Tagged Questions
0
votes
1answer
51 views
Efficient method of approximating a distribution with Gaussian
Given a univariate uni-modal density function $f(x)$ (very hard to compute its cumulative distribution function (CDF) $F(x)$, not to mention its inverse CDF $F^{-1}(x)$),
how to find the best ...
0
votes
1answer
52 views
How to estimate parameters of a normal distribution?
Suppose one knew that 105 workers were evaluated by their boss. Such evaluation is distributed according to a normal distribution with mean $\mu$ and std. deviation $\sigma$. We also know that 20 ...
6
votes
2answers
119 views
Why should Gaussian noise have fractal dimension of 1.5?
In a paper I'm trying to understand, the following time series is generated as "simulated data":
$$Y(i)=\sum_{j=1}^{1000+i}Z(j) \:\:\: ; \:\:\: (i=1,2,...,N)$$
where $Z(j)$ is a Gaussian noise with ...
1
vote
1answer
80 views
The distribution when combining two samples together?
Suppose $X\sim N(0,{\sigma}^2)$ and $Y\sim N(0,{2\sigma}^2)$ . $X_1, ..., X_m$ are the samples from $X$ and $Y_1, ..., Y_n$ are the samples from $Y$. And then combine two samples as a new sample ...
2
votes
1answer
43 views
Parameter optimization in probabilistic models
Task: Suppose we model a variable $y = Wx + \mu$ as a linear transformation of $x$ plus some Gaussian noise $\mu\sim\mathcal N(0,\sigma I)$. Our aim is to minimize the estimation error of $x$ given ...
3
votes
1answer
133 views
MLE of the mean of a heteroscedastic Gaussian time series
Suppose we observe $Y_i\sim \mathcal{N}(\theta_0 + \theta_1 x_i, \sigma_i^2)$, with $x_i$ and $\sigma_i^2$ known for all $i = 1,\ldots,n$ and $Y_1,\ldots,Y_n$ independent. Assume $\theta_0$ is ...
