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### Estimation of parameters from a complicated expression (double integration) with optime [migrated]

I am trying to estimate paramters of a function with optime This is the code: ...
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### Integration of product of functions of “x” with exponents/powers (binomial problem)

Original problem: A point X is randomly chosen from the interval (0,1). Suppose X=x is observed. Then a coin with P(Heads) = x is tossed independently n times. Let Y be the number of heads in n ...
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### Expectation of two identical lognormal distributions

I would like to compute the conditional expectation (on an interval from $c$ to $\infty$) of the minimum of two log normal distributions. Denote $X_1$, $X_2 \sim LN(0, \sigma)$, the associated ...
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### Overlap between two normal pdfs [duplicate]

I have two normally distributed random variables (estimated from two different sets of samples), and I'd like to know how "similar" those variables are (in order to compare the sets). I had the idea ...
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### How to deal with 'cut-off' selection bias/sampling bias? (truncated distribution)

In short When measuring an outcome with a normal distribution, but whos mean is below the detection threshold, can you still make statements about differences between populations? Example Say I ...
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### A Integral question

I am having problem with integral: $$\int_{-\infty}^\infty\frac{1}{2\pi} e^{-itx} \left( 0.5 \left( e^{-4t^2} + 1 +\cos(t) + \cos(2t) \right)\right) \,dt$$ @DilipSarwate I have proved lim sup(cf)=1 ...
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### Expectation of von Mises Fisher Distribution

The von Mises- Fisher distribution is defined as $$\frac{\kappa^{p/2-1}}{2\pi I_{p/2-1}(\kappa)}\exp(\kappa \mu^Tx)$$ It is defined over the unit sphere i.e. $||x||_2^2=1$. My question is what is ...
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### conditional expectations value

I need to calculate the following integral $$\int_{\mu+c}^{\infty} y\cdot \frac{1}{\sigma\sqrt{2\pi}}e^{(y-\mu-w)^2/2\sigma^2}dy$$ So essentially $y\sim N (\mu+w, \sigma^2)$ and im trying to ...
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### Compute the cumulative hazard of a time interval

I'm a little confused in calculating the cumulative hazard within a time interval. We know that $H(t)=\int^{t}_{0}h(u)du$, if I have $\Delta t=t_1-t_0$ (1) $H(\Delta t)=\int^{\Delta t}_{0}h(u)du$ (...
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### Explanation of density rewriting?

Can somebody please explain the math behind this statement to me? I am not sure how they represent the left hand side by that integral and finally how it is proportional to that. \begin{align} p(S_{t+...
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### [Revised]Proving the expected \bold{density} of being the Nth order statistics is decreasing in sample size

(Sorry that I've previously formulated the question in a wrong way, which confused everyone including myself. This is a better version of the question. Thanks!) Here's another order statistics ...
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Question: Consider $n$ random variables $x_1, x_2,\cdots x_n\sim \mathcal{N}(0,1)$. The expected value of the $i$th order statistic (the maximum) can be written as $E(\mathcal{O}^n_1)= \displaystyle\... 0answers 293 views ### Integrate first derivation - area under curve of first derivation I want to calculate the area under the first derivate. Can I do that with splinefun()? ... 1answer 76 views ### Moment generating function if the PDF is$f_z= Cz^{k-1}(1-\frac{z}{d})^bF(-a+k+1,b;b+1;1-\frac{z}{d})$Let$z$a random variable with PDF :$f_z= Cz^{k-1}(1-\frac{z}{d})^bF(-a+k+1,b;b+1;1-\frac{z}{d})$, where$0\leq z \leq d$,$F$is the Hypergeometric function,$k$is a positive integer,$-a+k+1 >...
I have an empirical distribution $G(x)$. I calculate it as follows x <- seq(0, 1000, 0.1) g <- ecdf(var1) G <- g(x) I denote $h(x) = dG/dx$, ...