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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.