Raj Jain
Imrich Chlamtac
Abstract
A heuristic algorithm is proposed for dynamic calculation of the median and other quantiles. The estimates are produced dynamically as the observations are generated. The observations are not stored; therefore, the algorithm has a very small and fixed storage requirement regardless of the number of observations. This makes it ideal for implementing in a quantile chip that can be used in industrial controllers and recorders. The algorithm is further extended to histogram plotting. The accuracy of the algorithm is analyzed.
- 1 Buchholz, W. File organization and addressing. IBM Syst. 1. 2, (196% 66-111.Google Scholar
- 2 Knott, G.D. Hashing functions. Cornput. 1. 18. 3 (1975). 265-276.Google Scholar
- 3 Knuth. D.E. The Art of Computer Programming. Vol. 3, Sorting and Searching. Addison-Wesley, Reading, Mass., 1973. Google ScholarDigital Library
- 4 Pearson, ES. and Hartley, H.O. Biometrikn, Tables for Stotisticinns. Cambridge University Press, Cambridge, 1972.Google Scholar
- 5 Peterson, W.W. Addressing for random access storage. IBM I. Res. Develop. 1. 2 (Apr. 1957). 130-146.Google ScholarDigital Library
- 6 Van der Pool, J.A. Optimum storage allocation for initial loading of a file. IBM J. Res. Develop. 16 (Nov. 1972), 579-586.Google ScholarDigital Library
- 7 Vitter, J.S. Implementations for coalesced hashing. Commun. ACM 25, 12 (Dec. 1962). 911-926. Google ScholarDigital Library
Index Terms
- The P2 algorithm for dynamic calculation of quantiles and histograms without storing observations
Recommendations
Performance analysis of triple-frequency ambiguity resolution with BeiDou observations
We investigate triple-frequency ambiguity resolution performance using real BeiDou data. We test four ambiguity resolution (AR) methods which are applicable to triple-frequency observations. These are least squares ambiguity decorrelation adjustment (...
Ionospheric tomography based on GNSS observations of the CMONOC: performance in the topside ionosphere
This study carries out a quantitative analysis of the performance of ionospheric tomography in the topside ionosphere, utilizing data of October 2011 collected from 260 Global Navigation Satellite System (GNSS) stations in the Crustal Movement ...
A satellite-based method for modeling ionospheric slant TEC from GNSS observations: algorithm and validation
AbstractTotal Electron Content (TEC) modeling is critical for Global Navigation Satellite System (GNSS) users to mitigate ionospheric delay errors. The mapping function is usually used for Vertical TEC ionospheric correction models for slant and vertical ...
Reviews
Leonard Francis Zettel
.abstract A heuristic algorithm is proposed for dynamic calculation of the median and other quantiles. . . . [T]he algorithm has a very small and fixed storage requirement regardless of the number of observations. . . . The algorithm is further extended to histogram plotting. . . . — From the Authors' Abstract The algorithm looks interesting and is presented in sufficient detail so that one could implement it. It requires the storage of ten numbers for the calculation of a quantile; thus, it would probably save storage on large samples of observations, since conventional algorithms require the equivalent to access the data sorted from lowest to highest. The analysis that accompanies the algorithm is best described as a lick, a promise, and a bit of arm waving. There is no formal analysis of execution behavior. Nothing is proven about the statistical behavior of the estimators that the algorithm produces. Results of Monte Carlo runs of 50 samples are given for various cases. Similar work presented in the Journal of the American Statistical Association would typically have sample sizes of 10,000.
Access critical reviews of Computing literature here
Become a reviewer for Computing Reviews.
Comments