# 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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### How do I go about choosing the right degrees of freedom for a simulation study?

How does one go about choosing the right degrees of freedom when sampling from a T-Distribution? I understand n-1 degrees of freedom is the theoretical rule of thumb, but my sample size is quite large ...
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### Why use the student's t-test rather than z-score?

Suppose we are given IID r.v's $X_1, \ldots, X_n$ that are not necessarily normally distributed. Mean $\mu$ and standard deviation $\sigma$ are unknown and we want to construct a confidence interval ...
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### Verifying Sampling Distribution of a Statistic

In the given question, I can easily show that option A and C are true but i am not sure about option B. I know that |$X_2$ +$X_3$| can be written as $($$(X_2 + X_3)^2$$)^{1/2}$ and then it can be ...
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### How to approximate the student-t CDF at a point without the hypergeometric function?

Is there a way to closely approximate the CDF of a student-t distribution at a point $x$ without involving the hypergeometric function? For example, by using a series expansion, or expressing the CDF ...
77 views

### What's the relationship between degrees of freedom of t distribution and tail exponent (alpha) of Pareto distribution?

I'm going to generate a set of data from a T distribution and truncate the body(so that we make it approximately Pareto distributed) of it and estimate the tail exponent(shape parameter) of the ...
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### Distribution of multivariate “$Z$-score”?

Suppose $\mathbf{X}_1, \dots, \mathbf{X}_n \sim N_p(\mathbf{\mu}, \Sigma)$ where $\mu \in \mathbb{R}^p$ and $\Sigma$ is a $p \times p$ covariance matrix. Suppose $\hat{\Sigma}$ is the sample ...
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### Linear regression with error dispersion dependent on the independent variable

Suppose $y=ax+z$ where $x, y, z$ are random variables with range in $\mathbf R$, $\mathbf E[x]=0$, the probability distribution $p(z|x)$ is 1) normal distribution $N(0,\sigma(x)^2)$ with mean $0$ ...
I'm an experimental physicist who mainly needs statistics for the calculation of uncertainties/confidence intervals. Since my results are usually normally distributed, I simply take $N$ measurements ...
I estimate covariances from data and want to calculate likelihood. For 1D case I know - if the sample size is $<40$, I use Student's t-distribution to calculate likelihood of the data since my ...