<em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

    <em id="zlul0"></em>

      <dl id="zlul0"></dl>
        <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
        <em id="zlul0"></em>

        <div id="zlul0"><ol id="zlul0"></ol></div>

        Stack Exchange Network

        Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

        Visit Stack Exchange

        In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.

        0
        votes
        0answers
        38 views

        Asymptotic distribution of $n\mathbb E_{\hat{P}_n}[g(Z;\theta)]^T\operatorname{Cov}_{\hat{P}_n}[g(Z;\theta)]^{-1}\mathbb E_{\hat{P}_n}[g(Z;\theta)]$

        Setup This question is a followup on this question. I'm interested in the asymptotic distribution of certain quadratic forms. So, let $Z$ be a $p$-dimensional random vector with (unknown) ...
        1
        vote
        1answer
        60 views

        Generalization of inverse transform sampling

        If X is a random variable over an arbitrary alphabet, is there a (deterministic) function f() such that X = f(U), where U is a uniform random variable over the unit-interval?
        0
        votes
        1answer
        22 views

        Cumulative Order Statistics of Independent Non Identical Distributions

        I understand that the p.d.f of order statistics for Independent Non Identical Distributions are given by the Bapat-Beg theorem as previously explained in another question. As explained in the article, ...
        0
        votes
        0answers
        24 views

        Rate of convergence of centered Hotelling's statistic to Chi-squared distribution

        Consider the Hotelling's statistic $H_n := n\mu_n\Sigma_n^{-1}\mu_n$, where $\mu_n$ (resp. $\Sigma_n$) is the empirical mean (resp. empirical covariance matrix) of a zero-mean random $d$-dimensional ...
        0
        votes
        0answers
        24 views

        Distribution of an arithmetic progression with respect to a monotonic sequence with distributed increment

        Let $T>0$, $\Delta>0$, $\Delta<T$, $\tau : N_e \rightarrow (0,\infty)$ be a sequence uniformly distributed on the interval $[T-\Delta,T+\Delta]$. Here $ N_e $ is the set of non-negative ...
        3
        votes
        2answers
        203 views

        Effect of perturbing the atoms of a measure on the Wasserstein distance

        Let $(X,d)$ be a metric space, $x_1,\ldots,x_N\in X$ and $x_1',\ldots,x_N'\in X$ be atoms, and $G=\sum_{i=1}^Np_i\delta_{x_i}$, $G'=\sum_{i=1}^Np_i'\delta_{x_i}$, and $G''=\sum_{i=1}^Np_i'\delta_{x_i'}...
        -1
        votes
        0answers
        19 views

        A simple function that preserves the ordering of Binomial CDF

        I am looking for a simple function $f(n, p, q)$ that exactly preserves the ordering of the cumulative probabilities $\mathbb{P}(\rm{Binom}(n, p) > n q )$, for all $n > 0$, $p, q \in [0, 1]$, ...
        1
        vote
        1answer
        130 views

        continuity entropy with respect gibbs measures

        Let $X=\{0,1\}^{\mathbb{N}}$. For simplicity I consider Bernoulli measures on $X$ only. Let $f:X\to \mathbb{R}$ be Holder continuous. The measure $\mu$ is a Gibbs measure with potential $f$ if there ...
        0
        votes
        0answers
        30 views

        Expression for the Markov Chain CLT variance for an arbitrary initial distribution

        Let $(\Omega,\mathcal A,\operatorname P)$ and $(E,\mathcal E,\pi)$ be probability spaces $(X_n)_{n\in\mathbb N}$ be a $(E,\mathcal E)$-valued stochastic process on $(\Omega,\mathcal A,\operatorname P)...
        1
        vote
        0answers
        20 views

        Expected value of inverse of complex non-central Wishart matrix

        I have a matrix $W$ that abides a complex non-central Wishart distribution. My question is what the expectation of the inverse is, i.e., how to compute $$\mathbb{E}(W^{-1}).$$ I have tried to read up ...
        0
        votes
        2answers
        72 views

        exponential tail in X~Poi($\lambda$) [closed]

        I've tried to show this but I really don't know how to proceed: X ~ Poi($\lambda$) and I need to show that Pr[X $\geq$ n] $\leq e^{-\Omega (n) }$ so what I did so far is this: say n > 2$\lambda$ ...
        1
        vote
        1answer
        116 views

        Asymptotic distribution of $\mathbb E_{\hat{P}_n}[Z]^T\operatorname{Cov}_{\hat{P}_n}[Z]^{-1}\mathbb E_{\hat{P}_n}[Z]$

        Under very general conditions on the random $p$-dimensional vector $Z$, what can be said about the asymptotic distribution of the (random) scalar quantity $R_n := \mathbb E_{\hat{P}_n}[Z]^T\...
        1
        vote
        0answers
        46 views

        Families of distributions with a certain symmetry property?

        Consider the probability distribution $\mathcal{N}_n$ on $\mathbb{R}^n$ whose density is $$(2\pi)^{-n/2}e^{-\frac{1}{2}||\vec{x}||^2} = \prod_{i=1}^n \frac{1}{\sqrt{2\pi}} e^{-\frac{1}{2}x_i^2}$$ ...
        6
        votes
        4answers
        246 views

        Improvement of Chernoff bound in Binomial case

        We know from Chernoff bound $P\bigg(X \leq (\frac{1}{2}-\epsilon)N\bigg)\leq e^{-2\epsilon^2 N}$ where $X$ follows Binomial($N, \frac{1}{2}$). If I take $N=1000, \epsilon=0.01$, the upper bound is ...
        3
        votes
        3answers
        165 views

        What is the probability distribution of the $k$th largest coordinate chosen over a simplex?

        Suppose we're selecting points uniformly at random from the $N$-simplex $S_N = \{x \in \mathbb R^{N+1}: $ all $ x_i \ge 0$ and $x_1 + \ldots x_N = 1\}$. One way to do this in practice is choose $N-...

        15 30 50 per page
        山西福彩快乐十分钟
          <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

          <em id="zlul0"></em>

            <dl id="zlul0"></dl>
              <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
              <em id="zlul0"></em>

              <div id="zlul0"><ol id="zlul0"></ol></div>
                <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

                <em id="zlul0"></em>

                  <dl id="zlul0"></dl>
                    <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
                    <em id="zlul0"></em>

                    <div id="zlul0"><ol id="zlul0"></ol></div>