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
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What mathematics will help me predict sales curves?

I'm a programmer and have a client who annually releases new products which have "long tail" type of sales curves, very heavy when initially released, tapering out until discontinued years later. He wants me to write some software that uses the…
Chuck
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I am running a series of experiments that I expect to have similar outcomes. What is the best method to measure statistical significance?

Following on from this comment on an answer to my previous question, I'd like to know two things: what the best statistical test I can use to measure significance on the experiments I'm running? (previously it was stated that I could potentially…
Josh
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Beta Distribution Sufficient Statistic

So I have this homework problem that I am struggling a little bit with coming to a solid answer on. The problem goes like this: Suppose X~Beta($\theta,\theta), (\theta>0)$, and let $\{X_1, X_2 , \ldots , X_n \}$ be a sample. Show that…
Perdue
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MLE of double exponential

I am given the double exponential distribution under the form $$f(x_i\mid\theta) = \frac{1}{2}e^{-\frac{1}{2}|x_i - \theta|}$$ and I need to find the MLE of $\theta$. I have two approaches until now. The first being \begin{align} L(\theta \mid…
Pavel Slavchev
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I have trouble solving the following statistics exercise:

A company produces lightbulbs with an average lifetime of 1000 hours and standard deviation of 50 hours. Find the probability that in a sample of 100 bulbs there are at least two which stop working before 900 hours of lifetime. When I was…
Elijah
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Non-unique Bayes rules admissibility

I have a question about non-unique Bayes rule. Are they in general inadmissible or admissible and why? Thanks in advance!
Roos Jansen
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t-distribution and Degrees of freedom

Why t- distribution have n-1 degrees of freedom? I know that it is used when population variance is not known but what determines n-1
Milan Amrut Joshi
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Show that $Y = 2\sqrt{X_1 X_2}$ has a $\Gamma(2p, 1)$ dist.

$X_1$ and $X_2$ are independent with $\Gamma(p, 1)$ and $\Gamma(p + 1, 1/2)$. Show that $Y = 2\sqrt{X_1 X_2}$ has a $\Gamma(2p, 1)$ dist.
Benzamin
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A/B test for statistical significance

I'm running an a/b test on an advertisement and I'd like to test for statistical significance. How would I design a test and prove whether or not conversions/clicks are statistically different from test A and test B? Test A: 1000 clicks, 900…
Tony
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The test statistic in the likelihood ratio test for nested linear models

Imagine that we have a family of probability disributions with p.d.f $f_{\theta}(z)$ where $\theta \in \Theta$. We also know that there is a linear dependence between parameters. As a consequence we can restrict to a nested model with p.d.f…
John Snow
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Monte-Carlo simulation

Let $X:=X_1,..,X_n$ iid $\sim P$-distributed where $P$ is a known distribution and $T_n(X_1,..,X_n)$ is a test-statistic with unknown distribution $P(T_n(X)\leq t)$. Furthermore I am interested in the probability $P(T_n\geq t_0)$ for some fixed…
Klaus
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Understanding degrees of freedom in statistics

I was reading some statistics book that said - "Usually, it is expensive to perform an analysis on an entire population; hence, most statistical methods are about drawing conclusions about a population by analyzing a sample." and went on to give…
Pratheek Ponnuru
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MLE of $\frac{1}{\theta}$ Uniform distribution.

Let $X_1,X_2...X_n$ be a random sample from $U(\theta-5,\theta+5)$ where $\theta \in(0,\infty) $ is unknown. Let $T=\max(X_1,X_2...,X_n)$ and $U=\min(X_1,X_2...,X_n)$. Then which of the following statements is TRUE? $(A) \dfrac{2}{T+U}$ is M LE of…
Daman
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degrees of freedom for a chi squared goodness-of-fit test

For a statistics project, I gave out a 20 question multiple choice quiz with each question containing five answers. I would like to run some hypothesis tests on the data by using a Chi squared goodness of fit test. However, I can not decide how many…
vandale
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Existence of UMP test of poisson distribution

Let $X_1, \dots, X_n \sim \mathrm{Poi}(\lambda)$. I know that (a) There exists a UMP test of $H_0: \lambda = 0.5 $ vs. $H_1: \lambda = 1.5$ (b) There exists a UMP test of $H_0: \lambda \leq 1$ vs. $H_1: \lambda > 1$. How can I show that the UMP…
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