Some Inequalities for Distributions with Monotone Hazard Rate

If Cournot oligopolists face uncertainty about the intercept of a linear demand function and if the realized market price must be non-negative, then expected demand becomes convex, which can create a multiplicity of equilibria. This note shows that if the distribution of the demand intercept has a monotone hazard rate and if another, rather weak, assumption is satisfied, then uniqueness of equilibrium is guaranteed.

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BAYESIAN NONPARAMETRIC ESTIMATION OF A MONOTONE HAZARD RATE

Series on Quality, Reliability and Engineering Statistics - System and Bayesian Reliability ◽

10.1142/9789812799548_0018 ◽

2001 ◽

pp. 301-314 ◽

Cited By ~ 1

Author(s):

Man-wai Ho ◽

A. Y. Lo

Keyword(s):

Nonparametric Estimation ◽

Hazard Rate ◽

Bayesian Nonparametric ◽

Bayesian Nonparametric Estimation ◽

Monotone Hazard Rate

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BOUNDS FOR LATTICE DISTRIBUTIONS HAVING MONOTONE HAZARD RATE WITH APPLICATIONS

10.21236/ad0618112 ◽

1965 ◽

Author(s):

Gamanlal P. Shah

Keyword(s):

Hazard Rate ◽

Monotone Hazard Rate

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Scheduling jobs by stochastic processing requirements on parallel machines to minimize makespan or flowtime

Journal of Applied Probability ◽

10.2307/3213926 ◽

1982 ◽

Vol 19 (1) ◽

pp. 167-182 ◽

Cited By ~ 89

Author(s):

Richard R. Weber

Keyword(s):

Probability Distribution ◽

Hazard Rate ◽

Parallel Machines ◽

Random Variables ◽

Expected Value ◽

Hazard Rates ◽

Stochastic Processing ◽

Identical Machines ◽

Exponential Random Variables ◽

Monotone Hazard Rate

A number of identical machines operating in parallel are to be used to complete the processing of a collection of jobs so as to minimize either the jobs' makespan or flowtime. The total processing required to complete each job has the same probability distribution, but some jobs may have received differing amounts of processing prior to the start. When the distribution has a monotone hazard rate the expected value of the makespan (flowtime) is minimized by a strategy which always processes those jobs with the least (greatest) hazard rates. When the distribution has a density whose logarithm is concave or convex these strategies minimize the makespan and flowtime in distribution. These results are also true when the processing requirements are distributed as exponential random variables with different parameters.

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