On the use of probability inequalities in random variate generation. (English) Zbl 0568.65002
The author shows by examples how some well-known probability inequalities such as Chebyshev’s inequality can help in the design of general nonuniform random variate generators having monotone densities on [0,\(\infty)\) with/without r-th moment \(\mu_ r\), unimodal densities on R with mode at known location, or densities with one or more known moments satisfying a known Lipschitz condition.
Reviewer: K.Uosaki
MSC:
| 65C10 | Random number generation in numerical analysis |
| 60E10 | Characteristic functions; other transforms |
Keywords:
unimodality; Chebyshev’s inequality; random variate generation; probability inequality; acceptance/rejection methodReferences:
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