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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Finding outliers using interquartile range

I am trying to find outliers using interquartile range and is having a few problems. I have read this article to understand how to find outliers and understood most of it. Now I am trying to apply this method in a program. But it seems that the data…
Wai Wong
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When running a t-test with a Control and Experimental group, are both groups Samples? Or is the Control group a Population?

When running a t-test with a Control and Experimental group, are both groups Samples? Or is the Control group a Population? I am pretty confused on this, since I've pretty much only ever worked with Samples, but have no idea when to switch to a…
Atlecx
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Find the asymptotic distribution of δ

Let $X_1, \ldots, X_n$ i.i.d. from the $\mathrm{Bernoulli}(p)$ distribution. Then $X = X_1 +\ldots+X_n$ follows the $\mathrm{Binomial}(n,p)$ distribution. We wish to estimate $g(p)=p(1-p)$ whose UMVUE is $$\delta=\frac{X(n−X)}{n(n−1)} $$ Find the…
anonyx2
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Covariance Matrix in PCA

Principal component analysis (PCA) uses one scatter matrix (an estimation of covariance matrix) to find eigen vectors of the original matrix. Suppose we have two scatter $V_1, V_2$ matrices for our observations (assume classical scatter and fourth…
Avv
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Can we find an unbiased estimator for $\theta$ which reaches the Cramer Rao Lower Bound?

Let $f(x)=\theta x^{-(\theta+1)}$ for $x>1$, where $\theta>1$ is an unknown parameter. Can we find an unbiased estimator for $\theta$ in this case which reaches the Cramer Rao Lower Bound? My attempt: To find such an estimator, I think I first need…
dreamer
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How can it be derived? (Law of the unconscious statistician)

On pg. 7 of Financial Calculus: An Introduction to Derivative Pricing by Martin Baxter & Andrew Rennie, it states: My Understanding I did try to derive this picture. But I don't understand how this outcome that is $S_0\exp(\mu -0.5\sigma^2)$ is…
user13232877
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Reading through a paper on got confused on this part

Look at the following please :) Assuming an uninformative prior for $N$ then $$ \begin{aligned} \log p(N \mid y) &=\text { const }+\log \mathrm{p}(\mathbf{y} \mid N) \\ & \approx \text { const }-\frac{1}{2} \mathrm{BIC},\ \ \ \ \ \ \ \ \ \ \ \ \ \…
Einstein69420
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How can I evaluate average with negative values, given I will apply this weight for both negative and positive values

I am more a programming guy than math one, so please be easy on me with math expressions Before I start describing to make it clear: I have 2 types of scores: reddit score and sentiment score. Reddit score can be of any value. Sentiment score ranges…
twmp
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Is there any specific meaning of the formula 2*(max-min)/(max+min)?

I'm a student who studies machine learning. When I studied this paper(https://dl.acm.org/doi/pdf/10.1145/335191.335388), I saw the following formula and explanation. $$(direct_{max} - direct_{min})/direct_{mean} = (indirect_{max} -…
beef stew
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What is is it meant by "analytically derive the expected value of an estimator?" in statistics?

Good evening, everyone. I am new to statistics, so I wanted to see if I could get guidance with this problem: Consider a variable Y which follows a distribution with mean µ and variance σ2 in the population. Suppose we take a random sample of Y of…
Alpaca Paw
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How to evaluate cumulative distribution function w/ sigma of given SRS?

I have been given a set of 10 positive values that make up an SRS (Simple Random Sample) of a population, which has a normal distribution. I then am asked to evaluate $a = \sum_{i=1}^n\frac{(x_{i}-\mu)^2}{\sigma^2}$ and provide the distribution.…
TheFiveHundredYears
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What does the term "unbiased estimator" mean?

In my textbook for my statistics class, it says that $s^2$, sample variance is a "unbiased estimator" for population variance, $\sigma^2$. Does this mean that when we use $s^2$ as a point estimator for $\sigma^2$, it precisely equals $\sigma^2$? So…
user865043
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P-values and statistical significance

The mean for the result of a regional test is $525$ points with a deviation of $80$. A $90$ students class did the test and got a mean score of $535$. Is the mean score of the class different from the regional mean score for a statistical…
jon smar
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Variance of a single random variable with two terms.

A random variable X, representing the time until some event occurs, has the following pdf. $$(14/99)e^{-0.5x}+(85/99)e^{-0.25x}$$. Using integration, I get the expectation as 14.303 via $\int_0^\infty xf(x)dx$, and a variance of 463.453 via…
Stephen
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Calculating the Rolling Variance of a set of numbers

I would like to subscribe to a WebSocket stream which will supply me with many numbers per second. From this data, I would like to calculate the variance of say the last 1000 numbers. How can I do this in a rolling fashion? That is, I would like…
Ben Crossley
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