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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10 views

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
45 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
52 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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0answers
18 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
104 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
123 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 $\mathbf{\beta}$ ...
0
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1answer
56 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
274 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
95 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 ...
2
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0answers
26 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
631 views

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 ...
3
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1answer
122 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 ...
2
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1answer
98 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 ...
2
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1answer
87 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
303 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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0answers
13 views

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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0answers
16 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 ...
7
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1answer
131 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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0answers
31 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, ...
3
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1answer
121 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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0answers
27 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 ...
2
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1answer
47 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
28 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
50 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 ...
3
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1answer
110 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 ...
2
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1answer
185 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
149 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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0answers
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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0answers
49 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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1answer
45 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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0answers
155 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 ...
0
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1answer
346 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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0answers
39 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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0answers
53 views

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 ...
7
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2answers
242 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
89 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 ...
2
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0answers
323 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 ...
2
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0answers
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 ...
3
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0answers
72 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?
3
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1answer
60 views

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
176 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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3answers
1k 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 ...
4
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1answer
147 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
246 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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1answer
85 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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2answers
2k views

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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3answers
123 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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1answer
86 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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2answers
382 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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1answer
186 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 ...