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

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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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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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Copula Quantiles in R? [migrated]

I have the following bivariate Copula models: Archimedean copula family:- Gumbel-Hougaard Copula ( Model-1) Frank Copula ( Model- 2) Elliptical copulas family Normal Copula(Gaussian Copula) ( ...
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1answer
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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
19 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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1answer
22 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
89 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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5answers
271 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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0answers
11 views

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
75 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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1answer
105 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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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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18 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
86 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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0answers
17 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
60 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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20 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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1answer
621 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
74 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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1answer
48 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
43 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
516 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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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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1answer
132 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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2answers
227 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
50 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 ...
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Estimating the 95th percentile of nitrate data using non-parametric Weibull method, with associated confidence intervals in R

I am currently involved in a project where I have to estimate the 95th percentile of nitrate data from different sample points, using the non-parametric Weibull method, to see if it breaches the ...
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1answer
56 views

Sum of percentile rank scores of two or more variables

I need to sum some variables that are on different scales to make a new one. I'm wondering If it's correct to calculate the percentile scores first, and then to sum them up. Imagine I have to ...
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How to evaluate similarity of datasets based on summary data?

I have summary data that I want to compare to my own data. For the summary data I do not have access to the underlying data, however, I know the percentiles as shown below (A). I also calculated ...
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2answers
89 views

How to determine overlap of two empirical distribution based on quantiles?

I'm looking for a method to calculate "threshold" at which the $\alpha^{th}$ quantile of one empirical distribution is equal to the 1-$\alpha^{th}$ quantile of another empirical distribution. I had ...
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2answers
123 views

Limits on conditional expectation with normal margins and specified (Pearson) correlation

I saw the following question on another forum: "Suppose that both height and weight of adult men can be described with normal models, and that the correlation between these variables is 0.65. If a ...
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1answer
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quantile regression with e.g. gamma distribution and log link

I have a basic question about quantile regression (I'm new to it): Why doesn't it seem possible to do a quantile regression with a specified family (e.g. gamma) and link function (e.g. log), as in a ...
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1answer
101 views

Approximating any percentile from 1st, 5th, and 9th decile

1) If I have the values for the 10th percentile, 50th percentile, and 90th percentile, can I find the value of any individual percentile? If not what assumptions would I need to make to determine ...
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Unique matching for quantiles from one half of the density to a subset of the other half?

I am interested in finding the median absolute distance to quantiles. So, for $Q_\alpha$ the $0 \le \alpha \le 1$ quantile, I would like to find $Q_\gamma^*$ such that $Q_\gamma^*$ satisfies ...
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1answer
89 views

calculating percentiles for transformation into standard normal quantiles

I'm trying to hand calculate a standard normal quantile plot. The first step involves transforming the data into percentiles. That sounded like the easy part, but apparently there are several ...
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64 views

z scores, highest percentile ranking, different distributions

Let a value $x$ have a z-score of (say) $+0.10$. With respect to which distribution(s) can $x$ have the highest percentile ranking: normal, positively skewed, or negatively skewed?
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What is the multivariate analog of the median?

There is a univariate mean: sum the points and divide by the count. There is a multivariate mean analog - the centroid, a point in a multidimensional space. (1). For the median one sorts the list ...
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2answers
170 views

Using bootstrap to obtain sampling distribution of 1st-percentile

I have a sample (of size 250) from a population. I do not know the distribution of the population. The main question: I want a point estimate of the 1st-percentile of the population, and then I want ...
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Quantiles written as the expectation of a transformation?

Consider a continuous random variable $X$, with finite defined mean $E[X]=\mu$ and variance $E[X^2]=\sigma^2$. Notice that the variance of $X$ can be written as the expectation of a transformed ...
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51 views

How to quantify the similarity between two samples using quartiles only?

I have several sets of samples I would like to compare. Each set is comprised of two samples, for which I only have the quartiles, min/max values and sample size for each sample. I would like to ...
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1answer
48 views

Empirical Distributions

I am working with a small data set that is clearly non-Gaussian. This data is bound within a fairly narrow range. I have been asked to estimate the quantiles of the population that this data is from. ...
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Quantile estimation based on non-random sample points

This is my first post. I am curious to understand that what is the effect of using non-random sample to estimate the population quantile with sample quantile? Let say, I need to measure the 10th ...
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1answer
56 views

Partial sorting: select at most N elements including for sure the top T elements

To whom it may concern. My "population" with known size P is a landscape and has not more than 4 peaks with about same high. Naturally top elements group locally within the population. I seek the top ...
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1answer
86 views

Find the degrees of freedom of a F distribution given its 97.5th percentile

Let's suppose I have a F distribution $f$ with unknown degrees of freedom $df_{numerator}=df_{denominator}=df$. If I know the 97.5th percentile $f_{0.975}$ such that $P(f>f_{0.975})=0.025$, is it ...
3
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1answer
106 views

Difference between the forecast and simulate functions in the {forecast} package in R

I have been using the forecast package in R to make forecasts based on an ARIMA model and have noticed a difference in the output of the forecast and simulate functions when calculating confidence ...
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1answer
202 views

Quantiles of a compound gamma/negative binomial distribution

Are there any formulae for the quantiles of a compound gamma/negative binomial distribution? That is, suppose we have $$N \sim \text{NegBin}(\alpha, \lambda)$$ and conditional on $N$, $$Y = ...
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1answer
70 views

When to report proportions and when to report median + IQR for ordinal variable

A colleague brought to my attention documentation for a standardised questionnaire which recommended using the median and interquartile range to describe summary variables created by combining ...
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1answer
122 views

Fitting an exponential distribution to data and finding third quartile problem

I have a data-set with range of 0 to 1. I'm fitting a distribution to it in MATLAB using ...
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1answer
138 views

Error on interquartile range

How can I compute the error on the interquartile range of a sample? By error I mean its std deviation (e.g. error on the mean = RMS/sqrt(N)). The sample is from a unimodal distribution, similar to ...