Estimation of intersection intensity in a Poisson process of segments

Tomáš Mrkvička

Commentationes Mathematicae Universitatis Carolinae (2007)

  • Volume: 48, Issue: 1, page 93-106
  • ISSN: 0010-2628

Abstract

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The minimum variance unbiased estimator of the intensity of intersections is found for stationary Poisson process of segments with parameterized distribution of primary grain with known and unknown parameters. The minimum variance unbiased estimators are compared with commonly used estimators.

How to cite

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Mrkvička, Tomáš. "Estimation of intersection intensity in a Poisson process of segments." Commentationes Mathematicae Universitatis Carolinae 48.1 (2007): 93-106. <http://eudml.org/doc/250217>.

@article{Mrkvička2007,
abstract = {The minimum variance unbiased estimator of the intensity of intersections is found for stationary Poisson process of segments with parameterized distribution of primary grain with known and unknown parameters. The minimum variance unbiased estimators are compared with commonly used estimators.},
author = {Mrkvička, Tomáš},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {complete statistic; Poisson process; segment process; sufficient statistic; intensity of intersections; complete statistic; Poisson process; segment process; sufficient statistic; intensity of intersections},
language = {eng},
number = {1},
pages = {93-106},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Estimation of intersection intensity in a Poisson process of segments},
url = {http://eudml.org/doc/250217},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Mrkvička, Tomáš
TI - Estimation of intersection intensity in a Poisson process of segments
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 1
SP - 93
EP - 106
AB - The minimum variance unbiased estimator of the intensity of intersections is found for stationary Poisson process of segments with parameterized distribution of primary grain with known and unknown parameters. The minimum variance unbiased estimators are compared with commonly used estimators.
LA - eng
KW - complete statistic; Poisson process; segment process; sufficient statistic; intensity of intersections; complete statistic; Poisson process; segment process; sufficient statistic; intensity of intersections
UR - http://eudml.org/doc/250217
ER -

References

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  1. Daley D. J., Vere-Jones D., An Introduction to the Theory of Point Processes, Springer, New York, 1998. Zbl1159.60003MR0950166
  2. Lehmann E.L., Theory of Point Estimation, Wadsworth & Brooks, California, 1991. Zbl0916.62017MR1143059
  3. Mrkvička T., Estimation variances for Poisson process of compact sets, Adv. Appl. Prob. (SGSA) 33 (2001), 765-772. (2001) MR1875778
  4. Mrkvička T., Estimation variances for parameterized marked point processes and for parameterized Poisson segment processes, Comment. Math. Univ. Carolin. 45 (2004), 1 109-117. (2004) MR2076863
  5. Stoyan D., Kendall W.S., Mecke J., Stochastic Geometry and its Applications (2nd Ed.), John Wiley & Sons, Chichester, 1995. Zbl0838.60002MR0895588

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