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

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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
47 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
22 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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28 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
27 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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75 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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20 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
38 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
89 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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55 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
65 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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26 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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18 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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37 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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96 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
36 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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29 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
35 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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47 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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16 views

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
83 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
49 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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2answers
79 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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63 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
58 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
202 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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44 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
254 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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66 views

Multidimensional quantiles

I have 1000 observations with 2 continuous variables : Observation ID | X | Y
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60 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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72 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
75 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 ...
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174 views

Modelling zero-inflated percentage data in R

I have a response variable of percent cover of vegetation in a quadrat. I have tried to arcsine square this data as recommended in the Crawley R book but I am not getting good fit. The data is ...
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1answer
95 views

Demonstration of sample quantile bias

While doing some simulations, I realised that the sample quantile is a biased estimator of the true quantile. And, according to my simulations, a potentially very biased one. I was surprised with ...
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95 views

Percentile rank transforming z-scores

I have been looking through methods to convert z-scores to positive values, without taking absolute values and somehow taking the sign of the score into account (I avoided taking absolute value, ...
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135 views

Using quantile regression to predict probability of surpassing threshold

Consider a continuous response $Y$ and design matrix vector $\mathbf{X}$. These are related through some function $f(X) = Y$. Suppose that I am interested in estimating the probability that $Y \leq ...
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1answer
83 views

CDF (cumulative frequency) of multiple samples in summed normals?

Say I have some normally distributed data. I have an application where I compute the percentile (or cumulative frequency less than sample) for a particular sample using a CDF function along with the ...
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1answer
85 views

Function to find the quantile in a vector corresponding to constant $x$ [closed]

Suppose I have constant x=0.1 in the language R and I have a vector vec = rnorm(200). Is ...
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1answer
514 views

Percentile to Z-score in PHP or JAVA

I am searching for a way to calculate the $z$-score for a given percentile $p$. I found this site doing such a calculation. They have given a formula for calculating $P(Z\leq z)$: $$ \Phi(z) = P(Z ...
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2answers
241 views

Calculating percentiles

Lets say I have multiple table representing 10 countries, and tables contains user_id, and user_score. Example: ...
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1answer
181 views

How to estimate a standardized mean difference from two samples' quartiles?

I'd appreciate ideas about how to estimate the standardized mean difference (SMD) for two independent samples from each sample's size and middle three quartiles (i.e., median and 25th and 75th ...
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1answer
108 views

How should sampling ratios to estimate quantiles change with population size?

I want to cut my data of size N into k equal-sized bins. But I am happy with roughly equal-sized bins, with some $\varepsilon$ error. As precise quantiles of the data are computationally costly ...
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68 views

Should percentiles of one set of samples from a distribution wrt another set be uniformly distributed?

I'd like to pose the following question which for some reason is proving to be unclear to me. Assume we have the Normal distribution, mean 0, sd 1. Let's say we take 1000 samples from it; call them ...
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4answers
309 views

Algorithm for a 5 star rating system

I'm creating a reporting tool that produces a data set and calculates a metric for each item in the data set. I have two algorithms that I'm working with: an algorithm that produces the metric and an ...
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1answer
124 views

Multimodal data - where does one tail end and the other begin?

I have some observed (i.e., not generated by any hypothesized distribution, but generated by real processes) data that I believe is bi-modal (it may have more modes than two). In this dataset, there ...
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15 views

Determine significant transitions in data values

I don't have much experience with statistics and suspect this is a common problem with a common solution. Normally I would just eye-ball the data and call it a day, but at some point you ought to ...
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1answer
63 views

The X quantile of the difference between two RV's

To first provide some context, I have two boxplots (displaying median, 25th, and 75th percentiles), and I'm wondering what a boxplot of the difference between these two boxplots would look like. The ...
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1answer
129 views

Derive percentiles from binned data

The question below was asked on a sister site (Stack Overflow) back in 2010 by a user still active there (to me it seems more suitable here, for example quite similar to 21422): I have a bunch of ...
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77 views

The Central Limit Theorem in Quantile Estimation

I don't have a very strong background in statistics so I have a few conceptual questions and there is a strong possibility I'm missing something obvious. Suppose I'm interested in estimating the 99th ...
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102 views

Using percentiles as predictors - good idea?

I am thinking about a problem which is to predict log(spend) of a customer using linear regression. I am considering what features to use as input and wondering if it would be OK to use the ...