# Tagged Questions

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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### code Welch's t-test in C++ using approximations for student's t values

I need to code a Welch's t-test between two populations in C++ without using external libraries like, for example, boost. I know that given my two populations of size $N_1$ and $N_2$, I can calculate ...
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### Generalization of degrees of freedom for t distribution for coefficients after multiple imputation

Donald Rubin has shown that regression coefficient estimates have fatter tails after multiple imputation and has provided a formula for the degrees of freedom to use as a t-distribution approximation ...
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### What is the original source for Jeffreys 7 degrees of freedom suggestion?

In a comment on this question Nick Cox mentioned that Jeffreys suggested that errors in data approximate t distributions with 7 degrees of freedom. Does anyone have a source/citation for this?
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### Calculating the t statistic

I recently came across a blog post (https://cssanalytics.wordpress.com/2014/02/12/probabilistic-momentum-spreadsheet/) that discusses calculating a t-stat as part of their model. However, the formula ...
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### How do I check if a random variable follows the T Distribution?

Let us say I have a data for a random variable X -- Is there a convenient test that can tell me how well it fits the T distribution? Code in R would be helpful.
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### Help Beginner Q: Explanation on pooled variance and when it is used

If I am conducting a difference in means hypothesis test, when do we use the pooled variance and why? Lets say the population variance was unknown for two samples, the sample sizes for the two means ...
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I have two different large samples, one is normally distributed (0,1) and the other one follows a t-distribution (df = 4). Can I compare whether the means or the st. deviations of both samples are the ...
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### Formula for confidence interval level doesn't give correct result

I am kind of new in calculation of confidence interval, so I hope it will not be a too basic question. I have a normal distribution (with slightly longer left tail) as you can see in the picture. The ...
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### Student t-distribution parameter/s and MLE

So I always thought of the Student t-distribution as having only 1 parameter, v, the degrees of freedom (as described by wikipedia). When I searched however on how to find the MLE of v I keep coming ...
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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ARMA(...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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.
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### 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? I'...