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I have some rudimentary questions on how to call/name certain things in terms of Stochastic ordering. I am using simple examples here but would like to know the language used in general cases.

  1. suppose we have uniform distributions on [x,2], where 0<x<1. If we compare these distributions, can we say hazard rate order or stochastic dominance order increases/decreases with x?

  2. suppose we have uniform distributions on [x, 2/x], where 0<x<1. Can we say the degree of dispersion increases/decreases with x?

Just to be clearer, I want to know the language used in Stochastic ordering, not so much the actual comparison. Thanks.

Adam
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  • To answer your questions, we need you to provide definitions of your phrases "degree of dispersion," "hazard rate order," and "stochastic dominance order." Otherwise we have no way of knowing what terms you are looking for! – whuber Jul 13 '21 at 17:29
  • I am in a catch-22 situation. I wanted to compare/order the distributions, but I don't know the language/method to be used. The phrases you mentioned were just examples used to give you some idea what I was looking for, but they are probably the wrong ones. I was hoping someone could tell me the correct ones to compare/order distributions. – Adam Jul 13 '21 at 19:05
  • Could you explain, using terminology and concepts you are comfortable with, how you want to compare the distributions? Let us volunteer any statistical terminology: that will be easy once you have communicated your intentions. – whuber Jul 13 '21 at 19:54
  • OK, let me try one more time. Suppose we have two distributions of the same class, but they differ in parameter values. As a result, for EXAMPLE, they have the same upper bound, but different lower bounds. Instead of stating the above, is there a concise term to describe how the distributions vary with the parameter values. If it is still not clear, please use my original post as a reference. – Adam Jul 13 '21 at 20:15

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