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

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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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80 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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19 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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57 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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24 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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53 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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27 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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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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84 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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23 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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51 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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101 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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59 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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71 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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26 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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40 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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98 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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38 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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36 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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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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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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50 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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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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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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60 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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234 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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46 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
289 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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67 views

Multidimensional quantiles

I have 1000 observations with 2 continuous variables : Observation ID | X | Y
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64 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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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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80 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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198 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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97 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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106 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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144 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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84 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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89 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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566 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
286 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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197 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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110 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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70 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
334 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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136 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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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 ...