Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [statistical-inference]

The area of statistics that focuses on taking information from samples of a population, in order to derive information on the entire population.

Statistical inference makes propositions about a population using data sampled from the population. To test a hypothesis about a population, a typical workflow is to select a statistical model of the process that generates the data and then deduce propositions from the model.

Statistical propositions include—

  • a point estimate, which is a particular value that best approximates some parameter of interest,

  • an interval estimate, for example, a confidence interval (or set estimate), which is an interval constructed using a data set drawn from a population so that, under repeated sampling of such data sets, such intervals would contain the true parameter value with the probability at the stated confidence level,

  • a credible interval, which is a set of values containing, for example, 95% of posterior belief,

  • rejection of a hypothesis, or

  • clustering or classification of data points into groups.

3930 questions
0
votes
0 answers

What is the critical region for this Poisson test?

Could someone help start part c of this question, is the Neyman-Person Lemma useful in c and d? *In order to satisfy quality control, the mean number of flaws in aluminum sheets must be less than or equal to 0.6 flaws per meter length. A length of…
Waitara Mburu
  • 1
0
votes
1 answer

How to arrive to the following expression for a set of r.v with min max

Let $X_1, \ldots, X_n$ be independent and $\mathrm{U}(0,1)$-distributed random variables, and let $M_1=\min \left(X_1, \ldots, X_n\right)$ and $M_2=\max \left(X_1, \ldots, X_n\right)$. It can be shown that $f_{M_1, M_2}\left(m_1,…
user654301
0
votes
0 answers

Confidence interval for prediction

If we have the following linear model for the response $y_i$, how does one compute a confidance intervall for the expected value of $y_i$?
user21312
  • 19
0
votes
0 answers

Can (1 - p-value) be the weight of a graph's edges?

I understand that the p-value can be translated as the strength of the statistical tests' results. From this perspective, can (1 - p-value) be the weight of an undirected graph's edges (like an adjacency matrix or weight matrix)? Example ex. We have…
Candentia
  • 1
  • 1
0
votes
0 answers

How does the [UK] Office of National Statistics make allowances for incomplete census information?

I entered into a rather ill-tempered argument with a stranger yesterday. It started going downhill when he asserted that there were in fact 90 million people in the United Kingdom, not the 60 that I quoted from my memory of the last time I looked at…
Korky
  • 1
0
votes
1 answer

When to adjust for multiple hypthesis?

I am potentially doing multiple pairwise comparisons in this question and the cited answer warns me to adjust for multiple comparisons using for example Bonferroni. However, I am not sure what p-values to adjust by how much. Szenario: I have a sack…
Sim
  • 208
0
votes
0 answers

difference between Mann-Whitney U-test and Wilcoxon Signed ranks test

What is the difference between the Mann-Whitney U-test and Wilcoxon Signed ranks test? I know that these two methods are testing whether there is a difference of two samples, but in which situation can I use Mann-Whitney and when Wilcoxon can be…
alex.wang
  • 1
0
votes
2 answers

Computing a confidence interval in Bernoulli trials

A dice is thrown 9000 times and a throw of 3 or 4 is observed 3240 times.Show that the dice cannot be regarded as a unbiased one and find the limits between which the probability of a throw of 3 or 4 lies? To show the dice is not unbiased, suppose…
clarkson
  • 1,907
0
votes
0 answers

Show that T is a sufficient statistic (not iid sample)

I am a bit confused with this exercise, since I never worked with samples of this type. I would appreciate if you can help me. The exercise is as follows: Let {Xi} ~ N(iθ, 1) for i = 1, .... , n be an independent, but not identically distributed…
John
  • 21
0
votes
1 answer

Expected Value of Maximum Likelihood Estimator for $\operatorname{Beta}(\theta,1)$

I am having some difficulty finding the expected value of the MLE for the $\operatorname{Beta}(\theta,1)$ distribution. Until now, I have found that the MLE for $\theta$ is: $$\hat{\theta} = -\frac{n}{\sum_{i=1}^n \ln X_i}$$ And I know that the…
Jackaba
  • 83
0
votes
0 answers

Hypothesis testing,difference between variances

It is suspected that the variance of the distribution of distances in kilometers that a model new car equipped with a diesel engine runs on 5 liters of fuel is less than the variance of the distance distribution covered by the same model equipped…
Carla Sandoval
  • 1
0
votes
0 answers

Unbiased MLE for the Uniform Density (θ,θ+1)

From http://math.stackexchange.com/a/1605995/321264 I have understood that any θ within the range defined by first and last order statistics can be MLE. Of these, how can we choose the one which is unbiased?
SrikRaja
  • 1
0
votes
1 answer

If $X_i \sim POI(\lambda)$ I need to know what is the sample mean and sample variance of $\overline{X}$

Consider a random sample from a Poisson distribution If $X_i \sim POI(\lambda)$ I need to know what is the sample mean and sample variance of $\overline{X}$ Ok I know that if $X_1, X_2, .. , X_n$ is a random sample of f(x) with $E(X)= \mu$ and…
wessi
  • 195
0
votes
1 answer

Determine whether each of the sequences has a limiting distribution, if so, then give the limiting distribution.

Consider a random sample of size $n$ from a distribution with CDF $F(x) = 1 − x^{−2}$ if $x > 1$, and zero otherwise. Determine whether each of the following sequences has a limiting distribution, if so, then give the limiting distribution. (a)…
Curious
  • 541
0
votes
1 answer

How to find a mean, mode, and variance of a distribution problem?

I'm really not good in math, please bear with me. I searched and found some questions which are similar to this question. However, I cannot understand them. I get doubt in this question for a day. It's quite easy but I don't know. If I have 3…
lvarayut
  • 111
1 2 3
…
8 9