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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Non-central t-distributions with different degrees of freedom

I have two non-central t distributions with CDF given by $t_{n,a}$ and $t_{m,a}$ with $n>m$ degrees of freedom respectively and the same non-centrality parameter $a$. The question is: for which ...
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22 views

quantile of standardized t distribution

How to show that, for any given left tail probability, the corresponding quantile of standardized t distribution is increasing in degree of freedom for left tail probability less than 0.5? This is ...
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17 views

parameter estimation of skewed student-t distribution in R

I am trying to fit skewed student-t distribution to fitted residual returns obtained from ARMA(1,1)-GARCH(1,1) The histogram of my data looks like I am using fGarch's sstdFit to estimate the ...
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15 views

How to rescale data for multivariate t-pdf?

I try to evaluate the pdf of a multivariate t-distribution in Matlab. Unfortunately the function is only defined for a correlation matrix and not for a covariance matrix. I guess i can rescale the ...
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1answer
19 views

Trying do determine how to rank water flow measurements?

I'm doing a study that involves waterflow measurements as it relates to erosion prioritizing. I'd like to rank between (0-1) a population of 160 values with a minimum of 2.1 and a maximum of 5.9 The ...
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8 views

Ranking data sets by means etc. (unequal sample size and variance)

I want to rank several lists of data by their tendency to be larger or their capacity to be larger when extrapolated. Is there a way to do this effectively?
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32 views

How do you determine when to use certain test statistics?

I've been trying to formulate this question and have struggled, so if it seems ill-worded, I apologize: A statistics book I have has a table in the back that says: For an inference test regarding a ...
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25 views

fitting t distribution with lighter tails

I am trying to fit a t distribution in R using the fitdistr function in the MASS package as follows ...
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25 views

Derivation of GARCH student t log-likelihood

I got the general PDF of the student t distribution, that is: $\frac{\Gamma[\frac{(\nu+1)}{2}]}{\Gamma(\frac{\nu}{2})}\,\frac{1}{\sqrt{\pi\,\nu}}\,\bigg[1 + \frac{x^2}{\nu}\bigg]^{-(\nu+1)/2}$ ...
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29 views

Expectation of t distribution

Find $E(T^{2r})$ of Student's t-distribution. My teacher has told me the answer.... it's something like $$ \frac{n^r \Gamma(r+(1/2)) \Gamma(n/2-r)}{\Gamma(1/2) \Gamma(n/2)} $$ From this I calculated ...
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33 views

Degrees of freedom in t dist in ML estimation using ugarchfit in R

I'm quite new to R, and is currently working on my master's thesis and have a question in that relation. I have been using the ugarchspec and ugarchit functions (rugarch package) to estimate my ...
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2answers
50 views

How to simulate from a t copula?

This is a question related to: How to simulate from a Gaussian copula? Suppose that I have two univariate marginal distributions, say $F$ and $G$, which I can simulate from. Now, construct their ...
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26 views

Maximum-likelihood estimation of student t distribution [duplicate]

I am a little confused about the Maximum Likelihood estimation of the student t distribution. Although it is said here that there is no closed form parameter estimation, I found in the MatLab ...
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8 views

Robust confidence interval for observations high/low variance

How to build consistent and robust confidence interval for lower (close to zero, =invariant) and higher variance observations? Example using R: The example includes confidence interval based on ...
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0answers
10 views

Standard deviation of sample mean differences used as the basis for calculating standard error of the two samples

I came across this problem in the OpenIntro Statatistics (it is very free) textbook: Now, in calculating the t-statistic for the difference of means, the same book shows that the Standard Error in ...
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0answers
23 views

Projection of a spherical t-distribution

I'm working with an $n$-dimensional spherical t-distribution for which the density is defined as $f(x) = \frac{\Gamma(\frac{n+\nu}{2})}{(\pi \sigma^2\nu)^{\frac n2}\Gamma(\frac \nu2)} \left( 1 + ...
3
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1answer
153 views

Does the standard error of the mean approach 0 as the number of samples increases?

The standard error of the mean (SEM) is often given as $s / \sqrt n$, where $s$ is the standard deviation and $n$ the number of samples. Does this mean that if we were to calculate the SEM with more ...
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1answer
54 views

Why does Naive Bayes use gaussian pf rather than Student's t?

Every source in the literature I could find about naive Bayes mentions using a gaussian's probability density function, using the mean and variance estimated from the data itself. This strikes me as ...
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87 views

Estimating DCC GARCH using a multivariate t-distribution in Matlab

What I want to do is estimate the DCC equation using a multivariate t-distribution, preferably in Matlab. There is a package/toolbox of Sheppard and Shephard. But that one only allows you to use a ...
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35 views

Multivariate t-distribution with different degrees of freedom per dimension

One way to define the multivariate t-distribution is: $ p(x | \mu, \Sigma, n) = c \left(1 + \frac{1}{n} \left(x -\mu\right)^T\Sigma^{-1}\left(x-\mu \right)\right)^\frac{-(n+K)}{2}$ with $K$ the number ...
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71 views

Fit generalised extreme event distribution in MATLAB/R

I have a location-scale t-student distribution $X$ $$ f(x,\mu,\sigma,\nu) = \frac{1}{\sigma} \frac{\Gamma(\frac{\nu+1}{2})}{\sqrt{\pi\nu} \Gamma (\frac{\nu}{2})} \left( 1 + \frac{(x - ...
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1answer
72 views

Is the Student-t distribution a Lévy stable distribution?

Let $X$ have a Student-t distribution, so that \begin{align*} f_X(x|\nu ,\mu ,\beta) = \frac{\Gamma (\frac{\nu+1}{2})}{\Gamma (\frac{\nu}{2}) \sqrt{\pi \nu} \beta} \left(1+\frac{1}{\nu}\left(\frac{x - ...
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63 views

Equality vs. Equality in Distribution ($t$-distribution for example)

A technical question that came up to mind as I was reading up on linear models today. Consider the $t$-distribution with $\nu$ degrees of freedom ($t_\nu$) for example. Let's say $T \sim t_{\nu}$; ...
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1answer
36 views

Informativeness of t-score?

My organization recently did a morale survey. Results were given as t-scores. I had never seen that before, so I embarked on a web journey. I found a very similar survey. My question isn't about the ...
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2answers
67 views

Uses and estimation of Student-t distribution

My question relates to a confusion between how the Student-t distribution is often documented versus how it is used. In the documentation the Student-t is used (from Wikipedia): when estimating ...
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1answer
47 views

What would be the method of moments (MOM) estimator of $\nu$ for t-distribution?

I recognize that method of moments is not the best way to estimate $\nu$ for the t-distribution, but I am just wondering how this would be calculated since $E[X^n] = 0$ if $n$ is odd. Here we're ...
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28 views

Importance Sampling of a Student-t with mean 0, $\sigma^2$ and degrees of freedom unknown

I want to calculate the posterior parameters of a Student-t by importance sampling. In order to tune the importance density I sample from the prior first. My data is demeaned, the degrees of freedom ...
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22 views

Sample from sum of squared independent $t_\nu$ distributed variables

I would like to specify radius r in a case where $P(Z_1^2 + Z_2^2>r)=a$, $a$ is known, where $Z_1,Z_2$ are i.i.d $t_\nu$-distributed. Since, this can be really challenging to do analytically, I ...
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17 views

Product of two multivariate t densities

Does the product of two multivariate t densities result in the density of a known distribution, that is easy to simulate from?
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132 views

Visualization of normality condition for t-test in R

I am working through the concept of the need for normality in the underlying population when performing a t-test. This is nicely expounded by @Glen_b here. The gist of the explanation, I think, is ...
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1answer
145 views

Issues with Importance sampling for flat prior

I am trying to draw Bayesian inference via importance sampling for a parameter $\xi$ attached with an (unbounded) flat prior. This seems problematic as this is clearly not a probability measure but ...
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1answer
43 views

Student's distribution tails

I do not understand why in some figures they put $t_{1-\alpha/2}$. Why is the subscript $1-\alpha/2$ used? I know that $t_{\alpha/2}$ and $-t_{\alpha/2}$ are used to construct confidence intervals. ...
5
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1answer
183 views

How to show mean and standard deviation of Normal distribution?

If a sample is normal with observations independent and identically distributed: $\mu|\sigma^2 \propto N(\beta \,,\,\sigma^2/\, n_0)$ How can I show that $\mu\,|\,x_1,x_2,....x_n\,,\,\sigma^2 \sim ...
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1answer
50 views

Students t-test

In comparing B6 levels in serum vs plasma, 20 volunteers were chosen. The objective is to determine if B6 concentrations differ when taking from serum or plasma. Each volunteer gave two samples, one ...
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414 views

t-distribution having heavier tail than normal distribution

In my lecture note, it says, "t-distribution looks like normal, though with slightly heavier tails." I understand why it would look normal (because of Central Limit Theorem). But I am having hard ...
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Sampling distribution question

I've been struggling with this question for 3 days and I cannot find the way to do this. I know the answer, but I can't solve it clearly. When I try to solve it, I get stuck here: How can I ...
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1answer
55 views

Simple Student Copula simulation

I want to simulate a t copula with given correlation parameter $\Sigma$ and $k$ degrees of freedom. I can't find any literature about practical simulation, so I am trying new approaches. (I also have ...
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23 views

Building confidence interval with t-distribution

I am wondering wether i have to use normal or t distribution in the following situation I have a population of 1000 individuals. I'm interested in $P$ the sum of all $x_i$ where $x_i$ is the value of ...
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1answer
25 views

Comparing a distribution law with its density function in R [closed]

I want to generate a sample of a student t distribution with a certain length and a certain degree of freedom and compare it in the same graphic with its density funcion. How could i aproach that? ...
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61 views

Student's t-distribution value calculation

I need to calculate the t-distribution values. While referring to literature I found that I need degrees of freedom for this. But while referring to my reference paper I find that author has used some ...
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1answer
43 views

Fitting upper and lower student-t separately

I'm doing some research on fitting marginal distributions to data, in particular distributions with a focus on heavy tails. In one report, albeit several years old, the authors suggested fitting a ...
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60 views

improving accuracy for sample skewness and kurtosis under Student's t distribution with low degrees of freedom

There is no skewness in Student's t distribution. Given the degrees of freedom, the kurtosis estimator is given by $\frac{6}{\nu - 4}$. However, when sampling form a t-distribution with low degrees of ...
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2answers
113 views

What is the equivalent of Student's t-distribution on an interval?

I have been using Student's t-distribution as a proxy for the Gaussian distribution estimated from a limited number of points in order to calculate alpha-intervals (for instance 95% confidence ...
3
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1answer
69 views

Is the $t$ test a special case of the generalized linear model?

The GLM consists of methods which model responses following a distribution from the exponential family. These distributions have a probability function which can be expressed as: $$ f(x; \theta) = ...
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1answer
35 views

$t$-distribution and finding probability of sample mean

There is a question from a statistics book: If four observations are taken from a normal distribution what is the probability that the difference between the observed mean $\bar x$ and the true mean ...
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69 views

Non-standardized Student's t distribution

If I compute the quantity $$ t = \frac{\mu}{\sigma}, $$ for a mean value $\mu$ and standard deviation $\sigma$ computed from some $n$-vector, $v$, is it then correct to state that $t$ follows a ...
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29 views

Externally studentized residuals

Assume the our model is simply $$Y = X\beta + \epsilon$$ with $\epsilon$~ $N_n(0,{\sigma}^2I)$. If we want to identify the existing outlier in our dataset, we use the externally studentized ...
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1answer
84 views

Sum of two elliptical distributions will it be again elliptical distribution?

What will be the sum of two elliptical distributions will it also be elliptically distributed? from this What is the distribution of the difference of two-t-distributions It says that sum of t ...
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90 views

Correct adjective for an RV with a Student's $t$-distribution

If a variable has a normal distribution, we say it is normally distributed. If it has an exponential distribution, we say it is exponentially distributed. What is the proper way to reference a ...
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1answer
50 views

Is my work correct (easy problem, confidence intervals)

The r.v. $X$ represents the time taken by a computer in company $1$ in order to perform a certain job, and $Y$ represents the same thing but for company $2$. A sample of $n_X = 12$ computers are taken ...