Questions tagged [non-central]
use for questions about socalled non-centrality parameters, in distributions such as t, F, chisquare, wishart and others.
95 questions
1 vote
0 answers
32 views
the method um of non-central chi-square using Laguerre expansion [closed]
I'm a student from China,and recently I read this paper(https://link.springer.com/article/10.1007/BF02595410).In this paper,β is scaling factor. But can β be arbitrary, as long as β>0 or dependent ...
6 votes
2 answers
341 views
Statistics – Linear Inference – What is the moment generating function of non-central t-distribution?
Non-central t-distribution, mgf. What is the moment generating function of non-central t-distribution?
- 61
2 votes
1 answer
216 views
Lower Tail Bound for Noncentral chi-squared distribution
A noncentral chi-squared random variable $Z$ is of the form $$ Z = \sum_{i=1}^k X_i^2 $$ where $(X_1, X_2, \ldots, X_i, \ldots, X_k)$ be $k$ are independent, normally distributed with mean $\mu_i$ and ...
- 23
1 vote
0 answers
72 views
Distribution of the number of iterations to achieve success
Let $Z=X+jY$ ($j$ is the imaginary unit), with $X\sim\mathcal{N}(\mu,1)$ and $Y\sim\mathcal{N}(0,1)$. I'm running an algorithm that at every iteration $k$ samples a complex number $z_k$ that follows $...
- 21
3 votes
2 answers
270 views
non-central F-statistic confidence intervals seem inconsistent with ANOVA p-values
I have done a series of one-way ANOVA tests. For each test I have calculated the corresponding alternative hypothesis F-statistic and confidence intervals, based on the degrees of freedom involved and ...
- 95
5 votes
1 answer
348 views
Can power decrease despite an increase in sample size?
I've analyzed fish density data (log(x+1) transformed) to see what power I'll have to detect a 30% increase and decrease in density from future surveys, and for which species of interest. Using ...
- 2,537
2 votes
0 answers
98 views
CDF for squared sum of Rayleigh random variables
In short, I am looking to estimate the distribution of $ \eta = \sum_{i=1}^N (X_i - z_i)^2$, for each $X_i \sim \text{Rayleigh}(1)$ and constants $z_i$. If $X_i$ were Gaussian, then this could be ...
- 21
5 votes
0 answers
272 views
sum of noncentral Chi random variables
if $X_1,...,X_n$ are independent random variables with noncentral chi distributions (same $df$ but different $\lambda$), What is the distribution of $\sum_{i=1}^{n}{X_i}$ Just wondering if it can be ...
4 votes
1 answer
647 views
How to approximate non-central chisquare distribution to Poisson weighted sum of central chi-square distribution in case of non-unit variances?
According to Statistics libre texts Equation 5.9.20, a non-central chi square distribution can be approximated as sum of Poisson weighted central chi square distributions. $\tag{1}g(y) = \sum_{k=0}^\...
- 127
3 votes
2 answers
562 views
Expected value of Rayleigh quotient, non-centered Gaussian vector
Let $X \sim \mathcal{N}\left(\mu, \Sigma \right)$, and let $A$ be a symmetric matrix. My understanding is that the Rayleigh quotient of vector $X$ is given by: $$R=\frac{X^T A X}{X^T X}$$ I've been ...
- 2,352
6 votes
1 answer
418 views
Random number generator for non-central chi-squared with non-integer dimension
Does someone know of a random number generation algorithm for a non-central chi-squared distribution with a non-integer dimension? PS By algorithm, I am interested in the detailed procedure or ...
- 63
1 vote
1 answer
318 views
Noncentrality parameter Repeated-Measures ANOVA - formula vs. G*Power
I am trying to figure out the correct expression for the noncentrality parameter $\lambda_{ws}$ for the within-subjects effect in a one-way Repeated-Measures ANOVA with $k$ trials/groups. Comparing ...
3 votes
1 answer
204 views
Distribution of $X'\Sigma^{-1}X$ for $X$ following a multivariate $t$ distribution
According to Golam Kibria & Joarder (2006, p.7) available here and Kotz & Nadarajah (2004, p. 19) visible in google, the distribution of $X'\Sigma^{-1}X /p$, for a known correlation matrix $\...
- 381
0 votes
0 answers
188 views
Which is the noncentral multivariate t distribuiton
In various documentations, I found out two definitions of the multivariate noncentral student $t$ distribution. The most commonly density (PDF) found is (e.g., wikipedia): $$\mathcal{T}(x;\mu, \sigma^...
- 381
2 votes
1 answer
217 views
The distribution of the difference between two correlated non-central t distribution
Suppose a binormal population $\{X, Y\}$ with means $\mathbf{\mu} = \{\mu_1,\mu_2\} \ne \{0,0\}$ and covariance $\Sigma= \sigma^2\begin{bmatrix}1 & \rho\\ \rho &1 \end{bmatrix}$. Let $S^2$ be ...
- 381