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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Simulating a joint distribution with the inverse method

I have the following joint distribution: $$f(x, y) = 3x^2y^xe^{-x^3}(1 + x),\quad x \gt 0,\ y \in (0,1).$$ I want to simulate a sample of this distribution through the inverse method but I don't know ...
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Generate given percentile (or data) from n, mean, median, standard deviation, p1, p25, p50, p75, p99?

I apologize if this should be asked elsewhere. I have the following information: Where N=1808 I am trying to calculate a given percentile (in this case p99.723), or ideally, if possible, generate ...
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How to interpret a point in the qq plot? [duplicate]

I am trying to understand the Q–Q plot. Suppose I create a sample according a exponential distribution ...
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Quantile Variance and Mean

As I read articles related to quantile measurements of moments, I only found quantile skewness and kurtosis definitions. However, I couldn't find any quantile estimation of variance or mean. Is it ...
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Lower confidence interval for quantile function [duplicate]

I have a real-valued, unknown distribution $\mu$ and would like to find the largest threshold $t \in \mathbb{R}$ such that $\Pr_{X \sim \mu}\left[X \leq t\right] \leq q$ with high probability $1-\...
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Which is the correct solution to the hypothesis testing: $H_0 : \lambda =65, H_1 : \lambda >65$ , $X$ is a Poisson ($\lambda$) ,$\alpha=0.05$

Given the following hypothesis test: $H_0 : \lambda =65, H_1 : \lambda >65$ , where $\lambda$ is the parameter of an $X$ distributed as a Poisson $\alpha=0.05$ . We have n=10 samples. Using as ...
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n-th quantile for bivariate variable

I generate a 2000 bivariate random samples which are negative correlated. I used np.quantile to generate 10 quantile from this random samples. The related point is marked in the following figure. I am ...
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Computing Gini coefficient for a 2 parameters density function

I have a random variable $X$ defined by the following the density function, \begin{equation} f_{\theta_1, \theta_2}(x) = \begin{cases} \frac{\theta_1 \theta_2^{\theta_1}}{x^{\theta_1 + 1}}, &...
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Which type of quantiles are safest to report in R?

With this topic in mind: If there is no censoring, can be the naive 3rd quantile different from the one calculated with from the Kaplan-Meier? I'm wondering which one is the safest option. Of course I ...
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Is it possible to find the 99th percentile using other percentiles?

I have the 10th, 20th, 25th, 30th, 40th, 50th (I assume this is the same as the mean), 60th, 70th, 75th, 80th and 90th percentile values of a data set. This is for the distribution of salaries in the ...
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Grouping using percentiles

I did visual binning process in spss and made three cutpoints like in this image: I did check off included I want to know the percentage range or value for each group. If I describe it in this way is ...
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Is percentile a good method?

Hello I'm an undergraduate student doing research about prevalence of carpal tunnel syndrome among college students I want to follow the method of this research (prevalence of carpal tunnel syndrome ...
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How to compare equality of the distribution at different quantiles

I have a dataset from which I am taking a set of descriptive statistics as follows: The value measured is productivity of a firm for each of the group at different quantile (I use Stata command: table ...
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Non parametric Monte Carlo estimation in R

Let's say that we have a dataset of a single vector : ...
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Bootstrap BCa Quantiles of the quantile function

Let's say I have a vector $x$ on $n=250,$ (in R) x = rnorm(250) The quantile of $\alpha=0.01$ is : ...
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conditional quantile and conditional expectation

I was reading some papers and I found some parts are tricky to understand. Assume I have price data , what does it mean to calculate the conditional mean of the price data given yesterday price ? ...
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Estimator for quantile of kernel of mixture distribution

I have a mixture distribution such as $$ X_t = \sum_{i} w^i_t X^i_t , \quad \text{with } w^i_t \in \{0, 1\}$$ and $\sum_{i} w^i_t = 1$. where $X^i_t$ are i.i.d , $\forall t$. I call the $X^i$ the ...
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Quantile of joint distribution

Give iid random vectors $(x_1,y_1),\dots, (x_n,y_n)$ from the two dimensional cumulative distribution function $J(x,y)$. The marginal CDF of $x$ (rep. $y$) is $F(x)$ (reps. same $F(y)$). They have ...
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Quantifying the bias of a quantile estimator based on order statistics, and its relation to asymptotic unbiasedness

From what I understand, the quantile estimator based on order statistics is asymptotically unbiased (and follows a Normal distribution). I have been looking for a quantification of the non-asymptotic ...
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Identifying the appropriate model for determining the dimension with the most impact on poverty

I am working on a research to determine the dimension (health, unemployment, education and standard of living) with the most impact on poverty. The response variable is the decile score obtained for ...
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Convergence of Percentile in Power Law

I have a probability distribution, that in its tail follows a power law. I've noticed, while I was simulating samples, and determining parameters experimentally, that as I increase the value of a ...
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Weighting the calculation of sample quantiles

Is there a general method for determining what the weights are when calculating sample quantiles? Specifically, how do you do this in the case of repeat measurements -- can (should) you take the ...
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Quantile estimation for discrete data

For quantile estimation for data coming from a discrete distribution, do you have to use one of the quantile estimators R-1, R-2, or R-3? For example, R-3 uses the nearest even order statistic after ...
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How do you do a qq plot in R for a discrete Weibull distribution?

To do this, I think I need to calculate the inverse CDF, but I have learned here that the discrete Weibull (type I) as given by: $$F_{I}(x)=1-\exp\left[-\left(\frac{x+1}{\alpha}\right)^\beta \right]$$ ...
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What is $\mathbb{E}\left( \Phi^{-1}(U)\right)$, $U \sim \mathcal{U}(0,1)$?

Let $\Phi(\cdot)$ denote the CDF of a standard normal random variable and let $U \sim \mathcal{U}(0,1)$. What can we say about $$\mathbb{E}\left( \Phi^{-1}(U)\right)?$$
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What is the effect of adding an independent summand on translated quantiles?

Suppose that $Y,Z$ are independent, continuous, non-negative random variables. Suppose also that for some $0<q<1$, $$\tau=\inf\{t>0:F_Y(t)\geqslant q\}$$ and $$\pi = \inf\{t>0:F_{Y+Z}(t)\...
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Quantiles from histogram?

Is it possible to calculate quantiles from a probability histogram P(x) rather than from the data x itself? I have an unbinned histogram for discrete random variables, and I'm wondering if I can ...
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Notation for Percentile Range of Sample

Let $X$ be a random variable with unknown CDF $F_X$ and PDF $f_X$. What is the notation for a percentile range $[0,p]$ on a sample of $X$ that allows discussing sample statistics over that range? My ...
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quantiles (monotonic transformation)

I'm trying to show that, $(-X)_p = -X_{(1-p)}$, that is, the $p$ quantile of $-X$ is equal to the $1-p$ quantile of $X$ after multiplying with $-1$. The results holds when considering quantiles of a ...
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Correct way to find proportion of events in quartiles

I am analyzing data on proportion of events occurring with respect to blood levels of chemical. The data is of 400 persons. They have been divided in 4 quartiles (100 persons in each quartile) based ...
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Combining quantile regression with binning

I'm trying to employ a framework where I uncover the marginal effects of the quantiles of one continuous variable on another continuous variable - something analogous to the Quantile-on-quantile (QQR) ...
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max subscription of 2 quantiles

I saw in literature the : $x^i_{\max(1-\alpha=0.01;\alpha=0.99)}$ which states that "is the maximum $(1-\alpha)$-quantile derived from the standardized empirical distribution of the same vector ...
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Finding percentiles without complete data set

I have a set of incomplete data for wealth of a given population. Whilst I have the wealth of these individuals (around 27% of the population), I do not have the wealth of every individual. I do have ...
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Is there a single regression quality metric for the median and the 95% percentile?

I want to evaluate the quality of prediction of two values the median and 95% percentile of a distribution. Is there a standard way to do this? I have thought about using "Mean Mean Average Error&...
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There are many different quantile definitions - what diffrentiates and motivates them?

First some standard notation. A probability triplet is $(\Omega,\mathcal F, P)$. You have a random variable $X : \Omega \to \mathbb{R}$ measurable function. The distribution function is $F(x) = P(X\...
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Calculating percentiles on log transformed data

I am trying to replicate results from a research paper that has the calculated 2.5 percentile and 97.5 percentile for a dataset, both with log10 transformed and untransformed versions. I can match ...
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How to test how accurate the quantile returned by quantregForest is?

Here is the example code from quantregForest. ...
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rank to quantile estimate?

R> x=c(92, 3, 1, 4, 15, 4) R> rank(x) [1] 6.0 2.0 1.0 3.5 5.0 3.5 Given the rank results of an input vector of sampled data, I can estimate the quantiles ...
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2 votes
1 answer
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Non-parametric test for two sample quantiles

I would like to know if there is a non-parametric test on quantiles. EDIT: My focus is on continuous distributions (e.g. Weibull distribution). In a general setting we define quantiles as $Q_X(p) = ...
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Nonparametric Methods for Two Sample Quantile Test

Background I want to compare two populations' quantile, e.g. 99.99% quantile, 95% quantile. So I am searching for methods for two sample quantile testing. Unfortunately, the population does not obey ...
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Approximate Posterior Predictive Quantiles with Numerical Methods

I have a posterior function which is easy to approximate using numerical methods (the posterior has only 2 parameters, and is approximately Gaussian because of the large sample). However, I need to ...
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2 votes
2 answers
53 views

Standard Formula for Calculating Percentiles

I have the following question about calculating percentiles (to illustrate my example, I will use the R programming language). Suppose I have the following data: ...
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1 vote
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How to estimate probable response times, from previous samples?

I'm a IT manager that deals with delays from various departments in a purchase process. In a given phase we have 25 handovers and thus 25 response times. So many variable times (and without SLA) ...
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How would one measure consistent high values for a dataset? Is it the same as measuring a high variance for a low percentile?

For a numerical dataset, you can measure the consistency of the data using variance, where lower variance means the data is closer to the mean/median, while higher variance means the data is spread ...
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Is this formula for percentile from z-score correct?

Preface: I am not a mathematician. I have a basic understanding of statistics but am not familiar with mathematical notation beyond high school algebra. I am a software developer maintaining medical ...
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2 answers
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I have data from an unknown, continuous probability distribution. How do I calculate a percentile/quantile?

I'm going to collect a sample of data that comes from an unknown, likely continuous, probability distribution. I don't really know anything about the data other than that it's somewhat chaotic. I want ...
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Why do Quartile, Decile, Percentile have plus 1 in their formula? [duplicate]

I searched this on the internet, but barely found anything, and what I found was not satisfactory. Quartile divides the data into 4 equal parts. Qi = i * (n+1)/4 where i=1, 2, 3 Decile divides the ...
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What determines y-axis scaling on a normal probability plot?

I've been investigating Q-Q plots, specifically the normal probability plot, to determine if a set of data I have is approximately normal. I.e., a plot of the data should be approximately a straight ...
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3 votes
1 answer
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Probabilistic interpretation of sum of quantile functions

We know that the weighted sum of CDF $$ F(x) = w_1 F_1(x) + w_2 F_2(x), \,\, w_1 + w_2 = 1 $$ is the CDF of the mixture distribution. Is there a probabilistic interpretation for weighted sum of ...
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"Representative" percentile across series of batches

I am running a workload in a typical client-server setup with latency as my metric. My workload generator tools output the percentiles of latency metrics for a batch of transactions every 5 mins. I ...
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