A Look at the Primary Order Preserving Properties of Stochastic Orders: Theorems, Counterexamples and Applications in Cognitive Psychology

Round 1

Reviewer 1 Report

See the attached file

Comments for author File: Comments.pdf

Author Response

Please see the attachment file. Thanks.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

The paper consists of two almost uncorrelated parts: a first more theoretical one in which two particular closure properties are discussed for some stochastic ordering, and a second part in which just one of the results shown before is applied to describe conditions on the parameters so that some parametric distributions are ordered according to the usual stochastic order.

I do not see any novelty in the theoretical results presented in the first part: almost all of them follow immediately from the closure of the stochastic orders considered here with respect to mixture (see the report for details). On the contrary, the second part of the paper is more interesting: The "only if" parts of two main statements (Theorem 5.3 and Theorem 5.8) seem new to me, with not immediate or trivial proofs, thus, suitable for publication.

Therefore, I believe that only the second part of the article deserves publication, so that I suggest accepting the paper only if the entire first part is removed (or condensed into a few paragraphs).

Comments for author File: Comments.pdf

Author Response

Please see the attachment file. Thanks.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

No comments to be add.

Reviewer 2 Report

The authors have adequately addressed comments raised in a previous round of review, and I feel that this manuscript is now acceptable for publication. 

Reviewer 3 Report

I am satisfied with the changes made to the paper, and believe it is now worthy of publication