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Subject Item
dbr:Schrödinger_method
rdfs:label
Schrödinger method
rdfs:comment
In combinatorial mathematics and probability theory, the Schrödinger method, named after the Austrian physicist Erwin Schrödinger, is used to solve some problems of . Suppose are independent random variables that are uniformly distributed on the interval [0, 1]. Let does not depend on λ (in the language of statisticians, N is a sufficient statistic for this parametrized family of probability distributions for the order statistics). We proceed as follows: so that
dcterms:subject
dbc:Theory_of_probability_distributions dbc:Erwin_Schrödinger
dbo:wikiPageID
891150
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1124519982
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dbr:Mathematics dbr:Order_statistic dbr:Statistical_independence dbc:Erwin_Schrödinger dbr:Combinatorics dbr:Random_variable dbr:Uniform_distribution_(continuous) dbr:Probability_theory dbr:Poisson_process dbr:Sufficiency_(statistics) dbr:Expected_value dbr:Parametrized_family dbr:Erwin_Schrödinger dbc:Theory_of_probability_distributions dbr:Poisson_distribution dbr:Statistics dbr:Power_series dbr:Conditional_probability dbr:Distribution_and_occupancy
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wikidata:Q5389080 n9:4jYqP freebase:m.03m6sv dbpedia-ro:Oscilatorul_armonic_liniar_cuantic_(metoda_analitică)
dbo:abstract
In combinatorial mathematics and probability theory, the Schrödinger method, named after the Austrian physicist Erwin Schrödinger, is used to solve some problems of . Suppose are independent random variables that are uniformly distributed on the interval [0, 1]. Let be the corresponding order statistics, i.e., the result of sorting these n random variables into increasing order. We seek the probability of some event A defined in terms of these order statistics. For example, we might seek the probability that in a certain seven-day period there were at most two days in on which only one phone call was received, given that the number of phone calls during that time was 20. This assumes uniform distribution of arrival times. The Schrödinger method begins by assigning a Poisson distribution with expected value λt to the number of observations in the interval [0, t], the number of observations in non-overlapping subintervals being independent (see Poisson process). The number N of observations is Poisson-distributed with expected value λ. Then we rely on the fact that the conditional probability does not depend on λ (in the language of statisticians, N is a sufficient statistic for this parametrized family of probability distributions for the order statistics). We proceed as follows: so that Now the lack of dependence of P(A | N = n) upon λ entails that the last sum displayed above is a power series in λ and P(A | N = n) is the value of its nth derivative at λ = 0, i.e., For this method to be of any use in finding P(A | N =n), must be possible to find Pλ(A) more directly than P(A | N = n). What makes that possible is the independence of the numbers of arrivals in non-overlapping subintervals.
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wikipedia-en:Schrödinger_method?oldid=1124519982&ns=0
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2755
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wikipedia-en:Schrödinger_method