Activity for mr Tsjolder‭

Type	On...	Excerpt	Status	Date
Edit	Post #289824	Initial revision	—	about 1 year ago
Answer	—	A: What is the probability density function for the tau distribution? I managed to find a reference to page 241 of the textbook "Mathematical method of Statistics" from H. Cramer, where the PDF of the tau distribution should be defined as $$p(\tau \mathbin{;} \nu) = \frac{\Gamma(\nu / 2)}{\Gamma\bigl((\nu - 1) / 2\bigr) \sqrt{\nu \pi}} \Big(1 - \frac{\tau^2}{\nu}\Bi... (more)	—	about 1 year ago
Comment	Post #289814	If it would be obvious what the PDF of $\tau_\nu$ is given the PDF of $\tau_\nu^2$. It is not obvious to me, but it might be for someone with a stronger mathematical background. (more)	—	about 1 year ago
Edit	Post #289814	Initial revision	—	about 1 year ago
Question	—	What is the probability density function for the tau distribution? The tau-distribution is typically defined in terms of the Student's t-distribution as follows: $$\tau\nu \sim \sqrt{\frac{\nu \, t{\nu - 1}^2}{\nu - 1 + t{\nu - 1}^2}}.$$ I would be interested to compute the mean and variance of this random variable. Because it seems daunting to directly compute... (more)	—	about 1 year ago
Edit	Post #289742	Post edited:	—	over 1 year ago
Edit	Post #289742	Initial revision	—	over 1 year ago
Question	—	Is it possible to show that a normalised random variable has zero mean and unit variance? Given some random variable $Xi$, is it possible to compute expectations of the normalised value, like: $$\mathbb{E}\biggl[\frac{Xi - \bar{x}}{s}\biggr],$$ where $\bar{x} = \frac{1}{N}\sum{j=1}^N Xj$ is the sample mean and $s^2 = \frac{1}{N - 1} \sum{j=1}^N (Xj - \bar{x})^2$ is the sample variance? ... (more)	—	over 1 year ago