A Model for Birdwatching and other Chronological Sampling Activities
Por:
De Loera, Jesus A., Jaramillo-Rodriguez, Edgar, OLIVEROS, DEBORAH, Torres, Antonio J.
Publicada:
3 jul 2023
Ahead of Print:
1 mar 2023
Categoría:
Mathematics (miscellaneous)
Resumen:
In many real life situations one has m types of random events happening
in chronological order within a time interval and one wishes to predict
various milestones about these events or their subsets. An example is
birdwatching. Suppose we can observe up to m different types of birds
during a season. At any moment a bird of type i is observed with some
probability. There are many natural questions a birdwatcher may have:
how many observations should one expect to perform before recording all
types of birds? Is there a time interval where the researcher is most
likely to observe all species? Or, what is the likelihood that several
species of birds will be observed at overlapping time intervals? Our
paper answers these questions using a new model based on random interval
graphs. This model is a natural follow up to the famous coupon
collector's problem.
Filiaciones:
De Loera, Jesus A.:
Univ Calif Davis, Dept Math, Davis, CA 95616 USA
Jaramillo-Rodriguez, Edgar:
Univ Calif Davis, Dept Math, Davis, CA 95616 USA
OLIVEROS, DEBORAH:
Univ Nacl Autonomous Mexico, Inst Matemat, Mexico City, Mexico
Torres, Antonio J.:
Univ Nacl Autonomous Mexico, Inst Matemat, Mexico City, Mexico
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