# All Questions

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### central limit theorem for Bernoulli distributions

Let $\xi_i$ be a Bernoulli random variable s.t. $\mathbb{P}(\xi_i = 1) = p$. Let $\hat{p} = \frac{1}{N} \sum \limits_{i = 1}^N \xi_i$. Given the random variable $\hat{p} = 55\%$ where $N = 1000$, ...
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### what is exactly code vector and quantization vector of self organizing map?

I have problem is the understanding of code vector in self organizing map. could anybody explain me intuitively what is it exactly ?
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### Poisson and Exponential Distribution- Is the following question correct?

Accidents occur with a Poisson distribution at an average of 4 per week. i.e. \lambda= 4 Calculate the probability of more than 5 accidents in any one week. What is the probability that at least two ...
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I have a question that might be trivial but I have not much knowledge on that method: I want to estimate a structural model with GMM and my model works in the sense that it estimated the right ...
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### Residual plot for simple linear regression

I'm trying to analyze a part of European Social Survey data. The outcome has to be treated as continuous, however it can take only discrete values from 1 to 6. The predictor variable is age. I fitted ...
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### Good PCA examples for teaching

I'm teaching linear algebra to a class of engineers, social scientists and computer programmers. We just did singular value decomposition, and we have an extra day, so I thought I'd talk about the ...
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### What's the best way to test the uniformity of location data?

I'd like a test to determine whether a number of collected spatial points (within, say, (0,1]) are distributed uniformly across the space. The points will be one or more 'paths' through the space. ...
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### How to do a for loop and if statement between data frames

I have two data frames. One of them contains 165 columns (species names) and almost 193.000 rows which in each cell is a number from 0 to 1 which is the percent possibility of the species to be ...
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### Why is one parameter estimate so high in logistic regression?

I am doing logistic regression on a model with a dependent variable of 4 different sizes of fish. I originally tried to do ordinal logistic but I ended up binning responses into "small" and "large" ...
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I want add to my regression additional features to complicate my model and lower bias, after searching around internet is seems a good idea is to add square features, that can help regression learn in ...
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### Test/score or measure for predicted versus actual long-run proportions/averages?

What I am doing is that I have categories A, B, C, D, E. I am computing predicted long-run proportions of falling into each category and computing actual long run proportions of falling into each ...
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### Zero inflate models vs generalized mixture model

Hi I am looking to compare the fit of a zero- inflated mixture model and a poisson mixture model, the random effects in both models are different. Comparing the fitted values of both models ignores ...
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### Sum of lagged coefficients (VAR)

I have come upon a paper where a VAR analysis is performed. Using 3 endogenous variables and some exogenous (control) variables, the results of the VAR analysis are shown in a table. For the ...
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### Generalization of Newton-Raphson method for maximization of log-likelihood?

Suppose $l(b; y)$ is the log-likelihood function we want to maximize, i.e. we want to solve $U = l' = 0$ for the ML estimation of $b$. Using Newton-Raphson method, we have \begin{align*} b^{(m)} = ...
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### Limiting Distribution of a Polya-Eggenberger Urn with Stopping Rule

I am trying to find literature on the limiting distribution of a Polya-Eggenberger Urn with a stopping rule contingent on the proportion of the two colors in the urn. To clarify, let's say that the ...
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### Distribution of sum of squares of T-distributed random variables

I am looking at the distribution of the sum of squares of T-distributed random variables, with tail exponent $\alpha$. Where X is the r.v., the Fourier transform for $X^2$, $\mathscr{F}(t)$ gives me a ...
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### Gaussian neighborhood function and non linear learning rate for SOM in R

I've been working on SOMs and how to get the best clustering results. One approach could be to try many runs and choose the clustering with the lowest within sum of squared errors. However, I do not ...
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### How to write answer in different rows in R? [migrated]

I have a code and the answer that gave me is in one row. I want that those answers whould be in different rows. ...
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### what is the role of central limit theorem in the meta-analysis of sample correlations?

The meta-analysis utilizes the estimates generated by different studies? Whether it has similar interpretation as in the case of primary data?
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### Mean residual life with censored observations and covariant eps

I have a time variable ( time of claim settlement after occurrence ) that may be censored ( claim still open at the moment of observation) and some additional covariates ( line of business, claim ...
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### Should I exclude predictor variables if used to create a new one?

I have a dataset that includes race, gender, income, and family size. In addition, a variable for "sliding fee scale" tier is included, which is determined by income and family size. Should income and ...
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### How to form a frequency distribution table from different survey results

I have a survey I have conducted on a certain market to determine whether or not we should consider reentering that market. After conducting the survey I was hoping to draw some conclusions from this ...
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### How can I estimate theta for the inverse hyperbolic sine transformation?

I would like help with R code to estimate theta for the Inverse Hyperbolic Sine Transformation. This transformation is useful to transform skewed data that contain negative values or zeros. There ...
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### At what point does LDA (Latent Dirichlet Allocation) not make sense to use?

I was wondering if anyone could provide some intuition about when the "documents" in LDA are too small for it to provide any benefit. For instance, I have seen papers where people have you used ...
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### How to train a HMM to recognize human gestures?

I got a dataset from Microsoft Research Cambridge online, the website is:http://research.microsoft.com/en-us/um/cambridge/projects/msrc12/. The dataset contains 6244 gestures in 12 types.Each gesture ...
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### Independence of numerator and denominator connected to independence of obs?

I was wondering whether the independence of the numerator and the denominator in the ANOVA F-statistic relates to the independence of observations and how?
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### Comparing two items with various parameters of different units

Not a big stats guy, but I dabble in programming and frequent stackoverflow and figured this would be a good place to turn. Here's what I'm looking for. I have a set of food items. Each has a number ...
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### Mathematical Explanations behind ANOVA

I was wondering: could someone could direct me to papers (preferably) or textbooks that give strong explanations of the mathematical background behind ANOVA?
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### Showing that E(E(Y|A))|B) = E(Y|A,B)?

Would $E( E(Y|A) | B) = E(Y|A,B)$? How does one show this? Intuitively, it make sense that conditioning on this one at a time would result in the same thing as conditioning all at once.
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### How to characterize/quantify the difference between two distributions?

Recent I met a question about how to characterize the difference between two distributions, except for their significance. Maybe the above-mentioned description is too vague to understand, and I ...
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### Response variable bounded by dependent variable

I have a problem: y~x1+x2+x3+x4 where the response variable y is always more than or equal to the explanatory variable x1 (for e.g. x1 represents the income of one person in a couple and y is the ...
The pi-lamda theorem states that if $Q$ is a pi-system contained in a lambda system $L$, then the sigma-algebra generated by $Q$ is also contained in $L$. We can use this to show that the CDF ...