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
3
votes
1 answer

Kullback-Leibler divergence of two Laplace distributions with different parameters

Let the Kullback-Leibler (KL) divergence of two distributions $p(x)$ and $q(x)$ be defined as $D(P||Q) = E_p(\log p(x) - \log q(x))$ Let $p(x) \sim \text{Laplace}(\mu_1, b_1)$ and $q(x) \sim \text{Laplace}(\mu_2, b_2)$ then $ \begin{align} D(P||Q)…
Rainymood
  • 181
3
votes
1 answer

Kullback-Leibler divergence of two exponential distributions with different scale parameters

The question is as follows: "Calculate the Kullback-Leibler divergence between two exponential distributions with different scale parameters. When is it maximal?" I have tried something but I come to a wrong conclusion (at least comparing with…
Rainymood
  • 181
3
votes
1 answer

Finding the expected value of the MLE of the multiple linear model

For context, the linear model is $$\mathbf{y} = X\mathbf{\beta} + \mathbf{\varepsilon} $$ where $\mathbf{y}$ is the vector of responses $y_i,i=1,2,\ldots,n$, $X$ is the deterministic design matrix $n\times p$ and $\beta$ is the vector of parameters,…
Natash1
  • 1,379
3
votes
1 answer

Type I and II Errors

Good evening, I am a little confused about type I errors. If you are given a population of students doing hypothesis tests for a certain condition at a certain significance level, is it possible to calculate: (a) how many students will fail to…
ImRellyBadAtMath
  • 35
3
votes
0 answers

What is the distribution of the sum of absolute differences?

Suppose there is a $2\times2$ matrix $O$ of observed values: $$O = \begin{bmatrix}o_{11}&o_{12}\\o_{21}&o_{22}\end{bmatrix}$$ and two matrices $E_1$ and $E_2$ of expected values: $$E_1 =…
Tori
  • 31
  • 1
3
votes
0 answers

UMP test and MLR of a distribution

Let $Y_1, \ldots, Y_n$ be a random sample from a distribution with the density function $$f_θ(y) = \frac{3θ^3}{y^4} \text{ for } y ≥ θ > 0.$$ Is there a UMP test at level α for testing $H_0 : θ ≤ θ_0$ vs $H_1 : θ > θ_0$? I've begun this question by…
Brandon Barry
  • 187
3
votes
1 answer

Breakeven Point

To examine the effectiveness of its four annual advertising promotions, a mail order company has sent a questionnaire to each of its customers, asking how many of the previous year's promotions prompted orders that would not have otherwise been…
Gill Dave
  • 75
3
votes
1 answer

Expected number of throws when encountering a pokemon

I have a question about using geometric distribution to analyze a spefic issue of the Pokemon Go game. First let me describe the context. When a player throws a ball to catch a pokemon, the success rate is a fixed number p. If the pokemon is not…
Proxima668
  • 33
3
votes
1 answer

Why does the sum of the residuals not equal to 0 when there is no intercept of SLR

As we all know that the residuals sum to 0 when there is an intercept. But why the residuals do not sum to 0 when we don't have the intercept in simple linear regression?
Fracblood
  • 39
3
votes
2 answers

Independence of X̄ for IID random variables

My question is that: Is $\overline X$ independent of $X_1 - \overline X$, given that $X_1,\ldots,X_n$ are IID random variables? I was thinking that it is independent, but i don't know the logic behind it.
Chin Huat
  • 133
3
votes
1 answer

What sample size do I need to justify my suspicions?

I have been told that an event occurs about once in 50 times. In my experience, it is more like once in 40 or 45, which would not be insignificant (if correct). However because this event does not happen very often I cannot be sure. What sample…
Wartin
  • 133
3
votes
0 answers

How to calculate recurring probability

I have a very basic understanding of statistics and probability. I just passed an intro college course on it. The problem is, there's one type of problem that I'd like to know how to do, and I don't have another statistics class, and it wasn't…
Ryan Park
  • 31
3
votes
3 answers

Can Statistics be made Rigorous

I am taking a statistics class this term, and this is really my first taste of the subject. We were given the following definition: Let $f_n(A)$ be the relative frequency of some random event $A$ occurring over $n$ trials. Then if $A$ occurred…
Ltoll
  • 1,968
3
votes
1 answer

Pearson's Chi Square Formula

The Pearson's Chi Square standard notation is a summation of $(O_i-E_i)^2/E_i$. However, I cannot really get why it is divided by $E_i$. For example, if I want to measure the distance between $f(x)$ and $g(x)$, then I would simply do the following:…
Commissar Vasili Karlovic
  • 207
3
votes
1 answer

Selecting the best statistical analysis

I'm going to begin an experiment about drying leaves. I want to learn about how some special kind of leaves are going to dry themselves in 2 different situation. A group of them will stay in a high density, and the another group I will spread out in…
Alex
  • 33
1 2 3
…
99 100