Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [statistics]

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory and other branches of mathematics such as linear algebra and analysis.

Statistics is the science of the collection, organization, and interpretation of data. It deals with many aspects of data, which includes the planning of data collection in terms of the design of surveys and experiments. (From Wikipedia)

More specifically, mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and mathematical analysis. (From Wikipedia)

For questions which are more generally about collecting and treating data, it is advised that you post your question on Cross Validated and DSSE.

37109 questions
5
votes
1 answer

Derive the bias and MSE of the estimator $\hat{\beta}$

Let $Y_1, Y_2, \ldots, Y_n$ denote a random sample of size $n$ from a population whose density is given by $$ f(y)= \begin{cases} 3\beta^3 y^{-4} & \beta \leq y \\ 0 & \text{elsewhere} \end{cases} $$ where $\beta > 0$ is unknown.…
user3370201
  • 447
5
votes
2 answers

A question about a proof of Neyman's factorization theorem

This question comes from the proof of Neyman's factorization theorem in Robert V. Hogg, Joseph W. McKean, Allen T. Craig, "Introduction to Mathematical Statistics", 6th edition, pp 376-377. In the proof, a one-to-one transformation is used which is…
Zhou Heng
  • 553
5
votes
4 answers

A question on confidence

So, I've been reviewing some of my old stats courses in preparation for an interview I have in a couple of days. I'm a bit stuck on a particular question and hope you could help. A drug trial gives the result that the drug works better than the…
Youler
  • 71
5
votes
1 answer

Which math class can I take to learn how to derive statistical models

I have taken several stats classes and. Have seen many models in action like the normal, poisson, dirchet, etc. and seen several inference tests in action like chisq, ttest and anova. However I'm interested in the theory behind such distributions,…
user60462
  • 833
5
votes
1 answer

In what situations should I use and not use a pooled estimator for $\hat{p}$

In a question, it says that a true-false exam is used to discriminate between well-prepared students and poorly prepared students. There are $\frac{205}{250}$ well-prepared students and $\frac{137}{250}$ poorly prepared students who answered a…
xenon
  • 3,438
5
votes
1 answer

UMVUE of $ \frac{1}{\theta}$ coming from $f(x) = \theta x^{\theta - 1}$.

Let $X_1, \ldots, X_n$ be i.i.d. sampled from the distribution $$ f(x; \theta) = \theta x^{\theta - 1}, $$ where $x \in (0, 1)$ and $\theta > 0$. Show that $$ T(x_{1}, \ldots, x_{n}) = - \frac{1}{n} \sum_{i = 1}^n \ln(x_i) $$ is a Unique Minimum…
kalybu
  • 51
5
votes
3 answers

Statistics: Where did this function for normal distribution come from?

I am studying normal distribution for the first time and I'm having trouble understanding where this formula came from: $$\phi(x) = \frac{1}{\sqrt{2\pi}}\, e^{- \frac{\scriptscriptstyle 1}{\scriptscriptstyle 2} x^2}$$ Could someone derive this…
Low Scores
  • 4,565
4
votes
1 answer

How are critical values derived for the Kolmogorov-Smirnov Test?

One appealing feature of the K-S test is that it is distribution-free. So this leads to my question - how are the critical values for the K-S derived, then? Is there a way to express the critical values as an integral, like for percentiles of the…
Clarinetist
  • 19,519
4
votes
2 answers

Should I use odds ratio or risk ratio?

I am doing a retrospective cohort study with sample size 600 and disease prevalence rate greater than 10%. I am leaning more towards using risk ratio because it is easier to interpret and because disease prevalence is over 10%. Do you have any…
Jay
  • 41
4
votes
1 answer

What is a bounded discrete random variable

I'm reading a definition in DeGroot's book that begins with the statement: "Let X be a bounded discrete random variable whose p.f. is f." Then he goes on to define the expectation of X. However, I cannot find a definition of what is meant by a…
David
  • 2,262
4
votes
2 answers

Control limit and population mean

A cola-dispensing machine is set to dispense $9.00$ ounces of cola per cup, with a standard deviation of $1.00$ ounces. The manufacturer of the machine would like to set the control limit in such a way that, for samples of $36$, $5$ percent of the…
user123733
4
votes
1 answer

What to do with the boundary values of a bin in a histogram?

Suppose I want to make a simple frequency histogram of the following data: $$\{3, 3, 4, 5, 5, 6, 7, 7, 8, 10, 11\}$$ I'm supposed to use bins of size $5$, starting with zero. Here's my question: Is there a standard way to handle the boundary values…
Dan
  • 65
4
votes
2 answers

Expected value given that distribution is positive vs. conditional expectation

Referring to Expected value of normal distribution given that distribution is positive Where is the difference between $E(X$1$_A)$, where $A=[X>0]$, and $E(X∣A)$? Both seem to express the expected value of $X$ given that $X>0$ which is equal to the…
user138776
  • 41
4
votes
1 answer

Show a statistic is not sufficient

Let $T$ be a sufficient statistic. Suppose $f(T)$ is not a one-to-one function of $T$. Show $f(T)$ is not a sufficient statistic.   I think this should be proved by contradiction. Since $f$ is not one-to-one, $\exists t_1 \ne t_2 \ni g(t_1)=g(t_2)$.…
user14108
4
votes
1 answer

Transition from parametric to nonparametric statistics: what is $\Theta$?

During my first statistics course I learned that a statistical model is a collection of probability measures $\mathcal{P}$, where we can index each measure by a 'parameter' $\theta$ such that $\mathcal{P} = \{P_\theta\,\,|\,\,\theta\in\Theta\}$. My…
Marc
  • 6,861
1 2 3
…
99 100