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

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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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21 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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34 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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43 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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78 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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28 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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13 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
35 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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27 views

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
54 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
56 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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1answer
53 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
56 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
35 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
38 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
86 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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1answer
21 views

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
77 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
66 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
31 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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37 views

Average of percentile ranks

I have a number of objects (e.g. students) and their scores (possibly transformed into percentile ranks) across various events (e.g. tests). I would like to identify the students who consistently ...
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1answer
31 views

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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99 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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39 views

expected shortfall and value-at-risk

I once read a R example of computing Value-at-Risk and expected shortfall as follows ...
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1answer
62 views

income elasticity + regression + household survey data

I'll try to be concise and up to the point: Problem: estimate income elasticities for various products from household survey data. Given: I have to big complex household survey datasets that uses ...
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1answer
113 views

Online estimation of quartiles without storing observations

I need to compute quartiles (Q1,median and Q3) in real-time on a large set of data without storing the observations. I first tried the P square algorithm (Jain/Chlamtac) but I was no satisfied ...
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70 views

Find parameters $\alpha$ and $\beta$ of a beta distribution, if I have one quantile and the mean [duplicate]

Suppose I'm given the mean and one quantile (e.g. the 95% quantile) of a random variable $x$, and I want to find the parameters $\alpha$ and $\beta$ of a Beta distribution that has the same mean and ...
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1answer
88 views

Confidence Interval for Percentile for Empirical Distribution

I have a bunch of raw data values that are dollar amounts and I want to find a confidence interval for a percentile of that data. Is there a formula for such a confidence interval? Thanks for any ...
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29 views

Categorizing personality outcomes

I measured the five factor model (extraversion, neuroticism, openness to experience, and agreeableness) and the results gave me a continuous value between 1-5. Using these values as an IV is giving me ...
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1answer
34 views

getting from Edgeworth expansions to Cornish Fisher Expansions

I am currently trying to work out how to get from the Edgeworth expansion to the Cornish-Fisher expansion. I use van-der-Vaarts "Asymptotics Statistics" and Hall's book on Edgeworth expansions and the ...
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44 views

Estimation of percentiles in multivariate posterior distribution

Background: I am using Bayesian inference to find a posterior density. The parameters are change points in a piecewise Wiener process, and I wish to calculate the hitting time of some threshold $a$. ...
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100 views

New Systematic Quantile Normalization

I think I've developed a systematic quantile normalization technique. I did this with music but I think it can also be done with light and other frequency based information. The algorithm is as ...
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1answer
44 views

45th and 55th percentile

I have a series of data from a household budget survey and want to do the following in SPSS: Identify the food expenditure shares of total household expenditure that are at the 45th and 55th ...
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31 views

A statistically valid method of comparing values lying outside of a distribution with values within that distribution

I recently interviewed farmers about their memories of annual crop production and compared this with diaries they had kept recording actual quantities harvested. I would like to know where ...
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1answer
37 views

(very basic) One-sample test for binary data

I've repeatedly measured a continuous variable and each measure has been assigned a populational percentile range it falls into (percentile ranges were estimated for general population in another ...
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50 views

Figuring out quantiles in quantile regression

Suppose I have a dataset $\{y_i,x_i\}$ $i=1,2,...n$. For the response variable, $y_i$ as per quantile regression I have the following likelihood: $$p(y_i|\beta,\alpha_i,\sigma) ...
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Analysis of model input resolution

I am using a fine resolution soil dataset to run a climate model, and want to explore the impact of aggregating the soil properties at different resolutions on model output. E.g. how do the results ...
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2answers
101 views

Is there a way to compute daily percentiles (median and 95th) using 24 hourly percentiles

Basically I have max, count, median and 95th percentiles for every hour for a data stream already pre-computed from an hourly workflow. Can I use these 24 snapshots to get an approximate median and ...
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1answer
51 views

What is a conditional quantile function?

What is conditional quantile of $Y(t)$ given $Y(t-1)$ where $Y(t)$ is a univariate time series (they call it conditional value at risk in risk management). Can anybody explain this? Thanks
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101 views

Estimate population quantiles from subpopulations' quantiles

Suppose there is a population partitioned arbitrarily into a set of subpopulations that completely cover the original population. Assume that for some variable, we know each subpopulation's quintiles ...
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72 views

Validating statistical tests for value at risk and expected shortfall

I am trying to figure out if value-at-risk (VaR, a quantile) type tests could capture if expected shortfall (expectations above a quantile) point forecast generated from a type of model could be ...
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1answer
67 views

Can you determine if variances are equal when quartiles are similar?

I am comparing 2 different data sets. I have broken down each set into quartiles. I am looking at the percentage of increase between the quartiles (example there was a 125 percent increase between ...
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2answers
319 views

Confidence interval of quantile / percentile of the normal distribution

What is the formula (if it exists) for the sample variance / confidence interval of a quantile / percentile of the normal distribution? For example, the 5th percentile for a standard normal ...
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57 views

Evaluating Expected Shortfall

I am writing my thesis on VaR and ES risk measurements and have encountered some issues with how to best test the accuracy of ES statistics. My understanding of the topic is that backtesting ES ...
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2answers
392 views

How can I get the percentile rank of a given score if I know the scores at standard percentiles?

For a distribution, let's say I know the scores at the 10th, 30th, 50th, 70th and 90th percentiles. I also know the interquartile range and range. Is it possible to get the exact percentile rank of a ...
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1answer
68 views

Multidimensional quantiles

I have 1000 observations with 2 continuous variables : Observation ID | X | Y
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81 views

Calculating confidence intervall for quantiles first by hand (than in R)

It would be great if someone can check whether my approach is correct or not. Question in short will be, if the error calculation is the correct way. lets assume i have the following data. ...
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77 views

What's the name of this quantile curve estimation technique?

I'm still working with the same dataset as in a previous question here. Quantile regression has taken me some way, and now I'm going further. The underlying relationship between these x and y ...
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1answer
90 views

Generate QQ plot for sets of different size

I'm coming from this question Similarity between two sets of random values (which still stands BTW) where @whuber suggested in the comments that I use a Q-Q plot to assess the similarity of two ...