# Questions tagged [t-distribution]

t is the distribution of the t-statistic that results from a t-test. Use this tag only for questions about the distribution; use [t-test] for questions about the test.

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### Moments of truncated Student's $t$-distribution

I performed random sampling on a Student's $t$-distribution. I used SciPy to calibrate my parameters and then truncated my allowable values to the maximum and minimum observation in the data for ...
62 views

### Is the t distribution a member of the exponential family?

From what I understand, the exponential family is defined as $$f(y;\theta,\phi) = \exp\left(\frac{y\theta - b(\theta)}{a(\phi)}+c(y,\phi)\right)$$ I've read (but not seen shown anywhere), that the ...
12 views

### Newton-Raphson method to solve for dof when performing MLE of a multivariate Student-t distribution using EM

I am reading the derivation of EM algorithm to estimate the maximum likelihood of a multivariate Student-t distribution $\mathcal{T}(\mathbf{x} \vert \pmb{\mu}, \pmb{\Sigma}, \nu)$ in Kevin Murphy's ...
15 views

### How do I read a t-table correctly?

Motivating Example: It is of interest to the medical profession to identify whether a given change in a measured quantity is real or due to noise, for purposes of a diagnosis. Precision from ISCD (...
39 views

### t-student or f-distribution?

I am reading 'Applied multivariate statistical analysis' by Richard Johnson and I do not understand that first to explain this test, talks about the t-student distribution. And then out of nowhere he ...
33 views

### What is Half-Inverse-Student-t distribution?

In the paper of Vanhatalo et al 2018, section 5.3 page 15, they use Half-Inverse-Student-t distribution as a prior: I have never heard of such distribution and I have problems finding it. What is it?
39 views

### Prior distribution of variance for normal distribution

In the wikipedia of "Student's t-distribution", "Bayesian inference" part, it is claimed that the prior distribution of the variance is taken to be $p(\sigma^{2} \mid I) \propto 1/\sigma^{2}$ but I ...
40 views

### Show that t distribution variance doesn't exist when df = 2

When DF = 1, t distribution is just Cauchy distribution whose mean does not exist. $E(T) = E(\frac{Z_1}{\sqrt{Z_2^2}}) = E(\frac{Z_1}{Z_2}) = E(Z_1)E(\frac{1}{Z_2})$ where the second expectation ...
12 views

### In-sample likelihood cannot be lower for student-t model compared to Gaussian model

I am looking at the solution of a question that asks us to briefly comment on how we can compare two linear models with different distributed $\epsilon_i$. For the first linear model $\epsilon_i$ is t-...
56 views

### Are confidence intervals only for a specific population parameter, like the mean? What about the whole population range, e.g. for outlier detection?

As someone with quite a weak understanding of statistics, I'd like to know: Is it possible to calculate confidence intervals for a population range in general from a sample? What I have learned so ...
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### Comparing WAIC from normal linear model and a student T with z scored data?

I am running multiple models and looking at Widely Available Information Criteria for them. Is it unreasonable to run two linear models, the only difference between likelihood distributions (one ...
34 views

### What is the integral of the t-distribution function?

The t-distribution probability density function is given by: $f(x) = \frac{\Gamma(\frac{\nu+1}{2})}{\sqrt{\nu\pi}\Gamma(\frac{\nu}{2})}(1+\frac{x^2}{\nu})^{-\frac{\nu+1}{2}}$ Is there an integral ...
148 views