## Top new questions this week:

### Examples of distributions with easily solvable quantile functions but hard to solve CDFs

I'm interested in examples of probability distributions where the quantile function $F^{-1}(p)$ exists in closed form or is easy to calculate but where the cumulative distribution function (CDF) $F(x)$...

quantiles cumulative-distribution-function
 asked by spencergw Score of 8
 answered by kjetil b halvorsen Score of 9

I have a sample of data $(x_i, y_i)$. I hypothesize that $y_i$ is not dependent on $x_i$, but the standard deviation of $y_i$ depends on $x_i$ More concretely, say I assume $\textrm{Var}(y_i | x_i) = ... regression data-visualization standard-deviation heteroscedasticity  asked by Lost1 Score of 6  answered by Frans Rodenburg Score of 6 ### ANOVA with unreliable measure I’m doing some literature review on sports science, in particular the effect of training on endurance. There is no standard endurance tests. Some consist in intermittent contractions until exhaustion ... statistical-significance anova group-differences reliability intraclass-correlation  asked by Experience111 Score of 5  answered by Eoin Score of 4 ### Standard negative binomial regression when counts are mainly zeros? This question must have been asked many times before but I can't find an answer. I'm getting very confused about when to use a zero-inflated negative binomial regression vs standard negative binomial ... regression count-data negative-binomial-distribution zero-inflation structural-zero  asked by Picapica Score of 5  answered by Stephan Kolassa Score of 9 ### Interpreting complex roots of$R^2$This is a common way to define$R^2\$ in a regression problem. $$R^2=1-\left(\dfrac{ \overset{N}{\underset{i=1}{\sum}}\left( y_i-\hat y_i \right)^2 }{ \overset{N}{\underset{i=1}{\sum}}\left( y_i-\bar ... regression r-squared complex-numbers negative-r-squared  asked by Dave Score of 4 ### I have count data, but it does not follow a Poisson distribution, what to do? My data consists of 3 variables, one is a numerical variable of the number of flower visits that I have counted on certain locations and on certain shrub species. My other 2 variables are categorical ... chi-squared-test poisson-distribution  asked by Geertje Score of 4  answered by Nick Cox Score of 2 ### Welch t-test p-values are poorly calibrated for N=2 samples I am performing a large number of Welch's t-tests (t-test with unequal variance) on very small sample sizes, often with only two samples per condition. I am finding the p-values are poorly calibrated: ... t-test p-value calibration  asked by emarti Score of 4  answered by Sextus Empiricus Score of 3 ## Greatest hits from previous weeks: ### Famous statistical quotations What is your favorite statistical quote? This is community wiki, so please one quote per answer. references history  asked by robin girard Score of 282  answered by Rob Hyndman Score of 279 ### What are the differences between Factor Analysis and Principal Component Analysis? It seems that a number of the statistical packages that I use wrap these two concepts together. However, I'm wondering if there are different assumptions or data 'formalities' that must be true to use ... pca factor-analysis  asked by Brandon Bertelsen Score of 267  answered by Jeromy Anglim Score of 186 ### Difference between confidence intervals and prediction intervals For a prediction interval in linear regression you still use \hat{E}[Y|x] = \hat{\beta_0}+\hat{\beta}_{1}x to generate the interval. You also use this to generate a confidence interval of E[Y|x_0].... regression confidence-interval predictive-models prediction-interval faq  asked by question Score of 133  answered by Charlie Score of 137 ### Percentile vs quantile vs quartile What is the difference between the three terms below? percentile quantile quartile descriptive-statistics quantiles median percentage  asked by luciano Score of 171  answered by stochazesthai Score of 201 ### How to determine which variable goes on the X & Y axes in a scatterplot? I am trying to do a scatterplot to see the relationship between literacy and baby mortality. How do I know if literacy is my X axis and baby mortality is my Y axis, or the reverse? How do I ... data-visualization scatterplot  asked by Beth Score of 10  answered by Glen_b Score of 17 ### Why square the difference instead of taking the absolute value in standard deviation? In the definition of standard deviation, why do we have to square the difference from the mean to get the mean (E) and take the square root back at the end? Can't we just simply take the absolute ... standard-deviation definition absolute-value faq  asked by c4il Score of 562  answered by Tony Breyal Score of 257 ### What is the difference between fixed effect, random effect in mixed effect models? In simple terms, how would you explain (perhaps with simple examples) the difference between fixed effect, random effect in mixed effect models? mixed-model fixed-effects-model definition  asked by Andrew Score of 436  answered by John Salvatier Score of 234 ## Can you answer these questions? ### Diffusion Model consistency term derivation question The consistency term of the diffusion model is written as:$$\mathop{\mathbb{E_{q_\phi(x_{1:T}|x_0)}}} \left[\log\prod_{t=2}^T \frac{p(x_{t-1} | x_t)}{q_\phi(x_{t-1}|x_t, x_0)}\right]= \sum_{t=2}^...

conditional-expectation kullback-leibler generative-models
 asked by Shawn_this_is Score of 1
 answered by cinch Score of 0

### Why is the threshold term incorporated into the weight vector in linear classifiers?

In the context of linear classifiers, such as the perceptron or logistic regression, I understand that the decision boundary is defined by a linear combination of input features and weights, plus a ...

regression machine-learning neural-networks bias perceptron
 asked by Narges Ghanbari Score of 1

### Rescale measures of association for meta-analysis (e.g., log-transformed independent variables)

I am carrying out a meta-analysis of studies evaluating the association between blood levels of specific environmental pollutants and health outcomes (binary). Some studies reported OR/RR/HR for ...

logistic data-transformation meta-analysis logarithm
 asked by msas Score of 1
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