# 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.

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### Real Application for Takagi-Sugeno?

my question is short: Can anyone give a concrete example where a Takagi Sugeno controller is used and what the rules would look like for this example? I'm not quite sure where a Takagi-Sugeno rule was ...
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### Determine the probability that any person is against government decisions

In one study, out of $80$ respondents, $23$ were against going to a concert. Determine if a person is against decisions to go to the concert if the confidence interval is 95%. Help me please. Thanks ...
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### What prior should I choose for a hypoexponential likelihood (sampling distribution) if I want an analytic posterior?

The hypoexponential distribution is the distribution resulting from multiple exponential distributions with different rate parameters. When they are all the same, it is an Erlang distribution. For ...
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### What is the best option of a graduate multivariate statistics book?

Right now I am in the middle of a graduate multivariate statistics but I am feeling to easy at the moment. As a mathematician I study univariate statistics from "The theory of statistical inference : ...
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### Why does the number of possible probability distributions have the cardinality of the continuum?

Wikipedia's article on parametric statistical models (https://en.wikipedia.org/wiki/Parametric_model) mentions that you could parameterize all probability distributions with a one-dimensional real ...
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### Fisher Information using Variance score [closed]

The answer to a question to find fisher information I don't understand how to get the variance of score. The distribution here is binomial.
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### NP Lemma and rejection region having the size.

quick question. I need to find the rejection region of H_0, meaning that I need to find the constant value for which if X=x belongs to the region H_0 is rejected. The pdf is c(1-x)^(c-1) with x ...
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### A baksetball probability question using Neyman–Pearson lemma

It is known that the probability of a basketball player to make his first shot is $p=0.6$ A player argues that it does not matter if he made the previous shot or not his odds stays the same. We say if ...
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### When and why do formulae involving sums over $x_i$ change to formulae involving $X$ in statistics? Specifically when dealing with likelihoods.

I've been reading up on stats recently and a question I'm working through involves calculating the log-likelihood of a distribution w.r.t a parameter $\beta$. From my understanding, for some ...
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### Why are you less likely to roll at least 1/6 of the dice as 6 when the number of dice increases?

So, I recently watched a V-Sauce video discussing a collaboration between Sir Isaac Newton and Samuel Pepys on a probability problem regarding the probability of rolling at least one six on six six-...
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### Parameter estimation truncated Laplace distribution

Hello to the community, I have a problem with the parameter estimation from a model. Let's guess we have a sample $X = (X_1,...,X_n)$, $\forall i=1,...,n$ $X_i$ follows a truncated Laplace ...
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### A research department is investigating the duration of a tire.The department wants to show it exceeds a certain value. Formulate the hypothesis

The research department of a tire manufacturer is investigating the duration of a tire using a new rubber component. 16 tires were produced and the duration was tested. The average duration and ...
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### Is it possible to combine two statistics which may be dependent on each other without access to the underlying data?

I'm trying to find the average salaries for college graduates of specific universities with specific majors. The issue I'm running into is that there isn't good data available for this issue. However, ...
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### Can we use both “Inferential Statistics” and “Statistical Inference” terms in an academic paper, interchangebly?

I've came upon these two definitions: Inferential statistics are techniques that allow us to use these samples to make generalizations about the populations from which the samples were drawn. ...
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### How to estimate the “innate speed” of a leaping frog?

The motion of a leaping frog is set by a "hidden parameter" $V_\infty$ that we want to estimate: it is the "innate average velocity" of such a frog. The frog jumps a distance $J_i \in \mathbb{R}^+$ at ...
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### Are these samples enough for a retention analysis? (T-Test)

I think that this is a dumb question but I would like to know if these differences in these KPIs are reliable or I have to change the sample in order to have statistically significant conclusions. ...
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### Example 7.2.19 from Casella & Berger (EM algorithm)

$X_1, ..., X_n \sim Poi(\tau_i), Y_1, ..., Y_n \sim Poi(\beta\tau_i).$ X and Y are mutually independent. However, $X_1$ is missing. I would like to use the EM algorithm to estimate $\beta$ and $\tau_i$...
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### Prove that $n \cdot\min\{T_1,…,T_n\}$ isn't allowable as an estimator of $\mu$

Let's suppose we have some electronic device which duration follows an Exponential distribution of unknown mean $\mu$. Some research team wants to estimate $\mu$ and uses a sample of $n$ devices to do ...
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### Which of this two estimators of $\mu$ is better (Exponential distribution)?

The problem goes like this: "Suppose we have some electronic device which duration follows an Exponential distribution of an unknown mean $\mu$. We want to estimate $\mu$ and two teams will take care ...
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### Fisher Information. Density function.

I'm reading about Fisher's information. However, a question arises. What is the difference between the density function $$f(x,\theta)$$ and the same density function when composing with the random ...
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### difference between bias vs variance

I am confused about variance and bias of function.How one can tell if function is overfitting or underfitting?how can you write formulas that express that?In machine learning if approximator has ...
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### How does the posterior density g(μ|x) change if we find out x could only be observed if it were greater than 0.

Given prior density g(μ) and observation X ∼ Poi(μ) , you compute g(μ|x), the posterior density of μ given x. Later you are told that x could only be observed if it were greater than 0. Does this ...
From ergodic theorem we can see that: $\frac{1}{N} \sum_{i}f(x_{i}) \to {E}[f(x)]$ as $n \to \infty$ Does this imply that in ergodic process we can similarly write: \$\frac{1}{N} \sum_{i}E[f(x_{i}...