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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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What is the difference between a zero-inflated and a zero-truncated poisson?

I'm trying to make sense of a question which uses a zero-inflated poisson model given by: $$ f(x; \lambda,\omega) = \begin{cases} \omega + (1-\omega)e^{-\lambda} &\mbox{if } x = 0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1)…
Lewy
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Testing significance of patterns of results

I'm a high school English teacher conducting an independent study, and I'm a total novice to statistical analysis, so please forgive me if I mischaracterize anything. I have gathered pretest and posttest data about student motivation from three…
Blake J
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statistic $t$-test for $2$ means

I'm just doing the exercises from Stock&Watson "Introduction to econometrics". $3.12$ is about comparing men and women salaries mean for men: $8200,$ SD $= 450, n_1=120$ mean for women: $7900,$ SD $=520, n_2=150$ I took $t=…
Emilia
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Tetrahedral dice throw

If we threw $30$ tetrahedral dice and summed the outcomes, how many values in the distribution would have a non-zero probability? a) If we calculate the distribution of the sum of two thrown tetrahedral dice, how many values have a non-zero…
mimi
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Bessel's Correction

I'm trying to understand the intuition behind Bessel's correction where $\sum (x_i - \overline{x})^2 / (n-1)$. My difficulty is stemming from the fact that the sample mean leads to a standard deviation that, when comparing it to hypothetical…
noodles
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PDF of product of uniform variables

I have encountered a problem in computing the PDF of a variable (call it $y_n$) that is the product of n uniformly distributed random variables $x$: $y_n=\prod_i^n x_i.$ In https://math.stackexchange.com/a/2812234 there is the solution for the case…
Alessio
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How can I safely make statistical inferences on abnormal data?

I have a data set in which the key data point is lap times in seconds around a small set of known tracks in a small set of known vehicles. (Karts around an indoor kart track.) The data comprises about two months of business and growing; about 4000…
JakeRobb
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A family of distributions induced by a metric

I'm interested in the family of distribution which can be expressed in the following form $f(x|\mu)=C \exp(-d(x,\mu))$ where $\mu$ is a parameter of the distribution and $d(*,*)$ is a metric. Normal distribution and Laplace distribution satisfy…
armando
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Statistics: Central Limit Theorem question

A commuter encounters four traffic lights each day on her way to work. Let $X$ represent the number of these that are red lights. The probability mass function of $X$ is as follows: \begin{array}{c|ccccc}x&0&1&2&3&4\\\hline\operatorname…
CurlyFry
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Actual meaning of Confidence Interval

I am a little confusing about the right understanding of confidence interval. $100$ random samples are taken to estimates the mean $\mu$. A $95$% confidence interval on the mean is $0.49 \leq \mu \leq 0.82$. Consider the following statement:…
Quang Dũng Đinh
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Biased coin hypothesis

Let's assume, we threw a coin $110$ times and in $85$ tosses it was head. What is the probability that the coin is biased towards head? We can use chi squared test to test, whether the coin is biased, but using this test we only find out, that the…
tach
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What are the constants in the relationship between point density and median point distance?

Given $\rho$ particles uniformly distributed on a plane within a unit square ($\rho > 1$), each particle has another particle that is closest to it; the median of those nearest distances is called $\tilde{d}$. Here's a graph where each point…
personak
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Density Question - Statistics

A point is picked randomly in space. Its three coordinates $X$, $Y$, and $Z$ are independent standard normal variables. Let $R = \sqrt{X^2+Y^2+Z^2}$ be the distance from the point from the origin. Find: a) The density of $R^2$ (don't get how to set…
mary
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If $T_1,T_2$ are two unbiased estimators, prove that $\rho(T_1,T_2) \geq \frac{2-\alpha}{\alpha}$.

Consider the following statement: Let $T_1,T_2$ be two unbiased estimators with common variance $\alpha \sigma^2$, where $\sigma^2$ is the variance of the UMVUE. Show that that $\rho(T_1,T_2) \geq \frac{2-\alpha}{\alpha}$, where $\rho$ is the…
Bergson
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Proving consistency for an estimator.

Let $Y_1,Y_2,...,Y_n$ be a random sample of size $n$ from a normal pdf having $\mu=0$. Show that $S_{n}^{2} = \frac{1}{n} \sum_{i=1}^n {Y_{i}^{2}}$ is a consistent estimator for $\sigma^2= Var(Y)$.
user67866
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