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
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Variance of sample variance?

What is the variance of the sample variance? In other words I am looking for $\mathrm{Var}(S^2)$. I have started by expanding out $\mathrm{Var}(S^2)$ into $E(S^4) - [E(S^2)]^2$ I know that $[E(S^2)]^2$ is $\sigma$ to the power of 4. And that is as…
MathMan
  • 1,319
100
votes
11 answers

What's so special about standard deviation?

Equivalently, about variance? I realize it measures the spread of a distribution, but many other metrics could do the same (e.g., the average absolute deviation). What is its deeper significance? Does it have a particular geometric interpretation…
aris
  • 1,335
57
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4 answers

how does expectation maximization work?

I'm reading a tutorial on expectation maximization which gives an example of a coin flipping experiment (the description is at http://www.nature.com/nbt/journal/v26/n8/full/nbt1406.html?pagewanted=all). Could you please help me understand where the…
Martin08
  • 767
51
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2 answers

Difference between Poisson and Binomial distributions.

If both the Poisson and Binomial distribution are discrete, then why do we need two different distributions?
Bareerah Ansari
  • 543
45
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3 answers

Is there a mathematical reason why chocolate chip cookies have 37% (1/e) chocolate in them?

Someone once briefly explained to me why it is that chocolate chip cookies have 37% chocolate in them. To the best of my memory it has to do with the way trying to place dots in a circle in a random and scattered way behave, which turns out to be…
atntias
  • 550
36
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2 answers

maximum estimator method more known as MLE of a uniform distribution

Let $ X_1, ... X_n $ a sample of independent random variables with uniform distribution $(0,$$ \theta $$ ) $ Find a $ $$ \widehat\theta $$ $ estimator for theta using the maximun estimator method more known as MLE
Daniel
  • 3,053
32
votes
7 answers

"Normalize" values to sum 1 but keeping their weights

I am not really sure what this operation might be called, but I have some numbers, for example: 40 10 I need to format these numbers so that they form the sum 1, but they should keep their "weight". In this specific case: 40 would become 0.80 10…
tmighty
  • 393
31
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6 answers

Is there a simple test for uniform distributions?

I have a function that (more or less) is supposed to select a small number $m$ of random numbers from the range $[1,n]$ (for some $n \gg m$) and I need to test that it work. Is there an easy to implement test that will give good confidence that it…
BCS
  • 633
28
votes
4 answers

Unbiased Estimator for a Uniform Variable Support

Let $ x_i $ be iid observations in a sample from a uniform distribution over $ \left[ 0, \theta \right] $. Now I need to estimate $ \theta $ based on $N$ observations and I want the estimator to be unbiased. I thought about simple estimator $…
Royi
  • 8,711
28
votes
5 answers

What is degree of freedom in statistics?

In statistics, degree of freedom is widely used in regression analysis, ANOVA and so on. But, what is degree of freedom ? Wikipedia said that The number of degrees of freedom is the number of values in the final calculation of a statistic that…
Jill Clover
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28
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2 answers

How to calculate standard deviation with streaming inputs?

Is there a formula that is capable of operating on streaming inputs and approximating standard deviation of the set of numbers?
SamFisher83
  • 463
26
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3 answers

What is the equation used to calculate a linear trendline?

What are the equations to calculate a linear trendline over a set of points? EDIT: "In excel it is done automatically but how to manually calculate a linear trendline over a set of points" was originally the question. At first I asked this question…
TecHunter
  • 700
25
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4 answers

Proof of the independence of the sample mean and sample variance

I've been trying to establish that the sample mean and the sample variance are independent. One motivation is to try and write the sample variance, $S^{2}$ as a function of $\left\{ X_{2}-\bar{X},X_{3}-\bar{X},\cdots,X_{n}-\bar{X}\right\} =A$ only.…
Nana
  • 8,351
23
votes
3 answers

Distribution of $-\log X$ if $X$ is uniform.

For $X$ and $Y$ random variables; $X$ follows the uniform distribution. (1): if $Y=-\log X$ (2): then it can be shown that $-\log X$ is distributed as $\exp(1)$ {i.e. exponential with mean 1}. Why is this so? Intuitively statement (2) make sense to…
student101
  • 567
23
votes
12 answers

Statistics: Why doesn't the probability of an accurate medical test equal the probability of you having disease?

Suppose there is a test for Disease A that is correct 90% of the time. You had this test done, and it came out positive. I understand that the chance that this test is right is 90%, but I thought this would mean the chance that you have a disease…
Muhammad Umer
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