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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19 views

Can the t-test be used to test the difference between percentiles of 2 samples?

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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24 views

Percentiles boundaries

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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How to do Rejection Sampling from a proposal density which 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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4answers
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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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1answer
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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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1answer
92 views

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 ...
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17 views

Optimizing PDF using CDF deltas

In the paper introducing PixelCNN++ they optimize the PDF of a logistic function by minimizing the difference between the CDF around the sample points (x ± epsilon). I am trying to understand when it ...
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1answer
26 views

Understanding of quantile plot versus remove outliers plot

I have sample height for some people sample with a quantile plot like this: I need to check that the sample belongs to normal distribution. I remove outliers <...
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0answers
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Quantile function confusion about $\min\{x \text{ | }F(x) \geq p\}$

I am currently reviewing the quantile function for discrete random variables but I am a bit confused. We use the following definition of the quantile function: $$ \tilde{x}_p = min\{x \in \mathbb{R}...
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36 views

Can we infer other distributions from the distribution of the 99th percentile?

This is a fairly weird question, but I'm analysing a paper that reports its findings in a curious way; for every subject, they passively took measurements every 10 seconds for 24 hours (8640 ...
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46 views

Measuring the distance between two probability measures using quantile functions?

There are many metrics on the space of probability measures on $(\mathbb R, \mathcal B)$. Most of the famous metrics use the distribution functions associated with the probability measures to ...
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Optimal hedge ratio and risk capital requirements

So I understand that the minimum variance hedge ratio minimizes the second moment of the portfolios. My question is how is it related to the size of the risk capital (which is calculated as the Value ...
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3answers
32 views

How can I rank values that are not normally distributed?

I have one metric value changing between 0 and 1 for 650 observations. When I analyze frequency distribution I see that the values are right skewed. I need to classify values as high/medium/low. I ...
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1answer
35 views

Acceptance- rejection-method with a uniform distribution

In the inversion method, when generating $Y$ from $g(y)$, do you just make $U$ equal to the function $g(y)$, then find the inverse (seen in notes) or are you meant to find the CDF or $g(y)$, then make ...
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Is there an equation for the median and percentile of a zero-inflated Poisson?

This question gives answer to the mean and variance of the zero inflated Poisson distribution, but is there an equation for the median or the percentile?
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Is logistic regression across a range of thresholds of a continuous target dual to quantile regression across some dual range of thresholds?

Are there any results about this? What I mean is create binary target $Y < y_c$ across a range of $y_c$. This is effectively learning a CDF. Quantile regerssion learns the inverse CDF. Are there ...
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Quantile of t distribution when the degree of freedom increases

I have a little issue : I want to prove that if $\{X_n\}_{n \in \mathbb N}$ is a sequence of random variables defined on a probability space $(\Omega, \mathcal{F}, \mathbb{P})$ such that $\forall n \...
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1answer
30 views

Generate random dataset from constrained quantile statistics [closed]

In order to study k-nearestneighbors with a more concrete example than the iris dataset with my students, I would like to generate data for age weight sex based on the statistics of [cdc.gov for ...
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Asymptotic Distribution and Quantile (Inverse) Function

For a concrete example: Question. Suppose I have iid random variables $X_1, \dots, X_n$ with pdf $f(x) = \frac{1}{6|x|^{2/3}}$ for $x \in [-1, 0) \cup (0, 1]$. Find the asymptotic distribution of $...
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How to obtain results in months from relative survival quantiles?

I am doing relative survival analyses of a metastatic colorectal cancer population. Instead of looking at the usual 1- or 5-year relative survival percentages, I am calculating 5 different survival ...
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1answer
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Calculating estimates of aggregate totals from percentile data

I'm working with wage data and would like to compute total aggregate wages earned for individual job classifications. The survey data I'm working from does not report aggregate wages, but it does ...
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Quantile Estimation from Independent Estimates

I need to estimate the 5th and 95th quantiles of a distribution. I have three independent quantile estimates for both the 5th and 95th quantiles. All estimates are obtained with the same technique on ...
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24 views

Can I use MCMC to estimate distribution quantiles?

I use MCMC to study a distribution. Thanks to the modified Central Limit Theorem found in Robert and Casella's Monte Carlo Statistical methods, one can approach the expectation of the distribution, ...
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1answer
48 views

Difference between quantile and qnorm

What is the difference between the R-functions quantile and qnorm? I have normal distributed data and want to calculate ...
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Average Coverage Error (ACE)

This paper mentions ACE. It is defined as following ACE = PICP - PINC where PICP and PINC stand for Prediction Interval Coverage Probability and Prediction Interval Nominal Confidence, ...
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1answer
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Hypothesis test with simulated data

A simulation gave me the following density of data (grey histogram, blue kernel density estimation). Having an alternative input $I^*$ with the same distribution (green line), I would like to check ...
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Determining quantiles given this data summary

Given the following data from a survey on "mobile phone usage while driving": I would like to determine any 2 quantiles using this data summary. These quantiles should represent the proportion $\...
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How to regress variables in quantiles in a Fixed-effects model? (one large model or multiple separate ones)

For my thesis I examine whether generating renewable energy influences a company's cost of capital (beta, cost of debt & leverage). In this, I split my variables into 3 quantiles of Firm size by ...
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Prove or disprove the Linearity of Expectiles used in Expectile Regression

For expectation (mean), there are many useful properties such as Linearity of Expectation: $\mathbb{E}[X+Y]=\mathbb{E}[X]+\mathbb{E}[Y]$ $\mathbb{E}[\alpha X]=\alpha\mathbb{E}[X]$ (The 2 equations ...
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Finding quantiles of scalar non-decreasing function of two independent variables

Let $X_1 \sim exp \circ N(\mu_1, \sigma_1)$ and $X_2 \sim exp \circ N(\mu_2, \sigma_2)$ be two independent lognormal distributions, and $f:R^2\to R$ such that $f$ is non-decreasing on both arguments. ...
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1answer
76 views

inverse transform method [closed]

Using Inverse Transform Method to solve parts of the problem below: (a) Suppose $X \sim \text{Exponential}(λ = 0.2)$. Use RN to generate 20 random realisations of $X$ $\{X_1, X_2, .., X_{20}\}$ ...
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61 views

How to simulate from a step (simple function) hazard function?

I have a step hazard function $h(t)$ (a simple function that jumps at specific times and it is constant between those jumps). Something like: How can I simulate survival times from this hazard ...
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22 views

Confused with percentile results [duplicate]

I'm trying to find out how accurate percentile is. I have used scipy.stats to calculate the rank of percentile. However, it doesn't match the one I have coded. I ...
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12 views

Recentered Influence Function and Quantiles

First of all, I apologise if my question is straightforward, but I'm having some troubles understanding the concepts. If someone could help me, I would be very grateful. I am reading the Firpo et al. ...
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2answers
292 views

Detect what is wrong with the R program for a Poisson Q-Q-plot?

I have a big vector, $x$, of observations constituted by integers 0-5 that represents how many claims occurred during a certain insurance-contract (111408 elements). I want to make a Q-Q-plot to show ...
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1answer
54 views

What's the 0-percent-quantile?

Today I was asked what the 0% quantile is. I am aware that this has no practical relevance, but now I am still wondering. At first I would have said it was the minimum of a sample. R says for all ...
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Quantile-calculation example: Why the term $c$?

I need help to interpret a solution to the following example: Based on historical claim amounts $x_1,...,x_{47}$, which are assumed to be outcomes from an unknown claim distribution, you are ...
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Outlier identification — 3s control limits or 1.5IQR

I am would like to implement outlier flag (extreme user) identification on our data system. We have a daily database that shows each user usage (in minutes). A simple statistical control would be ...
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1answer
77 views

how to find 10th, 50th, 90th percentile of a uniformly distributed data for all cases?

Here are some key data to use for calculation: initial population is 100, and average food consumption per person is 5lbs of rice each week 1~2% of population dies off every month 20~40 is added to ...
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1answer
52 views

How to invert a mixture of log-logistic distributions? [duplicate]

Say I have a CDF of the form $$F(x) = \sum_{i=1}^n \frac{ k_i }{ 1 + (x/\alpha_i)^{ - \beta_i } }$$ $$\sum_{i=1}^n k_i = 1$$ How do I find the quantile function, i.e. how do I invert F for n>1? I ...
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Prediction interval for OLS with non-normally distributed residuals

I'm estimating a multiple linear regression model (found in equation 19 of "The volatility of realized volatility", Corsi et al. https://www.econstor.eu/bitstream/10419/25467/1/515328057.PDF) using ...
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3answers
137 views

Find Q1 and Q3 from median and IQR

A study gives the following: $n = 67$ mean = 73 sd = 68 median = 55 IQR = 66 Is it possible from this information to get the actual Q1 and Q3 values? I used the $n$, mean & sd to get 95% ...
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1answer
130 views

Confidence interval for quantiles: distribution-free, asymptotic and assuming a normal distribution

An acquaintance of mine has been using this wrong inference formula for years: given a i.i.d. sample $\mathbf{X}={X_1,\dots,X_N}$ for a continuous RV $X$, sample mean $\bar{X}=\frac{\sum X_i}{N}$ ...
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Comparison of standard scores vs percentile scores or categorisation. Which one is more powerful?

I am researching on anxiety levels in a population including 80 subjects before and after an intervention that possibly might be cause to rise in anxiety levels. I wonder which method is more correct ...
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0answers
112 views

Convergence Rate of Quantile from Convergence Rate of Distribution

Suppose we have a sequence of distribution functions $F_n$ such that $F_n \rightarrow F$ as $n \rightarrow \infty$. Suppose that we know the convergence rate, given by $$ \sup_{x \in \mathbb{R}} | F(...
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How should I label and interpret cumulative probability graphs

I've used R's empirical cumulative distribution function (ecdf) to generate a chart that shows the cumulative probability of some cost data. I want to know if the heading of the chart is correct or ...
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Calculate percentiles of probabilistic functions

For easier understanding, let's assume we talk about sport betting. There are 3 independent games with team_A winning with a probability of 70%, 50%, 10% respectively. Each bet has its odds (odds_1, ...

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