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.
513 questions
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How to to approximate Student-t distribution with finite Gaussian mixture?
The goal is to parametrise Gaussian mixture weights $w_i$ and relative scales $s_i$ that reproduce the t-density within the quantile range $x \in [q_{0.0001},\,q_{0.9999}]$ and $\nu \in [2.5, 15]$. ...
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Hansen SkewT fast numerical approx for E[exp x] and inverse?
I want to fit Hansen $\text{SkewT}(μ, σ, ν, λ)$ with GARCH, fixing $E[e^{r_t}]$ instead of $\mu$.
This means at each step the $\mu_t$ will be adjusted. For normal case the adjustment is simple $\mu_t=\...
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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?
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Why does marginalizing over an unknown variance yield a Student's t distribution in the normal model? [duplicate]
In a univariate normal model with both the mean $\mu$ and the variance $\sigma^2$ unknown, one often places a normal–inverse–gamma distribution prior on $(\mu, \sigma^2)$. For example, the $\mathrm{NI}...
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Parametric bootstrap for a Student-t model when the degrees-of-freedom estimate has a very large standard error
I am analysing a sample of size $n = 200$ that appears to follow a Student-$t$ distribution fixed by design. Fitting the model yields $\hat{\nu} = 10.22$ but with a relatively large standard error of $...
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Expected value of the outer product of normalized, non-centered Student t vector
I was studying the expected value of the outer product of a normalized non-centered Gaussian vector and I found this very interesting and solved question and I am looking to generalize to a Student t ...
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t-distribution and log-t distribution relation
I am stuck for a while with this doubt. As we know, given a log normal distribution, like the series of equities prices, by taking the log of that series we get the normal distribution. By doing the ...
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Value-at-risk calculation for DCC-GARCH model in rmgarch package
I use rmgarch package for DCC-GARCH model fitting and making forecasts (covariance matrix and MUs) of my portfolio based on it (one-step). So, I use ...
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Using the normal distribution vs the t distribution when computing confidence intervals
I've seen both $\pm \operatorname{qt}(\alpha/2, N-1)\cdot SE$ and $\pm \operatorname{qnorm}(1-\alpha/2) \cdot SE$ being used as confidence intervals. In which case do we use each?
Say I have a list of ...
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How should introductory statistics material explain sample size estimation for means in the case of unknown population variance?
This is my first question here and I'm unfamiliar with statistics; I made an effort to search the site for duplicates, and there are related questions, but they don't quite address my question.
I'm ...
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What to do when one gets a decimal value as degrees of freedom?
I am trying to find the t value for a confidence interval of the difference in the sample mean of 2 random variables. The variance here is unknown and unequal, so the formula for v that one must use ...
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T-test when variance estimator is not sample variance [closed]
It is well known that if $x \sim \mathcal{N}(0, \sigma^2)$ and we have a sample size of $n$ observations of $x$, the distribution of $\frac{x}{\hat{\sigma}}$, where $\hat{\sigma}$ is the sample ...
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Connecting two different meanings of "degree of freedom"
I have heard at least 2 meanings of "degree of freedom".
The parameter in a t-distribution.
The the number of values in the final calculation of a statistic that are free to vary (like ...
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For a t-distribution, df = n-1. What does n represent? [duplicate]
Cross-posted from Math Stack Exchange as suggested by 2 people there.
I know that the $t$-distribution has one parameter: the number of degrees of freedom (df).
I also know that $\mathrm{df} = n - 1$.
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In a $t$-distribution, what is the meaning of "degrees of freedom"?
I know that the $t$-distribution has one parameter: the number of degrees of freedom (df).
I also know that $\mathrm{df} = n - 1$.
However, what EXACTLY does the $n$ represent?
I have heard several ...
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