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This tag is used for the saddlepoint approximation to density functions, probability mass functions, cumulative distribution functions, and so on. See Ronald W Butler: "Saddlepoint approximations with applications".

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How cost function for simple linear regression behaves under different settings with batch gradient descent? [closed]

In the linear regression problem, using a simple linear model with 1 variable & with 2 model parameters, performing batch Gradient Descent(GD) & assuming I am using Mean Square error as my ...
238 views

46 views

Saddlepoint approximation with weibull distribution

I have some trouble with this computation, I have the moment generating function of a random variable $S$ by: $$M_S(t)=\frac{\beta\mu t}{1+(1+\beta)\mu t-M_X(t)}$$ According to the text that I am ...
142 views

Variance of angle to $(X,Y)$ where both $X-\mu_X$ and $Y-\mu_Y \sim N(0,\sigma^2)$ independently

$X$ and $Y$ arise from observations contaminated by i.i.d. additive Gaussian noise $\sigma$. I seek the approximate variance of the angle from the origin to $(X,Y)$. What I've tried: The answer (...
37 views

What is the probability distribution for the squared distance between random points in an $n$-dimensional hypercube?

I choose random points $X,\,Y$ in $[0,\,1]^n$ (I assume all $2n$ Cartesian coordinates are $U(0,\,1)$ iids). What is the probability distribution of $\left\Vert X-Y\right\Vert _{2}^{2}$? Even the $n=1$...
473 views

“Weighted” Poisson binomial distribution

I have stones of different weights. For each stone, I flip the same fair coin. If it's heads, I add the stone's weight to a running total. Given the weights, can I find the distribution for the total ...
713 views

Finding the distribution of iid variables X, Y given distribution of X-Y

Say I know the distribution of $X-Y$, but I do not know the distributino of $X$ (or $Y$), but I know that they are statistically independent, and I know they have the same distribution. Is the problem ...
186 views

Asymptotic distribution of a weighted sum of chi squared variables beyond CLT? [duplicate]

I have a sum $$S = \sum_{i=1}^{n} d_i X_i^2,$$ where $X_i$ are independent standard normals, and $d_i > 0$ are fixed real numbers, for example $d_i = i$. The asymptotic distribution of this sum ...
5k views

How does saddlepoint approximation work?

How does saddlepoint approximation work? What sort of problem is it good for? (Feel free to use a particular example or examples by way of illustration) Are there any drawbacks, difficulties, things ...
545 views

Bound for weighted sum of Poisson random variables

Suppose I have some independent Poisson-distributed random variables $X_1 \ldots X_N$ with parameters $\lambda_1 \ldots \lambda_N$. These can be thought of as processes where each arrival/event ...
556 views

Simulation of PDF of sum of correlated Gamma random variables (in R)

My question is very related to the general sum of Gamma RVs question found in the following link: [The sum of two independent gamma random variables There is some helpful R code there for generating ...
262 views

Sum of random variables without central limit theorem

I know that using central limit theorem we approximate sum of random variables into Gaussian distribution. Is the any other approximation method available for finding the probability distribution ...
1k views

Expected number of dice rolls require to make a sum greater than or equal to K?

A 6 sided die is rolled iteratively. What is the expected number of rolls required to make a sum greater than or equal to K? Before Edit ...