TY - JOUR
T1 - On the identity of the smallest random variable
AU - Gerchak, Yigal
AU - He, Qi Ming
N1 - Funding Information:
The authors would like to thank two anonymous referees for their valuable comments. This research is supported by the Natural Sciences and Engineering Research Council of Canada.
PY - 2002/6
Y1 - 2002/6
N2 - We compute and analyze the probability that a particular random variable will assume the smallest value among a set of random variables. This work was motivated by wanting to predict the "winner" in R&D and patent "races". Some general results and comparative statistics are provided. For symmetric distributions we derive bounds on the probabilities of interest. We compute the probabilities of who will be the smallest (fastest) for normal, lognormal, Weibull, Pareto, binomial and PH-distributions. We also analyze several models of multivariate exponential distributions.
AB - We compute and analyze the probability that a particular random variable will assume the smallest value among a set of random variables. This work was motivated by wanting to predict the "winner" in R&D and patent "races". Some general results and comparative statistics are provided. For symmetric distributions we derive bounds on the probabilities of interest. We compute the probabilities of who will be the smallest (fastest) for normal, lognormal, Weibull, Pareto, binomial and PH-distributions. We also analyze several models of multivariate exponential distributions.
UR - http://www.scopus.com/inward/record.url?scp=0036604609&partnerID=8YFLogxK
U2 - 10.1023/A:1013974510215
DO - 10.1023/A:1013974510215
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AN - SCOPUS:0036604609
SN - 0740-817X
VL - 34
SP - 559
EP - 564
JO - IIE Transactions (Institute of Industrial Engineers)
JF - IIE Transactions (Institute of Industrial Engineers)
IS - 6
ER -