Questions tagged [statistics]
Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory and other branches of mathematics such as linear algebra and analysis.
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Expected value of an estimator of shape parameter of the generalized Pareto distribution
I would like to compute the expected value and variance of the kappa parameter for the generalized Pareto distribution, where
$$
\hat{\kappa} = \frac{\hat{\sigma}^2}{{s}}
$$
Where
$$
s = \frac{1}{n} \...
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Why divide probabilities when calculating conditional probability, when we can just divide the cardinalities?
So the "conventional" formula, if we could call it that, for calculating the probability of an event A occurring, given the event B has already occured is:
$P(A|B)=\frac{P(A\cap B)}{P(B)}$
...
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Interpretation of a PDF
I have the probability density function (PDF)
$$\frac{6}{5}(e^{-2x}+e^{-3x}),x>0 \text{ and 0 otherwise}$$
If I compare this to the two separate (PDFs):
$$2e^{-2x},x>0 \text{ and 0 otherwise}$$
$...
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Interpreting this Table [closed]
I was just wondering if there was a given name to these kinds of tables? I have trouble interpreting them and would like to do further research but don't know the name of said table.
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How to show $ \lim_{n\rightarrow \infty}\frac{E[\max_{1,2...,n} X_i]}{\sqrt{2\ln n}} = 1$ where $(X_i)$ is a sequence of iid gaussian rvs? [duplicate]
Let $(X_i)$ be a sequence of iid $N(0,1)$ random variables. I would like to show that
$$ \lim_{n\rightarrow \infty}\frac{E[\max_{1,2...,n} X_i]}{\sqrt{2\ln n}} = 1. $$
My first try was to find $a_n, ...
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Conditional expectation with random variables from different Probability spaces [closed]
Let $(X,\mathcal{F}_X,\mathbb{P})$ and $(Y,\mathcal{F}_Y,\mathbb{Q})$ be two probability spaces. I know that the expectation of random variable $Z:X\rightarrow \mathbb{R}$ is affected by the random ...
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How many maximum nearest-neighbor contacts exist in a self-avoiding walk of length $n$? [closed]
Consider the random, self-avoiding walk (SAW) on a 2D lattice as a mechanism for polymer growth. In this random walk, the possible steps the walker can take are along 8 direction, elements of the set $...
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Plug-in estimator of expected value
Let $g$ be the statistical functional defined by $g(\mu) = \int x \,d\mu$. Then the plug-in estimator is defined as $\hat{g}=g(L_n)$ where
$$L_n(\omega)=\frac 1 n \sum_{i=1}^n \delta_{X_i(\omega)}$$ ...
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Renewal reward process's reward tail probability
Suppose we are given a dice with $K$ faces, denoted by $k=1,\dots,K$, where the probability of realizing a face $k$ is $p_k\in[0,1]$ with $\sum_{k=1,\dots,K}p_k=1$.
Now, we roll the dice repetitively. ...
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Error contribution of two averages
Let's say I have a magnitude $\lambda=f(x,y)$ where $x$ and $y$ are quantities that I've experimentally measured so I have two series of values $ \{x_1, x_2, ... x_n\}$ and $\{y_1, y_2, ... y_n\}$. ...
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What does the spectral norm of a Wigner matrix converge to when the variances are not renormalised?
It seems that it is well known that for a $NxN$ Wigner matrix - that is a matrix that is symmetric (or Hermitian, but I am only interested in the case where all the entries are real) and has i.i.d. ...
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Limit to zero of Expected value of a function of random variable
I am trying to solve a problem but I don't know how to get out.
Let's say we have a composition of functions of random variable $f_{\theta}(g_{\phi}(X))$ (differentiable and invertible) and $X$ has $p(...
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Confusion about variance statistic in OMC
Adding context, I'm studying Markov Chain Monte Carlo and I'm currently on Ordinary Monte Carlo or Independent Monte Carlo where I have confusion about what it states as estimator of "Variance in ...
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Finding the Cramer Rao bound
Let $x=(x_1,\dots,x_n)$ be a sample of i.i.d random variables with pdf $$f(x;\theta)=(1-\theta)\chi_{[-1/2,0]}+(1+\theta)\chi_{[0,1/2]}$$ where $\theta\in(-1,1)$. Find the Cramer Rao bound.
So to do ...
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Probability that a probability will be less than a certain value
Suppose I have a nonnegative random variable $X$ and I don't know its expected value, but I know that its expected value is less than or equal to $a$ with at least probability $p^*$. i.e, $\mathbb{P}(\...
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