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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Why does the normalized z-score introduce a square root? (And some more confusion)

I am having a little trouble getting answers from the articles I have been reading. Referring to the "Standardizing in mathematical statistics" section here. Why does the substitution of $x$ with $\bar{x}$ result in a square root multiplier. Where…
user132716
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The law of the unconscious statistician

In Casella and Berger's Statistical Inference (2nd edition) it says at the start of section 2.2 (page 55) when defining expectations that If $ \mathrm{E} \,|g(X)| = \infty $ we say that $ \mathrm{E} \,g(X) $ does not exists. (Ross 1988 refers to…
Jori
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Why is the Kullback-Leibler divergence not symmetric?

As known the Kullback-Leibler Divergence: $$\operatorname{KL}=\sum_{i=1}^n \ln(\frac{P(i)}{Q(i)})P(i)$$ is not symmetric. I would like to know how this can be seen from the formula. I am aware that I could just try it out with exchaning Q and P for…
MiauPiau
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Why John Tukey set 1.5 IQR to detect outliers instead of 1 or 2?

To define outliers, why we cannot use: Lower Limit: Q1-1xIQR Upper Limit: Q3+1xIQR OR Lower Limit: Q1-2xIQR Upper Limit: Q3+2xIQR
Fan
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What is continuity correction in statistics

Can someone please explain to me the idea behind continuity correction and when is it necessary to add or subtract $\dfrac{1}{2}$ from the desired number (how do we tell whether we need to add or subtract), how do we tell when we need to use…
notamathwiz
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18
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2 answers

What's the difference between Rao-Blackwell Theorem and Lehmann-Scheffé Theorem?

I know that the Rao-Blackwell theorem states that an unbiased estimator given a sufficient statistic will yield the best unbiased estimator. Is the only difference between Lehmann-Scheffé and Rao-Blackwell that in Lehmann-Scheffé, you need an…
lord12
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What is the Difference between Frequency and Density in a Histogram?

I know count is simply the amount of times the observations occur in a single bin width, but what is density?
George Harrison
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Statistics: Could someone show why this exponential pdf integrates into this particular cdf

I have the following exponential distribution: $$f(\lambda, x) = \begin{cases} \lambda e^{-\lambda x} &\text{if } x \geq 0 \\ 0 & \text{if } x<0. \end{cases}$$ I need to show that this expression integrates into $$F(\lambda, x) = \begin{cases}…
Low Scores
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Statistics : Where did this degree of freedom formula for the T distribution come from?

I am on the hypothesis testing for two populations unit. I need some intuitive explanation as to why this formula is used. My statistics professor put this up on the board but he didn't explain why its true. For a T distribution, the formula for…
Low Scores
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Intuition about the Central Limit Theorem

I'm studying statistics, and would like to better understand the Central Limit Theorem. The proof I found on Wikipedia requires some previous knowledge I do not currently possess. Is there a quick intuitive explanation you can give as to why this…
chaoticdawn
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Can the maximum likelihood estimator be unbiased and fail to achieve Cramer-Rao lower bound?

If some maximum likelihood estimator (MLE) turns out to be unbiased (which does not necessarily holds), then does it achieve the Cramer-Rao lower bound (CRLB) even in finite sample? (It does when the parameter to estimate is the mean of some normal,…
atohs
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How to calculate relative error when true value is zero?

How do I calculate relative error when the true value is zero? Say I have $x_{true} = 0$ and $x_{test}$. If I define relative error as: $\text{relative error} = \frac{x_{true}-x_{test}}{x_{true}}$ Then the relative error is always undefined. If…
okj
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Fisher Information of a function of a parameter

Suppose that $X$ is a random variable for which the p.d.f. or the p.f. is $f(x|\theta)$, where the value of the parameter $\theta$ is unknown but must lie in an open interval $\Omega$. Let $I_0(\theta)$ denote the Fisher information in $X.$ …
Kashif
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Finding the maximum likelihood estimator

Find the MLE of the unknown parameter $\theta$ when $X_1,X_2,...,X_n$ is a sample from the distribution whose density function is: $$f_X(x) = \frac12e^{-|x-\theta|}, -\infty
woaini
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Given a 95% confidence interval why are we using 1.96 and not 1.64?

I'm studying for my test and am reviewing the solution to some example problems. The problem is: You are told that a new standardized test is given to 100 randomly selected third grade students in New Jersey. The sample average score is $\overline…
Ayoshna
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