# Tagged Questions

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### 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: whereas from a book (Carol Alexander Market Risk Analysis, ...
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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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### Variance of the Student's-t distiribution [closed]

Suppose I use the following form of the generalized Student's-t distribution: \begin{align*} f(l|\nu ,\mu ,\beta) = \frac{\Gamma (\frac{\nu+1}{2})}{\Gamma (\frac{\nu}{2}) \sqrt{\pi \nu} \beta} ...
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### 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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### 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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### 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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### 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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### Student's t vs Mann-Whitney U

Trying to choose between these two tests for data I've harvested from Android store. Basically, I want to see if there is any difference in the number of dangerous permissions requested by free vs ...
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### Comparing many means in JMP

I'm trying to compare several sets of experiment data, by comparing means. I read there are several different tests such as Each Pair, Student’s t and All Pairs, Tukey HSD, which give different ...
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### 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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### Student T CDF - How to read the hypergeometric function formula?

I am trying to program out a couple of statistical formulas with python. I am not concerned with efficiency or the fact that there already are tools to calculate the values, but I am doing it to ...
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### Appropriateness of K-S test and Kruskal-Wallis for assessing medical data set

I am analyzing some stats for a paper I am writing. I have statistics help available through my faculty but am not there for a couple of months so hoping you can help out. n = 463, 2 patient groups( ...
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### Confusing regarding when to use $z$-statistics vs. $t$-statistics

I was referring to this video lecture for calculating the confidence interval. However, I have some confusion. This guy is using $z$-statistics for the calculation. However, I think it should have ...
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### Asymptotic relative efficiency of median vs mean for Student t distribution

I am looking for a theoretical expression for the ARE of mean and median for student-t distribution against sample size (degree of freedom), exactly the blue curve shown in John Cook's blog. Can ...
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### Significance of difference in means

In “A Comparative Study of Nursing Home Residents …”, Aigner et al. write (p. 20) Acute visits were significantly higher for the nurse practiticoner/physician team at 3.0 visits per year (± 2.4) ...
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### Tracking down the assumptions made by SciPy's ttest_ind() function

I'm trying to write my own Python code to compute t-statistics and p-values for one and two tailed independent t tests. I can use the normal approximation, but for the moment I am trying to just use ...
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### Two questions on significance testing

Suppose you have a population and some measurement which you could do on each member of the population (e.g. the population could be all the people in the world, and the measurement could be height). ...
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### Why does a paired t-test (when appropiate) result in better variance?

I didn't quite get the wikipedia explanation here: http://en.wikipedia.org/wiki/Paired_difference_test#Use_in_reducing_variance I agree that both the unpaired and paired means are the same...then I ...
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### What is the distribution of the difference of two-t-distributions

... and why ? Assuming $X_1$,$X_2$ are independent random-variables with mean $\mu_1,\mu_2$ and variance $\sigma^2_1,\sigma^2_2$ respectively. My basic statistics book tells me that the distribution ...
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### Formula or procedure for computing standard statistical tables such as z table, Student's t-table, or chi-square table

How can the following tables be computed: Chi-Square table Student t-table I'm looking for a formula or procedure used to make these tables. For example: If I have a given 'x'-value, as ...
Let $t_i$ be drawn i.i.d from a Student t distribution with $n$ degrees of freedom, for moderately sized $n$ (say less than 100). Define $$T = \sum_{1\le i \le k} t_i^2$$ Is $T$ distributed nearly as ...