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.

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Combination Calculations with Sub Groups

Given 16 Trials equally distributed to 4 individuals ( 4 Trials per person). How many combinations are there where these conditions are met: Condition A: 5 Total Successes Condition B: 2 or Fewer Successes per Individual. I understand Condition A in…
Wellwoah
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Which of the following two estimators is better?

Let $X=(X_{1},...,X_{n})$ and $Y=(Y_{1},...,Y_{n})$ be independent simple samples from the distributions of $\mathcal{N}(m_{x},\sigma ^2)$ and $\mathcal{N}(m_{y},\sigma ^2)$, respectively. Which of the following two estimators: $T_{1}(X,Y) =…
Gackt
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is $\hat{\theta}$ unbiased

consider a random sample of size n from a distribution with pdf $f(x;\theta)=\frac{1}{\theta}$ $0
WiseStrawberry
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Showing a simple property in statistics

I know this is very elementary but I cannot remember how to show $\hat\alpha$ as below.
Kane Blackburn
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Find the gradient of a multinomial distribution with $4$ observations $x = (x_1,x_2,x_3,x_4)$

my question actually revolves around applying the secant method (optimization) to find the maximum likelihood estimator for $\theta$ where $$ \begin{align} p_1 &= (2+\theta)/4,\\p_2 &= (1-\theta)/4,\\p_3 &= (1-\theta)/4,\\ p_4 &=…
Jdev
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Why is $\beta=$Probability that we accept the null hypothesis, $H_0$ where $\beta$ is the probability of a type II error in a statistical test?

Is it because it's the likelihood that we get a test statistic under the conditions we set of $H_0$ and $H_1$, the alternative hypothesis that causes us to accept the null hypothesis when it's false? What is the reasoning behind this? Thank You
user865043
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Does the 80-20 Rule apply to the Buffon process?

Whether the needle crosses a line depends greatly on the angle the needle makes with the line, 90 degrees being of course the most favorable for a line-crossing. Does the 80-20 Rule apply to these angles? That is, since 20% of 90 degrees is 18…
Mike Jones
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Does the Law of Factor Sparsity apply to factorization?

Does the 80-20 Rule (also known as the Law of Factor Sparsity, the Law of the Vital Few, and the Pareto Principle) apply to factorization? That is, if x is a large positive integer, then are about 20% of the primes not exceeding x sufficient for…
Mike Jones
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Finding Mode from Histogram

In our High School Mathematics, we often find mode of a grouped data from a histogram. I am not talking about that process here.My question is why the process works to find the mode using the graph?
Swapnil MZS
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Control Chart of Exponential distributed data

I have 20 data exponentially distributed. I want to draw an individual Control Chart of the data to see if the Process is In Control or Out of Control. How can I compute the Control Limits? Thank You F. Galetto
Fausto Galetto
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How the false positive value affects accuracy?

I have two binary images, one of them is an output produced by my algorithm and the other one is the ground truth. For this two images I calculated the values true positive, false negative, true negative and false positive. I want to interpret this…
Alex544
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Is it even possible to compare two smples with the data I have?

I'm pretty new to statistics. and recently I learned how to check if the samples are equal. I want to learn how to find out which of the samples is greater. I have some friends in college, that are good at statistics, and they said that's impossible…
Ruslan Tolstsikau
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Statistics Question

This is probably super simple to most of you on here, but I was chatted by a friend earlier with a question. It reads just like this: A sample of n =7 scores has a mean of M =5. After one new score is added to the sample, the new mean is found to…
AndyWarren
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Find UMVU estimators for an exponential distribution

Let $X_1, \ldots,X_n$ be iid from an exponential distribution with density $$ f(x)=\begin{cases}\theta e^{-\theta x},&x>0, \\ 0,&\text{otherwise}.\end{cases}$$ Find UMVU estimators for $\theta$ and $\theta^2$. $$f(\textbf x\mid\theta)=\displaystyle…
Vons
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Proof of exponential family quality

The exponential family of probability density functions take the form $f(y,\theta, \phi) = \exp \bigg\{ \frac{y\theta - b(\theta)}{a(\phi)} + c(y, \phi) \bigg\}$. I know that $$ E(\frac{\partial \text{log-likelihood of }f}{\partial \theta}) =…
PiccolMan
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