The integral tag has no wiki summary.
0
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31 views
Difference of two gaussians [closed]
I got trouble understanding the following equation from a paper I'm currently studying [1]:
$\pi_{ij} \equiv \int^{\infty}_0 \mathcal{N}(s|\bar{s}_i - \bar{s}_j,2\sigma_s^2) ds$
...
1
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0answers
35 views
Can the proof of the central limit theorem be expressed as the limit of a convolution with an operator
The central limit theorem, as I understand it (engineer, non-statistician), says that the distribution comprised of means of some other reasonably behaved distributions converges to a normal ...
1
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0answers
63 views
Finding the integral of a fitted function
I have a function obtained by fitting some data, and I do not have access to the data itself. The fitting parameters of the function have confidence bounds. I need to obtain an expression for the ...
4
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2answers
124 views
Mean of log of cdf
Let $CDF$ be the cumulative distribution function for the standard normal distribution. Let $Z$ be a standard normal random variable.
Then $CDF(Z)$ is uniformly distributed on the unit interval, so ...
7
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1answer
102 views
Vector calculus in statistics
I'm teaching a class on integration of functions of several variables and vector calculus this semester. The class is made up most of economics majors and engineering majors, with a smattering of math ...
2
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2answers
150 views
Values for integral of square of standard Brownian process
I am trying to generate values in a table for the following function:
$$
W = \int_0^1 [B(t)]^2 dt
$$
Where $B(t)$ is a standard Brownian motion.
Example: $W_{0.05} = 1.656$, $W_{0.025} = 2.135$.
...
1
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1answer
64 views
Replicating integration results from a paper
I’m reading Wacek’s paper Parameter Uncertainty in Loss Ratio Distributions and its Implications and trying to figure out how to replicate some of the results.
Table 6, on page 190 of the paper, ...
1
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0answers
88 views
Confidence Interval in Monte Carlo integration
I want to integrate
$\int_{\mathbb{R}_+}\mathbb{1}_A(x) d\mathbb{P}(x)$, in other words I am interested in $\mathbb{P}(A)$. I did this numerically with two Monte Carlo steps.
First, I drew, say a ...
1
vote
1answer
160 views
Integral of a conditional uniform distribution leads to improper integral
I have two uniforms distributions, $X_1 \sim\it{U}(a,b)$ and $X_2\sim\it{U}(X_1+\delta,b+\delta)$. I would like to compute $P(X_2\in[a+\delta,b+\delta])$. So I do this:
$$\begin{eqnarray*}
...
3
votes
1answer
109 views
Is output of Deamer deconvolution not a density?
I have a Model Y= X+e and need the density of X. The deamer package deconvolves the density for X, but if I use the simpsons rule to integrate this density, I get values which are above 1.
The ...
0
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0answers
59 views
Nested integral - rescale weights?
Working on a nested integral that occurs in a t-copula credit model and my question relates to the correct rescaling of the distributions of the factors in the model.
The integration is over a ...
8
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1answer
219 views
Expected log value of noncentral exponential distribution
Suppose $X$ is non-central exponentially distributed with location $k$ and rate $\lambda$. Then, what is $E(\log(X))$.
I know that for $k=0$, the answer is $-\log(\lambda) - \gamma$ where $\gamma$ ...
1
vote
1answer
147 views
How to calculate a posterior for the given model?
Suppose we have a joint distribution on vector $[\mathbf{x}, y]$:
$$
p([y, \mathbf{x}] ) = \mathcal{N}\left(\begin{pmatrix} y \\ \mathbf{x}\end{pmatrix}| 0, \begin{pmatrix} k& \mathbf{v} \\ ...
1
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0answers
76 views
Differencing weekend fluctuations with R?
Suppose a time-serie like this on the left-top corner with weekend and daily fluctuations. This time-series need differencing due to the rising ACF (bottom-left) and portmanteau tests' p -values too ...
3
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1answer
264 views
Monte carlo integration in spherical coordinates
I was playing around with writing a code for Montecarlo integration of a function defined in spherical coordinates. As a first simple rapid test I decided to write a test code to obtain the solid ...
0
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0answers
75 views
Help evaluating a posterior probability expression
Consider $\boldsymbol{x}= [x_1,x_2,...x_n]$ and $\boldsymbol{y}= [y_1,y_2,...y_n]$ to be two multivariate Gaussians with an isotropic diagonal variance structure and uninformative priors so that:
...
8
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1answer
365 views
What is the expected value of modified Dirichlet distribution? (integration problem)
It is easy to produce a random variable with Dirichlet distribution using Gamma variables with the same scale parameter. If:
$ X_i \sim \text{Gamma}(\alpha_i, \beta) $
Then:
$ ...
