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

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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
24 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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51 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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16 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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14 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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53 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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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
44 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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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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215 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
70 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
28 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
36 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
207 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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25 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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1answer
83 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
209 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
43 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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92 views

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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45 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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65 views

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
56 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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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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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
81 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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77 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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54 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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68 views

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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134 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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31 views

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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38 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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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
80 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 ...
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101 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
145 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
62 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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100 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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114 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 ...
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Are there any inverse distribution graph that looks like this?

I want to generate random numbers according to a distribution curve like the inverse cummulative normal curve. But the curve should allow parameters to adjust the parameters as shown in the image, ...
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1answer
178 views

How to calculate standard error of sample quantile from normal distribution with known mean and standard deviation?

I know that the standard error of the mean for an iid sample is calculated as $$\frac{\sigma}{\sqrt{n}}$$ However, assuming a normal distribution with known mean and standard deviation, how do you ...
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25 views

Test for two confidence intervals

I would like to know if there is a test for the difference of to means m1 and m2 (continuous variables) if I have only information for mean, 2.5%- and 97.5%-quantiles. For example: $m1 \ \ \ = ...
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1answer
136 views

How to get percentiles from empirical density in R?

The density() function in R allows me to enter observations and get an empirical density that I can plot x and y values. I like ...
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1answer
35 views

Estimate Mean and Standard Deviation from Percentiles

I have a derived dataset that specifies the percentiles from the 10th to 95th in increments of 5 along with the total number of data points. Is there a way to estimate the mean of the original ...
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3answers
213 views

Top scoring students across a series of tests

I have a number of students and their scores across a series of tests, all of which have equal importance in my model. I would like to identify the top scoring students (e.g. top 10%). My first idea ...
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Can you do change of variables with quantiles? i.e. from quantile for the CDF $F(x)$ , get quantile for the CDF $F(x)^{\kappa}$?

I have a random variable $Z$ with some CDF $F(z)$ and quantile $Q(p) \equiv F^{-1}(p)$. I have $Q(p)$ in closed-form but not $F(z)$. Create a new random variable $\hat{Z}$ defined so that the CDF ...
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116 views

Conditional Expectation via Integral over Quantile Function

Following this thread "Does a univariate random variable's mean always equal the integral of its quantile function?" I tried to do a similar thing for a conditional expectation. It seems like my ...
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expected shortfall and value-at-risk

I once read a R example of computing Value-at-Risk and expected shortfall as follows ...