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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GARCH estimation, reduce outlier effect with t distribution

I am trying to estimate GARCH(1, 1) using MLE. As my data contains a lot of outliers, I think using t distribution to represent errors makes a lot of sense. But I am completely lost at how to ...
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8 views

VARMA with t-student innovations

I'm wondering if there is a possibility to estimate VARMA model with t-student innovations in R. I found package MTS, but all models here seem to be estimated assuming multivariate normal ...
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2answers
32 views

How to calculate how many standard deviations a number is from the mean [closed]

I have 25 integers and I would like to find how many standard deviations each of them is from the mean. Apparently, normal distribution is not applicable here and therefore I have to move on with ...
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1answer
33 views

Copula - Correlation Help

I need some help with copula. I am using the copula with either the multinormal or the student t kernel. I thought before that when I input in my correlation matrix, if I simulate enough random ...
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1answer
44 views

Which distribution do I get?

Be $X\sim N(\mu,1)$ and $Y\sim Inverse-Gamma(\alpha,\beta)$. For the Inverse-Gamma, I usually use the parameterization which leads to the following probability distribution function for Y: ...
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1answer
23 views

Multivariate t-distribution definition

I have the following marginal posterior of a vector $\phi$ ($p$ by $1$): $$p(\phi | Y) \propto \left[1+\frac{1}{h}\left(\phi - \tilde{\phi} \right)' \Gamma \left(\phi - \tilde{\phi} \right) ...
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2answers
135 views

Generating random samples with bivariate t-copula

I'm trying to generate a bivariate random sample of the t-copula (using rho = 0.8), without using the "copula" package and its function "rCopula" with method "tCopula". I'm using the following R-code: ...
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22 views

T-test for a small sample with unknown distribution [duplicate]

Consider a simple hypothesis test concerning the mean of a single sample. If the sample is normally distributed and the variance is known, the exact distribution of the sample mean is known ...
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1answer
34 views

Confidence interval for a multiple of regression coefficient

I am trying to model relationship between length of stay of patients in hospital(Y) vs Age in years(X). The data set I've got doesn't specify the unit of length of stay. So now estimated value of my ...
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2answers
69 views

How do I obtain a t distribution?

I performed an independent groups t-test and got a t value of 4.48. Each group is of 26 and I used a criterion of 0.05 (just because...). Before doing the t-test I had to transform my values because ...
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Is this estimator for the standard error of a sample mean difference biased and what is the relation to Student's t-test?

In the situation of two indepdent samples, the variance of the difference in sample means $\bar{x}_1$ and $\bar{x}_2$ is $$Var(\bar{x}_d)=\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}=\sigma_d^2$$ and ...
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1answer
62 views

Log-normal random variables and the distribution of shocks in AR(1) model

Assume, X and Y are jointly lognormally distributied and let X follow AR(1) process: $$X_{t+1} = \mu_t + \alpha X_t+ u_{t+1},$$ $\alpha < 1$. Thereafter, I can't come up with an answer to the two ...
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1answer
82 views

Regression with t-distributed errors and MASS::rlm

I have some data that I'm fitting a multiple regression to, with the twist that the error distribution is t (with user-defined degrees of freedom) instead of Gaussian. I've been coding up my own ...
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20 views

When do we “bootstrap” and then use “t-dist” versus just using “t-dist”?

I'm taking a Data Analysis class on Coursera, and we are learning about bootstrapping when you have a small sample size (>30). What I don't understand, is when do you bootstrap and then use the ...
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2answers
107 views

How can I work out the standard deviation of a t-distribution?

Given a t-distribution with a certain degrees of freedom, how can I work out what the standard deviation of that distribution is?
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1answer
212 views

Proof that the coefficients in an OLS model follow a t-distribution with (n-k) degrees of freedom

Background Suppose we have an Ordinary Least Squares model where we have $k$ coefficients in our regression model, $$\mathbf{y}=\mathbf{X}\mathbf{\beta} + \mathbf{\epsilon}$$ where $\mathbf{\beta}$ ...
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1answer
193 views

Using R to calculate qt (t-dist) using qf(f dist) help?

I am having quite some trouble using R to calculate, say, qt(0.975,6) using qf instead of qt. I know the relationship between the t-distribution and the f-distribution which I understand as follows: ...
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2answers
549 views

Explanation for non-integer degrees of freedom in t test with unequal variances

The SPSS t-Test procedure reports 2 analyses when comparing 2 independent means, one analysis with equal variances assumed and one with equal variances not assumed. The degrees of freedom (df) when ...
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3answers
145 views

Why not use the T-distribution to estimate the mean when the sample is large?

Basic statistics courses often suggest using a normal distribution to estimate the mean of a population parameter when the sample size n is large (typically over 30 or 50). Student's T-distribution is ...
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0answers
37 views

How do I calculate the standard error of the ACF if the errors are t-distributed?

I am modeling my data with ARIMA and to check if my model is good I have to compute the residuals and plot the correlation function and partial correlation function of the residuals. If the results of ...
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2answers
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Why does the t-distribution become more normal as sample size increases?

As per Wikipedia, I understand that the t-distribution is the sampling distribution of the t-value when the samples are iid observations from a normally distributed population. However, I don't ...
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1answer
250 views

Studentized residual distribution

I read that in a regression with $k$ regressors, the t-statistic corresponding to a certain coefficient follows a $t(n-k)$ distribution. However, later on I read that studentized residuals follow a ...
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1answer
135 views

Non-central scaled Student's t cumulative density function required (alternatively the pdf)

I need to cite the pdf(density) or cdf(distribution function) of a non-central scaled Student's t distribution. There is an article about the non-central Student's t distribution ...
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1answer
96 views

T-Distribution using Excel?

I was given this sample problem: Find the t-value such that the area under the t distribution to the right of the t-value is 0.2 assuming 10 degrees of freedom. So, I went poking around in ...
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2answers
426 views

Is the sampling distribution for small samples of a normal population normal or t distributed? [closed]

If I know that the population is normally distributed, and then take small samples from this population, is it more correct to claim that the sampling distribution is normal or instead follows the t ...
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Finding a proper t-distribution given a constraint about the weight of its tail

I wish to find the parameter $\nu>2$ for the student t-distribution such that the following constraint will hold: if $F_T$ is the CDF of that distribution and $F_N$ is the CDF of the normal ...
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18 views

Confused about GARCH innovation distribution

I'm a bit confused about the error distribution of GARCH models. I understand that several standardized distributions (i. e. expected value = 0, variance = standard deviation =1) can be used, for ...
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1answer
143 views

Is there a theorem that says that $\sqrt{n}\frac{\bar{X} - \mu}{S}$ converges in distribution to a normal as $n$ goes to infinity?

Let $X$ be any distribution with defined mean, $\mu$, and standard deviation, $\sigma$. The central limit theorem says that $$ \sqrt{n}\frac{\bar{X} - \mu}{\sigma} $$ converges in distribution to a ...
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37 views

Regression with t distributed autocorrelated errors

I am new, so please bear with me, until its correctly formulated: In short: I am doing simultaneous non-linear regression (parameter estimation) of two different parametric models to three different, ...
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1answer
158 views

Self-study question on t-Distribution

I am currently doing a True/False exercise. One of the questions as follows: A marine drill instructor recoded the time in which each of 20 recruits completed an obstacle course both before and ...
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28 views

Inconsistency in output from my implementation of noncentral t CDF and R's pt()

I am trying to implement a noncentral t CDF as expressed by Guenther (1978), Lenth (1989), and the Wikipedia article on the non-central t in R. I have got my algorithm half working: when the signs of ...
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1answer
57 views

Robust standard errors for cross-sectional data: what is a “large” sample size?

I know that others have asked about robust standard errors (Robust standard errors in econometrics and Always Report Robust (White) Standard Errors?). An answer to the latter question made this ...
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1answer
29 views

Why t distribution in confidence level for the mean?

This is a basic question, but when I was asked about it I only could give a weak answer. That's why I am asking it here. If we want to calculate the confidence level for the mean there is the ...
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1answer
62 views

Bivariate random variable with R [closed]

I am trying to transform this Matlab code into R. My goal is to generate a bivariate random variable with a pre-specified correlation. The code uses the idea of t-copula. I can't figure out how to ...
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1answer
144 views

Relationships between t distributions and normal distributions

In Gelman's Bayesian Data Analysis: The t distribution is the marginal posterior distribution for the normal mean with unknown variance and conjugate prior distribution and can be interpreted as a ...
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1answer
234 views

Estimating parameters for univariate skew t

How can I solve the MLE for the skew-t distribution via EM? I am comfortable with the EM methods for t, so could someone show it for the skew-t?
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1answer
186 views

t-distribution parameter estimation

I know there are already several threads on this, but none seem to explicitly cover what I want. I have a set of financial data (pulled straight from Bloomberg) and am trying to fit a t-distribution ...
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18 views

How to theoretically fit and test for t-distribution [duplicate]

I'm trying to test some data for the best distribution fit, and am looking to try the t-dist (all theoretically, no R computations) I think the best way to do this is to assume the distribution is ...
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1answer
50 views

Difference between pooled t-stat and normal t-stat

Suppose I have data like this - Val Bin -1 Y 5 N -2 N 4 Y so forth - where Bin is a binary value. I want to construct a 95% confidence interval for the ...
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1answer
191 views

What is the relation between the estimated standard deviation of a normal distribution and the scale of a t distribution when applied to normal data?

If I generate normally distributed data and then use this data to estimate the parameters of a normal distribution using, say, maximum likelihood I would expect the estimated standard deviation to be ...
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2answers
522 views

Questions about determining statistical significance in survey responses/methods tried

Background: I am studying the customer satisfaction scores from a random sampling of customers at a technology firm. I have a collection of 13 data points which consist of averages of customer ...
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43 views

Is there a known generalization of the doubly noncentral t-distribution?

Given $p$-variate normal $X \sim \mathcal{N}\left(\mu,\Sigma\right)$, consider the random variable $$ t_* = \frac{X_1}{\sqrt{\sum_{2\le i \le p} X_i^2}}. $$ For some values of $\Sigma$, this ...
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Does (matrix) t-distribution have a conjugate prior?

If my data Y follows matrix T-distribution, i.e. $ Y \sim T_{n,p}(\nu,0,\Sigma,\Phi)$, can I find an appropriate prior for $\Phi$ such that its posterior is in closed form? Inverse Wishart ...
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3answers
480 views

Intuition behind the t-distributions density function

I'm studying about Student's t-distribution and I started to wonder, how would one derive the t-distributions density function (from wikipedia, ...
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2answers
314 views

When n increases the t-value increases in a hypothesis test, but the t-table is just the opposite. Why?

The formula for $t$ in a hypothesis test is given by: $$ t=\frac{\bar{X}-\mu}{\hat \sigma/\sqrt{n}}. $$ When $n$ increases, the $t$-value increases according to the above formula. But why does ...
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1answer
98 views

Student's t-distribution

I have two functions that provide an implementation of the t-distribution. A webpage with a Javascript algorithm. The algorithm takes two input x-value and ...
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469 views

Generate data from a t-distribution with specified mean and standard deviation

How does one randomly sample from a T-distribution in R. From what I've found, the function rt in R doesn't let you specify the mean and standard deviation. For a ...
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68 views

Ratio of lengths of two confidence intervalls

I have two random variables: (1) With standard normal distribution. Confidence interval $I_1$, which is centered and has probability of $(1-\alpha)$ (2) With T-distribution. Confidence intervall ...
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How to prove that a t-distribution can be written as a ratio distribution?

If $X \sim N(0,1)$ and $Y \sim \chi^2(n),$ then it's "known" that $Z = X/\sqrt{Y/n}$ is $t$ distributed. Is there anywhere a proof for this? That in the end one can see the $t$ distribution?
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1answer
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Can the t-distribution be defined as the distribution on the true mean of a sampled normal?

Wikipedia says now, here in the introduction: http://en.wikipedia.org/wiki/Student%27s_t-distribution "... then the t-distribution (for n-1) can be defined as the distribution of the location of the ...