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

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Calculate the non centrality parameter (ncp) for non central chi squared distribution

I have the 0.975-quantile value (0.191) and the degree of freedom (k=1). How can i calculate the non centrality parameter ? in R if possible. Q0.975(k=1, ncp= ??) = 0.191
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Basic application of mean, median and percentiles [on hold]

The mean salary at an island t-shirt shop is \$28,400 with a standard deviation of \$5400. The median salary is \$27,400 and the 62nd percentile is \$28,900. Is the following True or False: ...
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15 views

Using quantiles for correlation

Here's hoping that people don't get irritated if this was a repeat question, or perhaps not the best place to post this question -- I'm new to the community. My stats skills are basic, but I will ...
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Equivalence of definitions of quantiles

Let us define the concept of quantile of order $\tau$ of a random variable $X\in F$ in two different ways: Definition $1$: $c_\tau$ is said to be a quantile of order $\tau$ if and only if $lim_{x\to ...
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1answer
10 views

Calculating age-adjustments for column percents

I am having trouble understanding how SUDAAN calculates adjusted column percents and I'm hoping someone can explain. Let's say I have 3 variables, gender(M/F), happyness (binary happy/sad), and age ...
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13 views

Calculate percentile from ranks

I am trying to come up with a formula to calculate my percentile finish in fantasy sports games while also learning some statistics along the way. Rather than trying to work with the complete list of ...
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30 views

Analytical properties of sample quantiles in statistical packages

When studying and proving properties of sample quantiles, such as its consistency or its asymptotic normality, every text I have seen uses the standard definition of this estimators. This is, given a ...
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1answer
38 views

Understanding The Algorithms Behind Quantile() in R

So I was trying to compute the quantiles from a dataset in R: c(3,5,7,8,12,13,14,18,21) using the quantile() function, and I realised that it was returning ...
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22 views

How to calculate theoretical quantiles of an odd dataset?

In order to calculate a set of theoretical quantiles I usually apply the following method: $\frac{1}{2. N} + \frac{x}{N}$ so here this makes: $\frac{1}{24} + \frac{6}{12}$ $\frac{1}{24} + ...
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10 views

Normaldistribution function of quantile [closed]

Im looking for an upper bound (not just 1) of the following $$ \Phi(\alpha_1 \Phi^{-1}(\alpha_2)) $$ where $\Phi$ is the distribution function of the standard normal and $\alpha_1$ and $\alpha_2$ are ...
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45 views

Meaning of a plot obtained by 'quantile' function of R

I have a following plot that is obtained by using the quantile function of R: Could anyone explain me what the plot means? The input X to the quantile function QUANTILE(X, P) is a '180x100 'matrix. ...
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37 views

How to calculate quantiles?

Could someone please show(!) and explain step-by-step how to calculate the theoretical quantiles for the following normally distributed dataset: {1,1,2,2,2,3,3,5,8,14,24,40} Given this table: ...
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How is $\beta$ of the $\beta$-Quantile called?

I was often wondering how to call $\beta$ of the $\beta$-quantile of a distribution. Of course, $\beta$ is a probability or proportion. But is there an official name for it? So instead of saying ...
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1answer
41 views

How can I calculate the mean and standard deviation given three percentiles using Matlab?

I have the percentiles of 3 values. The percentiles are 5th, 50th and 95th. The values respectively are 340, 365 and 385. How can I find the median and the standard deviation given that data follow a ...
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1answer
36 views

Calculating actual quantile from poorly defined lognormal distributions

I have a dataset in which the uncertainties in various parameters are modelled with a lognormal distribution. After the experiment I get a single number result. As part of a lookback to understand how ...
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11 views

Quantiles of big areas to calculate the associated quantiles of small areas

I have this question to solve and i don't understand it: How can i use quantiles of big areas to calculate the associated quantiles to small areas and construct a table that gives me the 0.05, 0.025 ...
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1answer
113 views

Asymptotic normality of order statistic of heavy tailed distributions

Background: I have a sample which I want to model with a heavy tailed distribution. I have some extreme values, such that the spread of the observations are relatively large. My idea was to model this ...
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13 views

How to compute the VaR(a) of the following cdf

I have to compute the mean value, the variance, the VaR and ES of the CDF F(x)= 1- (3/2x)^(-3) if x>= 3 F(x)=0 if x< 3 The mean and variance I have computed, but what about computing the value at ...
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42 views

Combine multiple Monte-Carlo estimates

I use a Monte Carlo simulation (say 100.000 runs) to estimate parameter in R. I have memory problems and my first thought is to run multiples times my estimation program (say 500 times) . My ...
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1answer
29 views

Linearly scaling a distribution (X) to have the same 5th and 95th percentile of distribution (Y)

As done in this paper here: I would like to linearly scale a distribution such that it has the same 5th and 95th percentile (0.05 and 0.95 quantile) as another distribution. That is, given two ...
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References on how to calculate quantile of a population from a small sample

I'm a novice in statistics. I need to study a problem that basically consists in checking if the 5% quantile of a population (that can be assumed normally distributed) is above or below a given value ...
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61 views

Linear Properties of the Quantile Function

Suppose $X$ is a random variable with continuous distribution function $F(x)$ and quantile function $Q_X(p)$ and let $Y = aX + b$ for some constants $a > 0$ and $b$. How can I prove that $Q_Y(p) = ...
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26 views

Asymptotic Distribution of Sample Quantile

My question is related to the proof below. Why can we say that $F^{-1}(Y_n(x))=X_{[np]}$? I would like to understand better the reason for that. Any help would be appreciated. I've also asked ...
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131 views

Relation between Quintiles and the Arithmetic Mean

I have a set of final exam grades for an entire year of students, and I need to calculate quintiles from them. How should I go about it? Also, is the range from the arithmetic average and the top of ...
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cdf based bias correction

I have three sets of climate data: obs, baseline (model) and future (model) data. I have calculated the cdf for all series of above data sets, I have also calculated the cdf of projected future. But I ...
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59 views

Quantile regression on non linear data

R and statistics beginner here, trying to do a quantile regression on a non-linear dataset. I want to identify datapoints that have a higher y axis value that expected given their value on the x ...
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72 views

Using quantile in predict for survival

I am working on survival analysis and fit a model: ...
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39 views

How does anova.rq compare estimates from quantile regression in the quantreg package for R

I am using the quantreg package in R to develop quantile estimates at different taus, then using anova to test whether the Beta ...
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1answer
83 views

Uncertainty of PDF quantile estimated from empirical PDF [duplicate]

I want to determine the quantile of a probability density function (PDF). I do not know the distribution, but I have a sample that was generated from it. I estimate the quantile of the distribution ...
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37 views

Quantile aggregation for a sum of dependent variables

I am currently working with a sum of dependent variables following complex laws. For these laws I have a vector of means, $\mu$ and a linear correlation matrix $\Sigma = \rho_{i,j})_{i=1..n,j=1..n}$. ...
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121 views

What are the consequences of removing the tails of a distribution?

I would like to know the consequences of removing the tails of a distribution by deleting observations above and below certain thresholds. For instance, if one were to calculate the percentiles of a ...
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1answer
115 views

Removing outliers and calculating percentiles with highly variable data

I want to be able to rank and get percentiles for groups of scores from a range of organisations. These percentiles will be used to judge other organisations. The organisation's scores are an average ...
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96 views

Estimation of quantile given quantiles of subset

Let's say we have sets $X=\{x_1, x_2, \ldots, x_m\}, Y=\{y_1, y_2, \ldots, y_n\}$ and we have some estimate (or exact) quantile information about them at some level $a$. How could we approximate the ...
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76 views

How many data points are in a given quantile in Quantile regression?

I hope somebody can help me with a, probably very fundamental, issue of understanding concerning quantile regression. My dataset is very skewed, so I've looking at the data with quantile regression ...
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1answer
39 views

Weighted median

I'd like to compute a median of measurements taken from a population with 3 subgroups, A, B, and C. I'd like to the median to be "weighted", in the sense that each of the groups should have equal ...
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38 views

Cox Regression Hazard Ratio in Percentiles

I computed a Cox proportional hazards regression in R. cox.model <- coxph(Surv(time, dead) ~ A + B + C + X, data = df) Now, I got the hazard ratio (HR, or ...
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Should I convert age as independent variable in my Quantile Regression?

I'm applying quantile regression to a dataset where the dependent variable is a measurement of load (utilization) of a specific technology. The model includes a number of independent variables ...
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110 views

Generalisation of the notion of correlation for $\alpha$-stable distributions

Pearson correlation is defined via variance and covariance, so will not work when applied to $\alpha$-stable distributions with $\alpha \neq 2$. Is there a way to generalise the notion of correlation ...
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1answer
91 views

How are percentiles distributed?

I was taking a look at this page, and I can't seem to understand why the frequency plot of the percentiles is uniformly distributed. Distances between percentiles are not equal, so why is the ...
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33 views

Percentile vs Percentile rank

I have the read the definitions many times and I still don't quite understand the difference. This article says: A statement such as: "A score of 600 has a percentile rank of 80" has a ...
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1answer
242 views

Expected value as a function of quantiles?

I was wondering where there is a general formula to relate the expected value of a continuous random variable as a function of the quantiles of the same r.v. The expected value of r.v. $X$ is defined ...
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What is the proper name for a Quantile Bar Chart?

What is the proper name for a Bar Chart plotting quantiles (like percentiles) in abscissa (X-axis) and a corresponding continuous variable in ordinate (Y-axis)? For example, if the chart is based on ...
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44 views

predicting the percentile of response variable via linear regression of zscores

Sometimes during modeling we are faced with non-normal data. One of the presumptions of linear regression is the response data being normal. I wish I found a better example data set to illustrate ...
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96 views

How to define percentiles for a joint-probability distribution [not the marginal..]?

Is there a reasonable definition for percentiles for a multivariate distribution? Say you have X and Y, Gaussian-distributed, and you want to define the, say "tenth", percentile of the joint ...
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38 views

Different quantile values for a predictor between the root data and and the data of a Predict() object

I want to plot a continous predictor using restricted cubic splines and indicating the distribution of the linear predictor using a box-and-whisker plot. However, the quantile values differ from those ...
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Reference for the use of moving upper quartile window

I'm currently writing a paper in which I used a moving upper quartile window to select some data, but I require some kind of reference for justifying it's use and I cannot for the life of me find ...
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1answer
283 views

Can quantiles be calculated for lognormal distributions?

I just talked to someone who stated that quantiles cannot be computed for lognormal distributions. or it does not make sense. Is this true?
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26 views

Calculating quantile for inverse transformed Gamma

I have an inverse transformed Gamma by the specific domain but I have a difficulty of finding quantile for this distribution. The issue is my quantile is smaller than my minim data set.
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58 views

Can quantile regression be used to pool multiply imputed count data?

I am using the mice package in R to impute missing data in small study. The study investigates the effect of a behavioral intervention on the frequency of a particular behavior, i.e., count data that ...
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692 views

Why use extreme value theory?

I'm coming from Civil Engineering, in which we use Extreme Value Theory, like GEV distribution to predict the value of certain events, like The biggest wind speed, i.e the value that 98.5% of the wind ...