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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Proof of how to calculate quantiles of a function with lognormal distribution

I'm struggling to find the proof of Eq. D.20 shown in the figure below, particularly the second part inside the exponential, i.e. $-0.5*Q^2$: The variable $b$ represents the “Least Squares” best-fit ...
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Quantile interpretation

If I have have the score for $q=0.9$, say $Y=y_{0.9}$. Does this mean that the probability of measuring a score $<y_{0.9}$ is 0.9? Edit: Basically I have one dependent variable, $y$ (a type of ...
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Possibilities for rolling two dice: one is six-sided and the other one is four-sided

I have seen a question from someone's old exam. Two dice, one has 6 sides and the other 4 sides. Question: a) What is the probability that the possible outcome(sum of two dice) would be at least 9? ...
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Bootstrap for probability of observing certain data

I am working with years data and I want to see how likely it is for something to have happened for the first time in, say, 1997 given other dates as well. Let me explain. I have something (a lab ...
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good quotation on the control part of statistical quality control?

I'm writing a paper making use of techniques from statistical quality control, and would like to include a quotation that expresses a sentiment something like this: Statistical quality control is not ...
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What information is required to aggregate percentiles

I have several thousand large datasets that are too big to fit into memory at once, so I need to keep them separate. It is easy enough to get the count, mean, std dev, min and max for the whole ...
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how to generate data from a distribution whose cdf is not in closed form? [duplicate]

I am working on a distribution whose pdf and cdf is $$f(x,\alpha,\beta)=\frac{(\frac{\beta}{\alpha})(\frac{x}{\alpha})^{\beta}}{(1+(\frac{x}{\alpha})^{\beta})^{2}}\frac{\sin(\frac{\pi}{\beta})}{(\frac{...
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Understanding the approach of considering the 95% quantile value as the 95% Confidence interval upper limit

I'm confused from the statistical approach described below. I'm not from this field but I had to use this approach in my study. Any explanation would be great!. According to my understanding the ...
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Name for generic quantile transform

Suppose I have two real-valued, continuous random variables, $A$ and $B$, with corresponding cumulative distribution functions $F_A, F_B$ with support $\text{supp}(A), \text{supp}(B)\subseteq \mathbb ...
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qqplot of inverse Gaussian distribution in r

I wanted to draw a qqline of my data with the inverse Gaussian distribution, however, the line printed does not seem to be right, for details see the picture attached. someone help me please thanks
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How to determine beta parameters in r given 2 percentiles without knowing the upper and lower bounds [duplicate]

I have a sample which I assume has a beta prior. Now I have to find the parameters of the beta distributions given two percentiles, the median and the 90th percentile. Both percentiles have values , ...
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I know the average (110) and a 75th percentile (120). Calculate the SD

I know the average (110) and a 75th percentile (120) of a normally distributed data set. I need to calculate the SD. I do not have access to the original data set. Can I calculate it in Excel?
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comparing differences between quartiles at two different conditions

I have calculated the difference between two independent groups in their quartiles and calculated the 95% confidence interval of that difference. These calculations have been performed twice (in the ...
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1answer
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Meaning of uniform percentile rank distribution?

I'm new to statistics and I've been following Think Stats 2. I've just gotten to Cumulative Distribution Functions. I have some questions regarding uniform distribution: What does it mean for the CDF ...
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1answer
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Quartiles of ungrouped data [duplicate]

For a set of 48 randomly generated points using runif(), I use the command quantile(x,0.25) to calculate the first quartile in R....
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How to robustly present a min and a max value?

I have a set of measurements from an air polution sensor. I want to determine the min and the max value in a period of time (let's say in a day). The min and the max don't have to be the true ...
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How does AWS Forecast make probabilistic forecasts at a given quantile?

I would like to know which method is used by AWS Forecast to generate lower bound and upper bound time series forecasts at a given quantile? More generally, what is the method employed to make ...
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Why does median() differ from quantile()[“50%”] in R and doesn't honor the type? Is this an estimator or sample quantile?

I just found, that when I want a specific type of quantile in R, say the number 3, it doesn't agree with median calculated in the "traditional way" in R. ...
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Descriptive measures

What is the percentage of people who earned between Rs 75 and Rs 125? If the given frequency table is below:
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Interpretation of a figure: mismatching confidence intervals and percentiles

I found a figure as follows, showing distributions of some scores at three time points: Considering the with of 25th-75th percentiles, how can 95% CIs be so narrow? Is this erroneous?
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Which of the 3 given exact methods of calculating the confidence interval for median is better (correct)?

I want to calculate CI for the median in R. I found a number of packages and functions doing that and noticed something interesting. I think the problem can be generalized to any statistical software. ...
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How is that possible, that in R, SAS or other packages there are so many ways to calculate quantiles? Isn't median just median?

As in the topic. I always thought, that we have a clear, well established definition of a quantile over a vector of numbers. For example - median is such observation, that splits the data set in so, ...
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Normalize skewed distribution

My data is right-skewed. Log-transform data only shifts it, not changing the distribution shape. Tried to use QuantileTransformer but output seems to be really messy. Any suggestions on how to ...
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Convert percentile change to Cohen's d

tl;dr: How do I convert from percentile change to Cohen's d for the whole distribution? A common measure of effect size is Cohen's d: the mean difference between an experiment and control group ...
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M estimator confidence intervals for quantiles

I try to understand the M estimator and make some quantiles estimation. I think I can see how we get the best theta (minimum point): I need to minimize the: $ \sum \rho_\tau(\epsilon_i) = \sum \tau \...
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Nonparametric Confidence Intervals from Sample Quantiles - Sample Estimate Outside Upper and Lower Confidence Limits

The Approach Say I have a 95% confidence interval $(l, u)$ for some true parameter of interest $\theta$ computed from the 2.5th percent and 97.5th percent quantiles of a given set of continuously-...
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Estimating user percentile using mean, min, max and previous percentile for multiple tests

I have a set of tests that a group of people take. The same people take all tests. I am given one person's score, along with the highest score, lowest score, and mean score and must estimate the ...
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Computing percentile rank best way to compare?

The following is a sample dataset, I'm only providing a snippet but there is more data than this. I need to know how compare each company is doing in terms of the different measures ( measure_1 and ...
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Quantile regression categorical data

I am planning to do an analysis on socio economic determinants of women health status. For health status, being my dependent variables, I have taken anemia as one of the variable. I want to do see ...
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If I have interval (binned) data from a D.G.P. with a truncated Pareto distribution, can I estimate the truncation point?

Suppose I have high-income data that I believe to be reasonably approximated by a Pareto distribution above some income level. I have mean and total income for several income ranges, including the &...
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Why is the Hyndman and Fan 1996 recommendation for sample quantile definition to standardize on not more accepted? [closed]

The 1996 paper Sample quantiles in statistical packages is often cited as the comprehensive source of sample quantile definitions and many a software package refers to the paper in the description of ...
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Small sample size fails to approach inverse CDF

When sample size $n$ gets large, we know that a sorted set of the $n$ samples approaches the inverse cumulative distribution function (CDF) sampled at $\frac{1}{n}, \frac{2}{n}, \dots, \frac{n}{n}$. ...
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Is $z_{0.025}$ equal to -1.96, or 1.96?

I'm unsure about the interpretation of $z_{\alpha}$. I've seen some source claim that $z_{\alpha}$ is equal to the z value with $\alpha$ of the area to the right of it. Under this view, $z_{0.025}$ is ...
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Characteristic Function and Quantile Function?

Characteristic functions (cf) are closely related to cdfs and pdfs of random variables, for example cf is the Fourier transform of the pdf Inversion formulae from Lévy and Gil-Pelaez Question: Is ...
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Is it possible to interchange the quantile operator and a measurable monotone function? $Q_\theta(f(X)) = f(Q_\theta(X))$

Let $Q_\theta(X)$ is the $\theta^{th}$ quantile of a random variable $X$, and if $f$ is a measurable strictly increasing function. I want to know if $Q_\theta(f(X)) = f(Q_\theta(X))$. I know that for ...
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Can the sum of these two quantiles be negative?

We already know that in a two sample t test, given alpha and beta, we can compute sample size: $$ N=\frac{4 \sigma^{2}\left(z_{1-\frac{\alpha}{2}}+z_{1-\beta}\right)^{2}}{\Delta^{2}} $$ Now if we want ...
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Model that takes two percentiles as input - what is the percentile of the output value

For some analysis I have two input variables with some (unknown) probabilities distributions. Of both the input variables I know the (assumed) 10th, 50th and 90th percentile. I have some simple model ...
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39 views

Should You Take the Average of Two Test Score Percentiles?

I have two different tests that measure the skill of participants in two different fields, leading to two different test scores for each participant. I want to combine both test scores to get an ...
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1answer
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finding median of multiple samples [duplicate]

I have the following problem: (1) I get a package with many samples with values (2) I have reasonable time to calculate whatever i want and keep in memory any info i want, but not all of the samples (...
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quantile regression parameter for desired confidence interval

I want to plot C% confidence intervals for a regressor (GradientBoosting in my case). I found this example on scikit-learn documentation https://scikit-learn.org/stable/auto_examples/ensemble/...
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Uncertainty and distribution of a percentile

In a Bayesian analysis (Normal case), it is possible to obtain a posterior distribution of the mean and variance. We can also obtain quantiles, median,... of these distributions. My question now is: ...
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Testing the statistical difference of two quantile parameters in a quantile regression

I have estimated a quantile regression at 15 different quantiles, I'd like to iterate a test to check that the most important quantiles are statistically different from each other. From "Roger ...
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1answer
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Can we sample from both pdf and cdf?

my question is quite generic. I am currently studying the algorithms calculating random numbers from distributions: In inverse transform method we get the cumulative distribution function in the end ...
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1answer
56 views

Median from two unmergable datasets

I am trying to calculate the "overall" median of a variable that is spread across two datasets. I have access to the raw data in each dataset but can't bring their raw data together. What ...
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1answer
58 views

The meaning of upper 100 alpha(th) percentile

Recently, I learned about the chi-square distribution. In my class, I was told about the upper $100\alpha^{th}$ percentile $\chi^{2}_{\alpha}(k)$ and given the following definition: $$P(X<\chi^{2}_{...
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Equality in distribution involving a uniform random variable and quantile function

I'm trying to show the following statement: "if $U$ is a random variable with uniform law over $[0,1]$, then $Q^2(U)$ has the same law as $X^2$". Here $Q(x)=\inf\{z\in\mathbb{R}:P(\lvert X\...
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Is minimizing Koenker-Bassett error the only optimization problem that gives sample quantile? [duplicate]

Sample quantile can be estimated by solving $\min_\theta \sum_{x \in X}f_\alpha(x-\theta)$ $f_\alpha = \alpha |x|$ when $x>0$, $f_\alpha = (1-\alpha) |x|$ when $x\leq0$. Sample expectile can be ...
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How to find the Percentile of this distribution?

Let say, we have 2 IIDs $X, Y \sim N \left( 0, 1 \right) + \eta $ Now $\eta$ has a discrete distribution with values 0(-10) with probabilities 0.991 & 0.009 respectively. Also assume that $Z = X+Y$...
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Max Likelihood Estimator of the quantile

Let $(X_1, \dots, X_n) \sim Exp(\theta)$ and so $$f(x; \theta) = \theta e^{-\theta x}$$ where $x>0$ and $\theta > 0$. I need to find the quantile $q_p$ as a function of $\theta$, the max-...
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How does one test the difference between two uniform distributions with only a median and confidence intervals?

If I have two uniform distributions characterized by a median and two percentiles, how should I go about hypothesis testing if they are different? For example, let's say I have the following ...

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