Questions tagged [quantiles]

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

Filter by
Sorted by
Tagged with
1
vote
0answers
14 views

Defining quantiles for complex survey samples

I am looking to accumulate a comprehensive list of definitions for quantiles under complex sampling that have been published or implemented in software. I'm not worrying about the separate problem of ...
0
votes
0answers
10 views

quantile-quantile plots theoretical z-scores

I looked on stackexchange and didn't not find any answers, hopefully someone can explain this intuitively. In quantile-quantile plots to see if my data is normally distributed, I understand that we ...
2
votes
1answer
56 views

Summing Differently-Distributed, Correlated Random Variables

I have four mutually correlated time series. Each contains 40 observations but is fundamentally and decisively differently distributed from its peers. The first series follows a Laplace distribution, ...
0
votes
1answer
31 views

What percentile is the following mark?

$24$ students took a test and they each scored a mark from $0$ to $100$. Gillian scored $71$. $18$ students scored lower than her and $5$ students scored higher than her. Gillian is the $19$th mark. ...
0
votes
1answer
31 views

Sampling from a continuous 2 dimensional probability distribution function for importance sampling

I just want to clarify a few points with regarding to sampling from a continuous 2-dimensional probability density function. If I want to sample from this pdf, I could sample from a 1D pdf, $P(x)$, ...
0
votes
1answer
22 views

Deriving Inverse of Cumulative Distribution function [closed]

let $f(x)$ be a probability distribution, and $g(x)$ be the cumulative distribution of that probability distribution (CDF) By definition, CDF is: $ g(x)=\int_{-\infty}^{x} f(x) dx $ Given $g(x)$, I ...
2
votes
1answer
23 views

Understanding notation in proof of probability integral transform

I'm attempting to understand one line of the proof for the probability integral transform as found on wikipedia: Suppose that a random variable $X$ has a continuous distribution for which the cdf is $...
0
votes
0answers
14 views

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 ...
2
votes
1answer
13 views

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?". ...
0
votes
2answers
20 views

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 ...
1
vote
0answers
11 views

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 ...
0
votes
0answers
33 views

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 ...
0
votes
0answers
19 views

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 ...
1
vote
1answer
45 views

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 ...
1
vote
1answer
24 views

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 ...
0
votes
1answer
25 views

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 ...
1
vote
1answer
30 views

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 ...
0
votes
1answer
50 views

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 ...
1
vote
4answers
55 views

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 ...
2
votes
1answer
50 views

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 ...
2
votes
1answer
93 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 ...
0
votes
1answer
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 ...
1
vote
1answer
27 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 <...
1
vote
0answers
31 views

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}...
2
votes
1answer
38 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 ...
1
vote
2answers
52 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 ...
0
votes
0answers
14 views

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 ...
0
votes
3answers
34 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 ...
2
votes
1answer
37 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 ...
1
vote
1answer
36 views

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?
0
votes
0answers
10 views

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 ...
2
votes
0answers
161 views

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 \...
2
votes
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 ...
4
votes
1answer
76 views

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 $...
0
votes
0answers
14 views

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 ...
1
vote
1answer
21 views

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 ...
1
vote
0answers
13 views

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 ...
0
votes
0answers
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, ...
1
vote
1answer
70 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 ...
0
votes
0answers
19 views

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, ...
1
vote
1answer
30 views

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 ...
0
votes
0answers
4 views

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 ...
0
votes
0answers
10 views

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 ...
1
vote
0answers
25 views

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 ...
0
votes
0answers
12 views

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. ...
1
vote
1answer
87 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 $X$ $\{X_1, X_2, .., X_{20}\}$ ...
1
vote
0answers
66 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 ...
0
votes
0answers
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 ...
0
votes
0answers
15 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. ...

1
2 3 4 5
14