deviations from the general trends, which we find to be explainable based on knowledge of the city structure and places of attractions. We show examples how some of the outliers can be related to external factors such as specific social events.


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