# Questions tagged [t-distribution]

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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### When does the sum of two $t$-distributed random variables follow a $t$ distribution?

In the scope of a project, I need to find the sum of two independent $t$-distributions. I know that in the general case, the sum of two $t$-distributed random variables is not $t$-distributed. However,...
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### Deriving the CDF of student $t$-distribution

I am trying to derive the cumulative density function(cdf) of $t$-distribution, define as in https://en.wikipedia.org/wiki/Student%27s_t-distribution#Cumulative_distribution_function I derive it by ...
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### Understanding the relationship between a 'sampling distribution of a statistic' and a 'population distribution' in the context of a 'hypothesis test'

I would like to confirm that I am understanding the relationship between a sampling distribution of a statistic (an example of a 'statistic' would be a sample mean $\bar{x}$) and a population ...
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### T-Statistics vs. Z-Statistics [duplicate]

If Z-statistics, when population variance is unknown, is a close approssimation of the T-statistics, which is better suited for the case, why do we overcomplicate things by using Z if sample size is ...
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### How can I sample from a shifted and scaled Student-t distribution with a specified mean and sd in R?

I'm currently building some Bayesian models with the brms package and the default intercept prior is student_t(3, 0, 6.3) and so ...
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### How do I determine the distribution of an additional sample $x_{n+1}$ given sample mean, variance $\bar x, s^2$ of a normally distributed $x$?

Suppose I draw $n$ samples $x_1...x_n$ of a random variable $x$, which is normally distributed with an unknown mean $\mu$ and variance $\sigma^2$. From those samples, I compute a sample mean $\bar x$ ...
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### Frequentist Justification for using Student's t-Distribution to Construct Confidence Intervals

In my most recent statistics class, the general1 frequentist approach to constructing confidence intervals2 for an estimator (of any kind) was described as follows: Specify the estimator and the data ...
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### Why is in order to normalise t-distribution the following function is used $t = z*s$, shouldn't it be $t=z*\frac{\sigma}{s}$?

I am trying to answer the following question: Suppose there is a new genetically modified species of pine, with an expected fully grown height of 14 metres and a standard deviation of one metre. The ...
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### Why I get high observation when I generate data from t-distribution in R

I want to generate 200 samples from t-distribution with the degree of freedom=1 and sample size is 10 and in R I use this code ...
1 vote
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### How many degrees of freedom do the estimators of a panel regression have?

I have multiple observations for multiple people stored in a panel. Here's a sample of my data (where id is a unique person identifier and ...
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