# Tagged Questions

33 views

### Estimate the minimal values of a gaussian normal distribution

My first question here and i hope that its not to obvious or stupid. My problem: I have a number of $x$ values ( $x$ can vary) that follow a normal distribution. I can calculate all normal descriptive ...
67 views

### Generating normal random samples given covariance matrix and observations on some components?

Suppose we have n by n covariance matrix of n normal random variables. Is there program where we plug in sample values for k of the n variables and the program, by using the covariance matrix and ...
22 views

### CLT in a Monte Carlo simulation, small sample

A CLT says that asymptotically the sampling distribution of the sampling mean converges to the Normal. I would like to run a Monte Carlo simulation using information on one of the model's variables ...
59 views

### Estimating variance of center-censored Normal samples

I have normally-distributed processes from which I get small samples (n typically 10-30) that I want to use to estimate variance. But frequently the samples are so close together that we can't ...
34 views

### How to estimate a pdf of x under the model of y = x+n, when the pdf of y and the pdf of n are given

I guess I come up with a classic question, but I failed to find any useful solutions by far. My question is about the following model $$y=x+n$$ where $x$ is a hidden random variable that cannot be ...
20 views

### Hypothesis testing of normal distributions when mean and range on variance is known

Hypothesis testing problem: $H_0: y \sim N(m_1,v_1)$ $H_1: y \sim N(m_2,v_2)$ . The means $m_1, m_2$ are known and variances $v_1, v_2$ are unknown but upper and lower bounds on $v_1, v_2$ are ...
31 views

### Estimating parameters of inifinite scale mixture from data

Suppose that I have an infinite scale mixture of zero-mean normal distributions, whose mixing distribution is gamma with parameters $\alpha$ and $\beta$. The data is thus distributed according to a ...
63 views

### How to combine variances from sensors where each observation has its own variance?

I have a set of measurements $x_1$ ... $x_n$. These measurements are normally distributed, measuring the same value. However due to the way the data is measured, each $x$ has its own standard ...
92 views

I am a software developer and am frequently asked by prospects to provide a workload estimate for a potential project. I would like to implement a statistical approach to estimation that works as ...
110 views

152 views

### Finding the UMVUE of the variance of a gaussian with mean zero

Given $Z_1, ..., Z_n, \sim\mathcal{N}(0, θ^2), θ>0$. Define $X_i=|Z_i|$ and consider estimation of $\theta$ and $θ^2$ on the basis of the random sample $X_1,...X_n$. Find the uniformly minimum ...
170 views

### Estimating parameters of a normal distribution from noisy observation of samples

Suppose I have a number of samples drawn from a normal distribution $x_i \sim \mathcal{N}(\mu,C)$ with $i = 1 \dots n$. I can make observations $z_i = x_i + e_i$ for those samples which are perturbed ...
503 views

### Estimating parameters of a normal distribution: median instead of mean?

The common approach for estimating the parameters of a normal distribution is to use the mean and the sample standard deviation / variance. However, if there are some outliers, the median and the ...
498 views

### Maximum likelihood of function of the mean on a restricted parameter space

I've been trying to teach myself some of the fundamentals of statistics by trying to work through old qualifying exams. Here's a problem: Suppose $X_1, \ldots, X_n$ are a random sample from a normal ...
468 views

### How to estimate the parameters of a Gaussian distribution sample with outliers?

I have a sample of length $N$, mostly taken from a Gaussian distribution with unknown mean and variance. Of those $N$ samples, some proportion of them (typically less than 1-2%) are outliers, taken ...
55 views

### How to pick from a set of random variables the one with the highest mean using a fixed number measurements?

Suppose we have $N$ approximately normally distributed continuous random variables $X_1, X_2, X_3, \ldots,X_N$, each with an unknown mean and variance. I'd like to find the random variable with the ...
209 views

### Estimating the parameters of a sum of a Gaussian and an $\alpha$-stable random variable

Let's assume I have a set of samples of a random variable $$X = Y + Z \>,$$ where $Y$ is Gaussian (with a mean of zero and variance $\sigma^2$) and $Z$ has a symmetric $\alpha$-stable ...
218 views

### Consistent estimator for probability density function at a given point

I am trying to conduct a simulation study on a variation of the kernel density estimator. In that experiment, there is a parameter in one of my formulas that involves the value of the unknown pdf at a ...
191 views

### Accuracy in approximation with central limit theorem

I have set of random values with the same distribution $y_1, \ldots, y_N$ $$T = \frac{1}{N}\sum_{j = 1}^{N} y_j$$ I want to find the confidence interval for the mathematical expectation $E(Y)$ ...
270 views

### Estimation of white noise parameters in Gaussian random walk model

I want to estimate the parameters (mean , variance ) $e(t)$ for the random walk model $X (t) = X (t-1) + e(t)$. (where $e(t)$ is the white noise with a Normal distribution). By using the fact that ...
188 views

### The distribution of an estimator

I was reading the Wikipedia article on Robust Statistics: http://en.wikipedia.org/wiki/Robust_statistics#Properties_of_M-estimators What is meant by the distribution of an estimator, as used here, ...
90 views

### Estimating a 1-D Brownian motion process using noisy observations

This question is a follow-up on my previous question. Suppose I have a Brownian motion process that is defined as follows: at time $i=1$ random variable $X_1\sim\mathbf{N}(\mu,\sigma^2)$, and, for ...
211 views

### Bayesian updating using $n$ noisy observations of Brownian motion

I am very new to Bayesian inference and can't figure out what may be an elementary problem. Also, please forgive me if I am screwing up the notation -- this is my first foray into Bayesian ...
336 views

### Mean and standard deviation of Gaussian Distribution

I have some random numbers which are generated from Gaussian Distribution. But I don't know the mean, standard deviation of that distribution. How can I find them using random numbers?
95 views

### Cross validation for a biased estimator of a Gaussian mean

Consider the mean estimator $$\hat{\mu}(\lambda) = \lambda \frac{1}{n}\sum_{i = 1}^nY_i$$ (for $n$ iid Gaussian variates $Y_i$). After calculating the bias and the variance of this estimator, I ...
264 views

### Estimating the variance of poker win rates

Suppose you have a casino with n poker players. Each player has a win rate - the amount of money he wins or loses per hand. We assume that these win rates are normally distributed with a mean of 0. ...
81 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: ...
94 views

### Using an OLS coefficient to estimate a non-linear coefficient

Using OLS, I've estimated the following equation: $y_i = \alpha_0 + \alpha_1 X_i + \epsilon_i$ I know that theoretically, the following should be true: $y_i = a + (1-e^{-\lambda 60}) X_i$ Is ...
334 views

### Estimating parameters for a spatial process

I'm given an $n\times n$ grid of positive integer values. These numbers represent an intensity that should correspond to the strength of belief of a person occupying that grid location (a higher value ...
856 views

### Parameter estimation for normal distribution in Java

Given a set of data (~5000 values) I'd like to draw random samples from the same distribution as the original data. The problem is there is no way to know for sure what distribution the original data ...
369 views

### Get distribution curve characteristics by selecting peak point?

I have no math or stats background, so this may be a real dumbo question. I'm developing a time estimation app which would let user enter her worst case and best case estimates, and then select a ...
457 views

### Estimating distribution parameters from few data points

Say I'm doing stats on the height of adults from various countries. I assume the heights of adults from one country are normally distributed, and ignore sex differences (I also ignore the fact that ...
402 views

### What is the minimum mean squared error estimator of the mean of two normally-distributed variables?

Let $Z=(X+Y)/2$, where $X$ and $Y$ are independent normally-distributed random variables with known variances $\sigma^2_X$ and $\sigma^2_Y$ and unknown (and possibly different) means. Given a sample ...
Let $Z=(X+Y)/2$, where $X$ and $Y$ are independent normally-distributed random variables with known variances $\sigma^2_X$ and $\sigma^2_Y$ and unknown (and possibly different) means. Given a sample ...