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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Quantile regression with a pre-existing cutoff point in the raw score of dependent variable
This is probably a dumb question, but I have never used quantile regression so I'm unsure.
I have the following situation: there is a continuous, numerical self-report measure with a certain, pre-...
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Transform sample data from different populations to increase sample size
I have n = 6 for each of six different normal distributions with different means and possibly same (or similar) stdev. So the distributions have similar shape with different position of center. I ...
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How can I order or sort many distributions, then summarize the "quantiles" of this ordered list?
What are the best practices for sorting a large number of distributions? What are some of the pros and cons of different ways to do this?
Let's say I am working with Likert responses to a survey ...
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What is the formula for the value of a given percentile in a normal distribution [duplicate]
I'm trying to figure out the formula to give back the value at percentile $p$ given that the values are normally distributed with mean $\mu$ and stddev $\sigma$.
If i recall correctly, the value is ...
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Integral of Normal and Poisson Process
I'm trying to find the percentile function of a random variable
$$Y=e^{-at+b_1\sqrt{t}Z+N_t(\mu+\sigma^2Z)}+\int_0^te^{a\cdot s+b\cdot \sqrt{t-s}Z+(N_t-N_s-1)\cdot[c+g\cdot Z]}ds, $$
where $a, b_1, \...
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AB-test percentiles difference
I have two groups in AB-test, where I am measuring start of program running.
Since I have both A and B large observation samples, I put data randomly into N buckets. Inside each bucket I calculate ...
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Influence function of quantile functional - I think the standard formula has a mistake
Let $F$ be a cumulative distribution function. Assume a nice situation where $F$ is (absolutely) continuous, strictly increasing, with probability density function $f$. Let $T(F)=F^{-1}(p) = \inf \{ x:...
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Quantile regression to compare two populations at different time points
I am trying to compare two different populations (e.g., 2001 and 2011) on the same variable. These are different, independent populations (this is NOT a longitudinal study; rather, two cross-sectional ...
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When trying to find the quartiles for discrete data, do we round to the nearest whole number?
I have 2 cases:
First, I want to find the first quartile to the set data: 1,2,3,4,5.
Normally we calculate the qaurtile as:
Now $Q_1 = \frac{2+1}{2} = 1.5$.
But they never state if its continuous (i.e....
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How to determine the percentile with a certain confidence? [duplicate]
The so called characteristic strength of a material should be the lower 5 % percentile of the population, according to the Eurocode when verifying the load bearing capacity of construction works. The ...
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How can you calculate Q1 and Q3 for even numbers? [duplicate]
I've searched this question everywhere, but I've found different answers and none of them result in the same answer Numpy gave me.
I have the following data:[0, 1, 2, 3, 4, 4, 5, 5, 6, 8]
When using ...
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Confusion in calculation of percentile of a "toy" data [duplicate]
Question
Calculate the 25th percentile of the following data:
1,2,3,4,5,6,7,8,9,10.
My approach
The required answer is such that 25 percent of the data should be below it, and 25 percent of 10 is 2.5. ...
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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) $F(x)$...
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Combining information from different quantiles
I have a number of "mostly" Gaussian distributions (in truth a Gauss core and longer tails). I am interested in the width of this distributions.
Given that I do not know the amount of tails ...
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Assessing whether a dataset follows a distribution using Q-Q Plot
I recently found myself answering a question on Stack Overflow about adjusting a dataset to a unknown distribution.
Adding my two cents to the community, I have provided a script to draw a Q-Q Plot in ...
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Calculating the mean and error for correlated measurements involving different estimators and quantiles
My goal is to find a way to report a mean $\pm$ error for different estimators and quantiles of the same distribution (same measurement).
I am measuring the width of a distribution (Gaussian core and ...
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Question about CDFs
Suppose that I have two arbitrary random variables $Y,X$ with strictly increasing CDF. Let $\omega(X)$ be a known function of $X$ that is known in advance and $\mu$ be a scalar parameter. Assume that ...
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Evaluating estimator of expected value plus variation
I know that for a typical, the estimator can be evaluated based on the mean squared error (MSE) of the predictions. How can I evaluate an estimator that instead gives a value that is the prediction ...
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Calculate mu and sigma of a log normal distribution from p50 and p99 in javascript
I'd like to generate realistic sample data in javascript for monetary donations. I've chosen to model them as following the log normal distribution.
I think a fairly intuitive way for a lay person to ...
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How can I reconstruct a normal distribution from a set of percentiles?
I have the 3rd, 10th, 50th, 90th, and 97th percentile values of a normally distributed variable, and I wish to generate a dataset that will allow me to query for other percentile values (say, the 67th....
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What is the formula for the conditional inverse function for the Ali-Mikhail-Haq and the Farlie-Gumbel-Morgenstern Copulas?
I am trying to do a Monte Carlo simulation and want to define a function for the conditional inverse function for the the Ali-Mikhail-Haq and the Farlie-Gumbel-Morgenstern Copula. Here is an example ...
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Numpy implementation of the Quantile function [duplicate]
I am trying to wrap my head around the implementation of the quantile function for finite samples and, specifically, in numpy (main reason to do this: I am working ...
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Why divide data into 4 parts for IQR, and not into parts of 20 or 10 percentages each?
Why divide data into 4 parts for IQR, versus into more parts, such as 20 or 10 percent per part?
I know that interquartile range by definition means 25%, but that is not my question.
I think that ...
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How to resolve the residual versus predicted quantile devation (Dharma plot)?
I have been trying to perform beta regression modeling with random effects. I have sex ratio (0.561, 0.765 etc) as the
response variable, and climatic variables + years (1970-2021) as predictor ...
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Percentiles of a distribution of weighted summary statistics
Suppose I have a collection of different independent probability distributions, $\{ P_i(X)\}_{i=1}^N$, each with their own support $I_i$. I know that the $10^{th}$ percentile of a given distribution ...
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How can I calculate the standard deviation when knowing the P10, P25, P75, P90, mean and median? [duplicate]
I'm trying to find the standard deviation from some simulated task duration results. The results provided the following:
Mean - 430
Median - 374
P10 - 371.8
P25 - 372.4
P75 - 440.5
P90 - 588.6
From my ...
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Median of a set with even number of elements
Consider the following sample of numbers:
9,18,11,14,15,17,10,69,11,13
Since there are 10 elements, the median of the set would be (13+14)/2 = 13.5
However, is it wrong to say that median is one of 13 ...
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Distribution of $F_n^{-1}(3/4)-F_n^{-1}(1/4)$ [closed]
Given $X_1,X_2,...X_n\overset{\text{iid}}{\sim}F$, find the distribution of the sample inter quartile range, $F_n^{-1}(3/4)-F_n^{-1}(1/4)$ in terms of $F$ where, $F_n$ is the emperical distribution ...
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Bootstrapping moderately extreme quantile regression
Let $(Y_1, X_1), \dots, (Y_n, X_n)$ be iid sequence drawn from $F$. For a fixed $q\in (0,1)$, consider the linear q-quantile regression $Q_Y(q|x) = \beta_qx$, where $Q_Y(\cdot\mid x)$ is the ...
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Calculating VaR from copula-GARCH using rmgarch
I'm new to both R and copula, nevertheless I want to compare VaR estimations for 25 days ahead using a GARCH and a copula-GARCH model in R.
To calculate VaR for the GARCH model seems pretty straight ...
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Why does creation of a Q–Q plot in Excel need an adjustment by 0.5?
I am aware that different statistical packages provide Q–Q plots using code or via a black box. For example, minitab with R integration for Q–Q plot from here.
I am trying to do this manually via ...
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Determining percentile of a salary within a survey of salaries
I am not a statistics expert, so forgive me if this question is too simplistic.
I have the following salary survey for a position:
Someone internally is making:
What is the easiest way to calculate ...
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What is the quantile function of a Skellam distribution?
Reading Is there a formula for the 95% confidence interval for the Skellam distribution or difference of two Poisson r.v.'s?, I realized that I would rather have the quantile function. Unfortunately ...
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How to calculate quantiles for a gamma distribution?
I would like to compute quantiles for a gamma distribution. I found a purported example here given as
$$\text{quantile}(a, b, p) = \frac{\gamma^{-1}(a, \Gamma(a) p )}{b}$$
where $\gamma^{-1}$ is the ...
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Are sample quantiles consistent with population quantiles?
The Wikipedia page about quantiles describes two approaches to the definition of quantiles: population quantiles, and sample quantiles. The section on sample quantiles lists nine different flavors of ...
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Seaborn Boxplot's quartiles
I'm trying to understand how to properly interpret seaborn-generated boxplots.
Consider the following code:
...
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Can the 90th percentiles of two sub populations both be lower than the overall?
Consider two populations, $A$ and $B$. $A + B = C$. Meaning $A$ and $B$ are mutually exclusive and collectively exhaustive of $C$.
Given the above if I calculate the 90th percentile of some metric for ...
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Real-world example of quantile loss used for evaluation
We can use quantile loss (a.ka. tick or pinball loss) for training a model or for evaluating predictions. (It is helpful to distinguish the two clearly, e.g. as done here.) I am interested in the ...
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Statistical significance of percentile (quantile) difference
I want to test for statistical significance of the difference between two independent samples of normally distributed measurement.
However instead of comparing means or overall distributions I want ...
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How do quantile time series forecasts work?
My office leadership is interested adopting “quantile time series forecasting”, the idea is query the model to predict the 5th, 25th, 50th, 75th and 95th percentiles of an RV given features such as ...
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Is there a way to estimate or calculate the expected P99 of a sum of distributions?
Suppose I have an event X whose latency I cannot measure directly, but X consists of a bunch of sub-events X_0, X_1, X_2, ..., X_n whose latency I can measure individually only in isolation.
...
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Versatility and validity of aggregate algorithm for a multiple criteria decision problem (averaging)
I'm trying to aggregate different variables in multiple scales and distributions. The distributions are not known beforehand, but I want to generate a general statistical value that represents all the ...
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Compare 90th percentiles of two samples (confidence interval, test)
I have a dataset of ambulance response times before and after a quality improvement change. I'm looking to see if there is a difference in response times before and after the change. Specifically, I'm ...
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Formal testing for differences in kurtosis between two samples when bootstrapping suggests a difference
My question is similar to Testing difference in kurtosis between two samples where a comment suggested
Unless you are looking for an enormous difference in kurtosis, it's
unlikely any physically ...
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Can I estimate the mean of a dataset if I have its standard deviation and a portion of the full data that is higher than some threshold?
I have a partial set of measurement data that is limited due to my tool's sensitivity. I know that the data is approximately normally distributed and I have a standard deviation from another data set ...
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Z score comparison in longitudinal studies
I have a longitudinal study with two time points (before/after), whereas a particular score was standardized across all individuals and time points, and thus provided only in terms of z-scores.
(Edit: ...
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Is my intuition behind the weight matrix correct for quantile regression?
Motivating Question
I was asked by a colleague today why one would run a quantile regression on quantiles that are "extreme" (such as $.10$, $.90$, etc.), if there are too few observations ...
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Algorithm to determine sufficient range for numerical integration of PDF to get quantiles
Given a probability density function (PDF), we want to use numerical integration to find a quantile at $\alpha \in (0,1)$. Are there standard algorithms for determining a sufficient and optimal range ...
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Quartiles as interaction term in regression analysis
Hello to everyone in this community. I am feeling like fish out of water writing in this community, but I know that I am at the right place.
Currently, I am conducting a research to assess the impact ...
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