# Questions tagged [quantiles]

The quantiles of a distribution refer to points on its cumulative distribution function. Some common quantiles are quartiles and percentiles.

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### Confidence interval determination for skewed bootstrap parameter distribution

I have been reading around the literature and have been trying to work out the correct way (or most accurate way) to calculate a 68.3% confidence interval using bootstrapping for my particular data ...
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### Removing outliers renders a new distribution that has its own outliers

I'm trying to remove all the outliers from a data set. However, after removing them, data points that weren't outliers before are now outliers due to the new distribution. What is the correct ...
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### Best method of quantifying probability of new datum belonging to either of two distanced normal distributions?

I have two samples A and B from two separate normally distributed populations. The population mean of B is higher than that of A, but both are unknown. My aim is to find a threshold value between the ...
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### Creating a Probability Plot of a Custom Distribution

Let's say we have some icdf function, which I will paste below: ...
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### Difference between quantiles

As far as I understood from its definition, quantile borders should divide a dataset into equal parts (or at least into almost equal parts, if the dataset doesn't have enough entries or has an odd ...
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### R's survey package interpolation handling for median estimates

This is a question concerning Lumley's survey package for R. Specifically, its handling of interpolation for median estimation, after several hours of looking into ...
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### Pinball loss as a synonym for quantile loss: misleading?

I have the impression that the term pinball loss refers to the same as quantile loss (a.k.a. tick function); e.g. see the thread "How to calculate pinball loss for quantiles and for point forecasts?". ...
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### Value-at-Risk formula with GARCH-model

I'm totally aware of that if we look at some loss process $L_t$, then $\text{VaR}(\alpha)$ is a quantile of the loss distribution. If we assume that $L_t=-X_t$ is the negative returns and they follow ...
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### Estimating tail deviation from Q-Q plots

I am running experiments and for certain cases am able to find a suitable distribution for the data. However, in most cases, depending on a certain parameter, the observed vs fitted distributions have ...
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### The quantile of prob=0.05 and mean

What is the meaning of the difference between the quantile of prob=0.05 and mean for a sample form a specific distribution? In other words, I would like to understand the relationship between ...
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### Calculating probability with multiple conditions

I am trying to understand something. Let's say we have 2000 samples and two different conitions. If we use condition #1, we get a result but if we use condition #2, we get different result. Is there a ...
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### representing quantile like quartile in form of normal distribution curve

I learned in statistics the first quartile, 2nd quartile, and 3rd quartile can be represented in the figure1 below I came across this part of the article Step 4 - Feature Engineering.In this portion ...
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### Can the t-test be used to test the difference between percentiles of 2 samples? [duplicate]

For example, instead of testing the difference in mean, I want to test the difference in the 75th percentile of the 2 groups. Does the central limit theorem hold? and what would be the equation for ...
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### Percentiles boundaries [duplicate]

When a distribution is cut into percentiles, is there any rule whether it should be included the lower or the upper bound inside the percentile? Example: 1,2,3,4,5,6,7 The median is obviously 4. If ...
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### How to find the upper outlier threshold in a right skewed distribution?

Say we have a right skewed distribution (tail on the right side) like income. Above what value can I consider data points to be outliers? One way could be Q3 (75th percentile) + 1.5 * Interquartile ...
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### Rejection Sampling when the proposal is a mixture of two distributions

Given a density $f(x; \alpha, 1) = x^{\alpha-1}\exp(-x)/\Gamma(\alpha)$ and a proposal density $q(x) = \alpha_1.q_1(x) + \alpha_2.q_2(x)$ I want to generate random samples using Rejection Sampling ...
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### Calculating the 50th percentile in a small data set

I'm trying to learn the concept of percentile. Question: Given these numbers: {1, 2, 3, 900}, I'm trying to calculate the 50th percentile. My answer: 3. But different websites are saying: 2.5 My ...
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### XGBoost question on weighted quantile sketch described in paper

The right-hand-side of Equation (3) in the XGBoost paper is $$\sum_{i=1}^n [g_i f_t(\mathbf{x}_i)+\frac{1}{2}h_if_t^2(\mathbf{x}_i)]+\Omega(f_t) \tag{3}$$ In the Section 3.3 "Weighted Quantile ...
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### Estimating user percentile given avg, min, max for multiple tests

I have data that given me both a user's score for a test, along with the high, average, and low across the class for every test. How would I estimate the user's percentile with this data? We know ...