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

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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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29 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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23 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
110 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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1answer
23 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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19 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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4answers
437 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 ...
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8 views

Quantile in Gaussian Mixtures [duplicate]

Given a Gaussian mixture on real numbers $\mathbb{R}^1$ with $N$ Gaussian components, having means $m_1, m_2, m_3, ... m_N$ and variances $v_1, v_2, v_3, ... v_N$, mixed with weights $w_1, w_2, ... ...
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2answers
309 views

Calculating SD for normal distribution with only mean and 5% and 95% quantile values

As part of a Bayesian method to estimate the divergence times of species, priors have to be set with values based on previous literature or known fossil dates. These priors can have different ...
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43 views

Find the values between percentiles in a frequency distribution

In the distribution below, how would I find the values that lies between 30% and 50% of the distribution? R code would be handy but not essential! 28, 28, 29, 30, 30, 31, 31, 31, 31, 32, 32, 32, 34, ...
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2answers
60 views

Get quantile function of dynamic mixture model

I have a dynamic mixture distribution fitted to my risk data (i.e., I have all parameters) of Weibull and Generalized Pareto, with a Cauchy CDF mixing function, that can be written as: $mixture(x): ...
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525 views

Percentile vs quantile vs quartile

What is the difference between the three terms below? percentile quantile quartile
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15 views

Calculate the 95th percentile of a population from a set of 95th percentiles calculated on subsets

I need to calculate the 95th percentile of large collection of streamflow measurements. The resolution of the measurements was originally hourly, but then were transformed into daily means. There ...
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11 views

sadists package/ Sum of (non-central) chi-squares to a power

I try use "sadists" package in R to compute quantiles and probabilities on sum of non-central chi-squares distribution, but there are some issues in this package. I give an example: wts = ...
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1answer
115 views

How do you classify based on percentile ranking when most scores are the same?

I am dealing with a simple dataset of test scores. It was an easy test -- 98 out of 100 persons got a perfect score. 1 person got a 2% and one person got a 3%. Here's what it looks like in ...
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1answer
44 views

Comparing two data sets by using only their percentiles

Lets say I have two data sets A,B (I have only access to percentile of two data sets and some more statistics like count , min , max). I'd like to compare how close these data sets are. I am failing ...
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36 views

Is there a name for the $n=50$ quantiles?

For $n = 5, 10, 20, 100$ we have quintiles, deciles, vigintiles, and percentiles. Is there a name for $n = 50$? A candidate would be quinquagintiles, but I can't find that having being used.
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62 views

Difference between rexp and qexp in R

I need to write a simulation that requires the use of exponential distribution. I was wondering what is the difference between the following two approaches in drawing random numbers from an ...
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68 views

Tail of the inverse cdf

I am almost sure I have already seen the following result in statistics but I can't remember where. If $X$ is a positive random variable and $E(X)<\infty$ then $\epsilon F^{-1}(1-\epsilon) \to 0$ ...
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Name for phenomenon which causes bias in estimation of extreme percentiles of a distribution fitted to points with large error bars

I have a series of small numbers (say 25-45) of values which were generated, and each value has an uncertainty associated with it. I also have a theory that says these points are supposed to fit well ...
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21 views

Choose $m$ out of $n$ distributions s.t. the union of them likely contains top $k$ elements

I have $n$ sets of items. Each item in each set has a certain score. I want to select top $k$ items out of all available (i.e., out of the union of $n$ sets). However, explicitly calculating the union ...
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2answers
56 views

truncated quantile regression in R

I have used the "quantreg" package in R to find quantiles for my data. All my data, both predictors and responses are limited between 0 and 1, while a number of quantiles given by "rq" or "rqss" ...
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34 views

What quantile method is ideal for a moderate sample size of data?

I have several samples ranging $n =$ 15 to 40 coming from a population with a presumed non-normal distribution. I'm trying to calculate the 25th and 75th percentile but find differences between the ...
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40 views

Quantiles in R for two-dimensional data

I have a two-dimenstional data set, which consists of "values" in the one column $V$ and "numberOfOccurrences" in the other column $W$. Hence, for each observed value, it is recorded how often that ...
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75 views

Finding Percentile (Basic but confusing)

I have been unusually confused with finding percentile question. First question is: So if I want to find the median, for such a case like this, can we use the method of finding median, which is ...
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Confidence Intervals of a Given Width

I'm working through some questions on confidence intervals. My answer doesn't match the book, but the book's answer was a number I had a few steps before the end. I have ten numbers which are a ...
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1answer
36 views

Does it make sense to calculate the variance of a percentile measurement of a timeseries?

Developers often look at a percentile measurement of how long a task takes to complete as a measure of performance (e.g. 95th, 99th percentiles of page render time). However, in order to measure the ...
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1answer
24 views

How to compute the $\chi^2$-table values?

How one can compute the values of $\chi^2$-tables? I saw two tables where was given for example that if degree of freedom is $1$ and $p=0.001$ then table value is in one table $10.827$ but in the ...
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23 views

data dependent quantiles

Could you please explain, what does "data dependent quantiles" mean, as mentioned in the following paragraph: Quantiles appear intuitively appealing to epidemiologists as they can be thought of ...
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1answer
101 views

Is it possible to compute income percentile, given the median and the average?

In Romania, the median net income in 2013 was 284 EUR/month, the average net income (unfortunately, in 2014, not in 2013 as the previous data point, but lets assume the same amount for 2013 for ...
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352 views

How to convert sport odds into percentage?

I am wondering how to convert sport odds to the percentage format. There's this example: ...
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Is quantile multinormal distribution same as negative multinormal disribution?

May I know whether the quantile multinormal distribution is the same as negative multinormal distribution? If not, may I ask what the quantile multinormal distribution function look like? Thank you ...
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1answer
147 views

How to calculate critical values for Dunnett procedure given alpha, df1 and df2

I am looking for an R function that can calculate critical values for a Dunnett multiple comparison procedure for any family-wise error rate and degrees of freedoms. In short, I need similar ...
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160 views

When would we use tantiles and the medial, rather than quantiles and the median?

I can't find definitions for either tantile or medial on Wikipedia or Wolfram Mathworld, but the following explanation is given in Bílková, D. and Mala, I. (2012), "Application of the L-moment method ...
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28 views

Using quantile regression with a linear equation bounded by 1

I am trying to replicate the research of Ducey and Knapp (2010)* with my own data using the quantreg package in R. My question/problem might be algebraic rather than statistical, but I thought I would ...
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20 views

Is there a Cornish Fisher expansion asymptotic in variance?

The 'usual' implementation of the Cornish Fisher approximation (i.e. AS 269) arranges the terms in order of $n^{-1/2}$, assuming one is estimating the quantile of the normalized sum of $n$ independent ...
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1answer
150 views

Estimating quantiles by simulation

I'm a bit confused about how I would go about estimating quantiles by simulation. Say I have some statistical model $f(x,\theta)$. I can estimate the parameter $\theta$ and am able to generate random ...
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19 views

Inferences about a distribution given running maximum values

Here is a question inspired by this question from StackOverflow. Suppose you have observations of a variable which is measured once a minute, but the values are only recorded if they are greater than ...
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1answer
110 views

Compute quantile of sum of distributions from particular quantiles

Let's assume $N$ independent random variables $X_1, ..., X_N$ for which the quantiles at some specific level $\alpha$ are known through estimation from data: $\alpha = P(X_1 < q_1)$, ..., $\alpha = ...
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25 views

Metrics for regression error

Suppose I undertake a least squares regression on some data. I end up with a function such as $\hat{f}(x,y,\ldots)=\hat{\beta_0}+\hat{\beta_1}\cdot x+\hat{\beta_2}\cdot y+\hat{\beta_3}\cdot ...
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3k views

Finding Quartiles in R

I'm working through a statistics textbook while learning R and I've run into a stumbling block on the following example: After looking at ?quantile I attempted ...
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1answer
79 views

How to obtain the quantile function when an analytical form of the distribution is not known

The problem comes from page 377-379 of this [0] paper. Given a continuous distribution $F$ and a fixed $z\in\mathbb{R}$, consider: $$L_z(t)=P_F(|z-Z|\leq t)$$ and ...
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122 views

Is calculating a percentile the same as evaluating a cumulative density function?

I'm trying to make the jump from the idea of a percentile, say, over the real number line (where the nth percentile is simply the position in which n% of data points are below it, and 100-n% are above ...
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1answer
58 views

How to Map Desired Confidence Interval to a Quantile value

I want to calculate the N% confidence interval for some time-series data set. I have the standard errors for this data series and the error variance of the time-series is assumed to be Gaussian. I ...
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3answers
1k views

Standard deviation to describe variation in positively skewed data?

I'm wondering how useful the standard deviation is when applied to positively skewed data? The standard deviation implies that 68% of data will lie within one standard deviation of the mean, but ...
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38 views

Percentile or actual values for multiple regression in studies involving children?

I have to perform multiple regression where the outcome variable is a non-negative continuous health variable (call it yvar) which is in the range of 50-150, and age, gender, height and weight as ...
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191 views

Different quantiles of a fitted GPD in different R packages?

I am performing an extreme value analysis for meteorological data, to be precise for precipitation data available in mm/d. I am using a threshold excess approach for estimating the parameters of a ...
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259 views

Best method to create growth charts

I have to create charts (similar to growth charts) for children of ages 5 to 15 years (only 5,6,7 etc; there are no fractional values like 2.6 years) for a health variable which is non-negative, ...
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1answer
54 views

Finding predictors of upper level of a variable

I am analyzing data on a health variable and its relation to age, gender, height etc. I am more interested in 90th percentile of the health variable, which can be called upper limit of 'normal'. How ...