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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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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32 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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62 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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55 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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75 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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22 views

Fitting a Non-Central t-Distribution with Location and Scale Transformations

I am trying to fit a distribution function to empirical observations that have the following properties: Non-zero mean Non-unit variance Heavy tails Asymmetric about the mode I am considering ...
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34 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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112 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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77 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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29 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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157 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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68 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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174 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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63 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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64 views

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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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 ...
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1answer
108 views

Generic test for unimodality given sample

Are there any generic tests to validate if a given sample follows a unimodal distribution, like a Gaussian, Cauchy, Student's t or a chi-square?
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547 views

Generating random numbers from a t-distribution

How can I generate random numbers that follow a student-t distribution? From several sources I understand that this can be done using a random sample of size $n$ drawn from a normally distributed ...
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1answer
100 views

Does inference from a heteroskedasticity-consistent covariance matrix follow the t-distribution or the normal?

Background I'm currently looking into how reliable confidence intervals are on bounded scores (EQ-5D) and I compare regular asymptotic, robust and botstrap-based confidence intervals. The robust ...
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1answer
175 views

Statistical notation in plain English

I have a very limited understanding of statistics, and am having trouble translating an answer to this question from quant.SE, "Separating the wheat from the chaff", the answer being: Larry Harris ...
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77 views

Can we never have a normal distribution?

Since the population variance can never be estimated, will we always have a t-distribution instead of normal?
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Estimating parameters of Student's t-distribution

What are the maximum-likelihood estimators for the parameters of Student's t-distribution? Do they exist in closed form? A quick Google search didn't give me any results. Today I am interested in the ...
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90 views

Normality of a lognormal variable having a spike in 0?

I have two very right-skewed datasets which I must study for difference in means. Given the skewness, I transformed using log 10 scale after adding 1 to be able to take the log. In other words: ...
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198 views

Grouping similar subjects based on slopes

I have 500 subjects for which I am studying their response to temperature increase using a linear regression on each degree of temperature (from 10°C to 28°C). Thus, it was possible for me to compute ...
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73 views

What is the distribution of the ratio of two t-distributed random variables?

x is t-distributed; y is t-distributed. How is x/y distributed? Does it have a closed-form formula?
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316 views

Formula to calculate a t-distribution

I am writing an application that will be dealing with <30 observations in a normal distribution. My understanding is that this point I would need to use t-distribution. The thing is, this is easy ...
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165 views

Correct formula for standardized Student's t-distribution

I am wondering about the correct formula of the standardized Student's t distribution. In the rugarch package on page 15 it is given as: Substituting $\frac{(\nu-2)}{\nu}$ into 49 we obtain the ...
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T values of ARIMA parameter estimates

The SAS proc ARIMA documentation states that "The t values reported in the table of parameter estimates are approximations whose accuracy depends on the validity of the model, the nature of the model, ...
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41 views

Degrees of Freedom for Multivariate t distribution

I have a data.frame of retruns - ...
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219 views

Code for fitting multivariate t distribution (ECME)

I am looking to fit some data with central multivariate t distributions. I understand an ECME algorithm is the most promising way to do this. I wondered if anyone knew of any existing code for ...
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69 views

Entropy of noncentral multivariate t distribution

I am looking at calculating the entropy of a multivariate noncentral t-distribution. I found in the central case (mean is zero) the entropy is the same as multivariate normal with a correction for ...
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1answer
107 views

quantile transformation with t distribution

I'm wondering about the monotonic quantile transformation in case of a t distribution. First, for explanation, lets consider a normal distribution: \begin{align*} f(l | \mu , \sigma ...
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1answer
161 views

quantile threshold of t distribution and normal distribution

I want to calculate the quantiles of a t distribution and a normal distribution fitted to my data (can be found here: http://uploadeasy.net/upload/nk0f.rar). The t distribution is leptokurtic, ...
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156 views

The mgf and cf of Student's t distribution

A student's t distributed rv $X$ has characteristic function but no moment generating function. I wonder if cf(X)=$E[e^{itX}]$, why we cannot take $t=-iu$ to get the mgf $E[e^{uX}]$? (This question ...
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113 views

Testing for mutual exclusivity

So first, sorry if I use non-standard vocabulary, since I am not an expert. Please feel free to correct. I would like to know if a set of genes in a patient cohort are mutated by a mutually exclusive ...
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286 views

The ratio of the dependent normal rv and chi rv is?

(I hope this question may be too easy for some experts here). It is well-known that if $X$ is normal rv and $Y$ is a chi-square rv, then $Z=X/\sqrt{Y/n}$ follows student's $t$ distribution, where $n$ ...
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67 views

Test with Student's t

What kind of null hypothesis can be tested using a Student's t? It's very likely to be one of the questions of the statistics exam. In order to test a null hypothesis using the Student's t, does it ...
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1answer
607 views

Confidence intervals for mean, when variance is unknown

When calculating the confidence interval for the population mean and the variance is unknown, I take it that you have to use the t-distribution. However, do you use the one-tailed or two-tailed test ...
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1answer
272 views

t-distribution confidence intervals for non-Gaussian data but large n

I have a question concerning a claim I read in statistics books concerning the applicability of the t-distribution to compute confidence intervals for large $n$ if the data is not normally distributed ...
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With a small sample from a normal distribution, do you simulate using a t distribution?

I want to simulate temperature data for some "what-if" calculations. The problem is, I only have a time series of 10 actual temperature data values. I want to use temperature as an input to the ...
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Finding t distribution values for uniform and exponential functions

I know that a basic one-sample $t$ statistic can be calculated by $$t = \frac{x - \mu}{s / \sqrt{n}}$$ I also know that the following 4 functions $x\sim\mathcal{U}(0,1)$, $x\sim\mathcal{Exp}(2)$ ...
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1answer
173 views

How to estimate the probability that the mean of an unknown distribution is over a threshold given small sample size

I am trying to quantify my concerns regarding a proposed incinerator in our community. The company is basing its potential to emit dioxins (a class of chlorinated organic compounds with a reference ...
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When is the distribution of $(\overline{x}-\mu)/{\rm SE}(\overline{x})$ normal and when is it $t$?

When estimating the mean of a population, two distributions seem to be useful, the normal distribution and the t-distribution. Is it correct to say that $t=(\overline{x}-\mu)/{\rm SE}(\overline{x})$ ...
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63 views

“t-Chart” value

I wonder what is wrong with my own answer for the problem which I have shared below, could you please help me some about that: " Suppose that we have 12 observation units $ ( n=12 ) $ in a ...
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1answer
629 views

Is Hansen's skewed-$t$ distribution the same as the skewed-$t$ distribution which is a special case of GH Distribution?

I recently studied two asymmetric t distribution both with a name of skewed-$t$. I am confused with their differences or are they actually the same? The first one is introduced by Hansen (1994) with ...
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123 views

Is there standard nomenclature for Confidence Distributions?

I am wondering if there are standard naming conventions in general for confidence distributions or for the particular cases of the non-centrality parameters of (non-central) $t$- and ...
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1answer
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Calculating P-value for Spearman's rank correlation coefficient example on Wikipedia

The Wikipedia article Spearman's rank correlation coefficient contains an example for calculating ρ. At the end of the sections is the statement "...with a P-value = 0.6864058 (using the t ...
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t-test and t-distribution etymology

Okay, I'm aware of the fact that Gosset came up with t distribution, but what is the etymology of "t". How did "t" end up in t-test and t distribution?