TY - JOUR
T1 - On the minimum of independent geometrically distributed random variables
AU - Ciardo, Gianfranco
AU - Leemis, Lawrence M.
AU - Nicol, David
N1 - Funding Information:
This research was partially supported by the National Aeronautics and Space Administration under NASA Contract No. NAS 1-19480 while the authors were in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681. * Corresponding author. E-mail: {ciardo, leemis, nicol} @cs.wm.edu.
PY - 1995/6
Y1 - 1995/6
N2 - The expectations E[X(1)], E[Z(1)], and E[Y(1)] of the minimum of n independent geometric, modified geometric, or exponential random variables with matching expectations differ. We show how this is accounted for by stochastic variability and how E[X(1)]/E[Y(1)] equals the expected number of ties at the minimum for the geometric random variables. We then introduce the "shifted geometric distribution", and show that there is a unique value of the shift for which the individual shifted geometric and exponential random variables match expectations both individually and in their minimums.
AB - The expectations E[X(1)], E[Z(1)], and E[Y(1)] of the minimum of n independent geometric, modified geometric, or exponential random variables with matching expectations differ. We show how this is accounted for by stochastic variability and how E[X(1)]/E[Y(1)] equals the expected number of ties at the minimum for the geometric random variables. We then introduce the "shifted geometric distribution", and show that there is a unique value of the shift for which the individual shifted geometric and exponential random variables match expectations both individually and in their minimums.
KW - Exponential distribution
KW - Geometric distribution
KW - Order statistics
KW - Stochastic ordering
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U2 - 10.1016/0167-7152(94)00130-Z
DO - 10.1016/0167-7152(94)00130-Z
M3 - Article
AN - SCOPUS:33645570891
SN - 0167-7152
VL - 23
SP - 313
EP - 326
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
IS - 4
ER -