Questions tagged [stochastic-ordering]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
5
votes
1answer
30 views

When to test For Equality of Medians, and when Stochastic Equality?

In statistics, we are very often interested in investigating whether some score (let's say life satisfaction) tends to be bigger in one population (let's say rich people) compared to another ...
0
votes
0answers
9 views

Does the mean preserving spread of a distribution constitute a mean preserving spread of the joint distribution of two iid draws from it?

Let random vectors $X_1, X_2 \sim F, \;i.i.d, X_1, X_2 \in X $. Now replace $F$ with its mean-preserving spread (MPS), say $G$. My question is, does that constitute an MPS of the joint distribution of ...
1
vote
0answers
35 views

Stochastic dominance and mean preserving spread

I need someones help on understanding the concepts of stochastic dominance and mean preserving spread. I have an exercise which could be used for explanation. Consider the following lotteries: L1 ={...
2
votes
1answer
58 views

First Order Stochastic Dominance

I'm trying to solve an exercise about first order stochastic dominance, and there is this one question that I'm not able to answer. Here are the hypothesis of the exercise: Let Y ∼ F and Y' ∼ G, ...
2
votes
0answers
21 views

Kruskal-Wallis Test: Identically Shaped Distributions

I'm currently working with the Kruskall-Wallis test and had a question about what people mean when they speak about 'Identically Shaped Distributions' and how I could identify whether my data fits ...
0
votes
0answers
7 views

Testing First-Order Stochastic Dominance of Two Samples from Discrete Distributions

Suppose that $X$ and $Y$ are two independent random variables with common finite support on $\mathcal S =\{0,1,...,K\}$ and let $F_X$ and $F_Y$ be their CDFs. Let $\{X_i\}_{i=1}^n$ and $\{Y_j\}_{j=1}^...
0
votes
0answers
15 views

NLP: Permute the order of constituent phrases in an English sentence

I'm looking for a solution that is not knowledge-base dependent or domain-specific, i.e. for general English text. For the sentence, "I went to the store today", one can identify constituents ...
3
votes
1answer
33 views

R: How can I represent partially-ordered time series in R?

I believe that this is a statistics rather than a programming question, though I am tied to an R implementation and hope for a reply in kind. I have data that constitutes several time series. I ...
2
votes
0answers
21 views

Testing against non-dominance of discrete distributions

I have two discrete distributions $A$ and $B$ with independent draws. What tests can I use against $H_0$: $A$ does not first-order stochastically dominate $B$?
1
vote
0answers
29 views

Proof of likelihood ratio ordering implying hazard rate ordering

I'm studying stochastic orders and am stuck in the proof of likelihood ratio ordering implying hazard rate ordering. Definitions: Let $X$ and $Y$ be two random variables with respective densities $f(...
4
votes
0answers
125 views

Are these equivalent (for p-values): super-uniform, stochastically larger than / dominating the uniform, conservative?

In the literature and online, I have found three different wordings that I think refer to the same concept: stochastically larger than uniform (which I take is ...
1
vote
2answers
99 views

Two distributions, same mean, different variance: Stochastic dominance for deviation from mean?

Say you have two (bounded) random variables, $X$ and $Y$, on the same discrete probability space, such that $E(X)=E(Y)$ but $Var(X) < Var(Y)$. Do I know that, for any $k \geq 0$, $$ \text{Prob}(|X-...
9
votes
1answer
334 views

Are unbiased efficient estimators stochastically dominant over other (median) unbiased estimators?

General description Does an efficient estimator (which has sample variance equal to the Cramér–Rao bound) maximize the probability for being close to the true parameter $\theta$? Say we compare the ...
4
votes
1answer
89 views

Stochastic order does not imply (nor is implied by) mean residual life order

Let $X,Y$ be nonnegative random variables with cummulative distribution functions $F$ and $G$ respectively. Then $X\le_{\text{st}}Y$ iff $1-F(x)\le 1-G(x)$ for all $x\ge 0$ annd $X\le_{\text{mrl}}Y$ ...
8
votes
5answers
466 views

Why care so much about expected utility?

I have a naive question about decision theory. We calculate the probabilities of various outcomes assuming particular decisions and assign utilities or costs to each outcome. We find the optimal ...
4
votes
1answer
136 views

Second Order Stochastic Dominance and $\Pr[X \leq Y]\leq1/2$

Let $X$ be a random variables with continuou cdf $F$ in the support $[a,b]$. Let $Y$ be another r.v. with cdf $G$, which is continuous in $[a,b)$ and has an atom at $b$. $X$ and $Y$ are independent. ...
1
vote
1answer
102 views

Stochastic ordering

I'm a bit stuck with the following. Assume $X$ ~$N(0,1)$ and $Y$~$N(1,1)$. Is $Y$ stochastic bigger than $X$? And the same question goes for $X$~$N(0,1)$, $Y$~$N(0,4)$.. I simply don't have a clue ...
3
votes
0answers
18 views

Class of density functions that p(ax)/p(x) is non-decreasing for a<1

What are the probability density functions $p_X(x)$, with support $\subset [0,\infty)$, that for all $a<1$, $\frac{p_X(ax)}{p_X(x)}$ is a non-decreasing function of $x$ over the support of $P_X (x)...
3
votes
1answer
98 views

Class of density functions that f(x-c)/f(x) is non-increasing

I am looking for a class of probability density functions $f_X(x)$, with support $\subset [0,\infty)$, for which there exist a non-empty subset of $\mathbb{R}^+$ denoted by $S_X$, such that $\forall ...
4
votes
1answer
585 views

X is stochastically increasing in Y $\implies$ $E\left[Y| X\right]$ increasing in X

I have two random variables, $X$ and $Y$. I know: $\text{pr}\left(X \le u | Y\right)$ is a decreasing function of $Y$ for all $u$. Does this imply that: $\mathbb{E}\left[Y | X\right]$ is increasing ...
3
votes
1answer
478 views

How can I prove stochastic dominance if I don't know the CDF?

Is there a smart way to show that one variable stochastically dominates the other without knowledge of the CDF? Thanks so much!
3
votes
0answers
250 views

Characteristic functions can establish stochastic dominance?

In an answer to the question here What is the purpose of characteristic functions? people answered the general question about characteristic functions. One answer mentioned that one can use it to ...
5
votes
1answer
1k views

Probability of uniformly drawing N numbers less than the expected second highest value

In the case of 3 draws (N=3) from Uniform[0,1], the expected second highest value would be 1/2. Although unlikely it could happen that all three numbers were less than 1/2. It is exactly this ...
4
votes
1answer
350 views

First-order stochastic dominance and truncations

Suppose we have two distributions $F$ and $G$ over $\left[0,1\right]$. Suppose $F(x) \leq G(x)$ for all $x$, i.e. $F$ first-order stochastically dominates $G$. Is it true that $F(x|x\leq k) \leq G(x|x\...