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

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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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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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29 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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38 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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30 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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45 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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45 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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50 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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80 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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32 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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134 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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57 views

Multidimensional quantiles

I have 1000 observations with 2 continuous variables : Observation ID | X | Y
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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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60 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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57 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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131 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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85 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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70 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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111 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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68 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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61 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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341 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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157 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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150 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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92 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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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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235 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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102 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 ...
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56 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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95 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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67 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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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 ...
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395 views

How to determine quantiles (isolines?) in a multivariate normal distribution

I'm interested in how one can calculate a quantile on a multivariate distribution. In the above picture, I have drawn the 5% and 95% quantiles on a given univariate normal distribution (left). For ...
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306 views

How to convert percentile rank into z score in R

I have a vector of percentile ranks. I want to convert them into z-scores, so it will be interval scale. I have to do it in R, but I could not find a function or package that can do this. Does anyone ...
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99 views

Standard Deviation of percentages

Say I have a bunch of weighted coins that should show heads 90% of the time. I take a bunch of them, throw them in a box, and calculate the percentage of coins that landed on heads. I do this a bunch ...
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261 views

Are there techniques to merge two cumulative distribution functions?

I'm trying to estimate quantiles from cumulative distribution functions. Given N CDFs are there techniques that can be used to merge them to form another CDF from which a quantile can be estimated ? ...
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Method for calculating percentiles for a set of time series

I have a set of time series for a given quantity (e.g. CPU). The measurements are roughly evenly spaced, but the data points aren't synchronised between sets and some sets have missing measurements. ...
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48 views

Estimating number of data points in specific range from percentile data

If I have a dataset broken down into percentiles, such that I know there are n values, and 10% of these values fall below x1, 20% are below x2 and so on, how can I estimate an answer to the following ...
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98 views

Why we use infimum in the definition of Quantile function

I looked up the definition of Quantile function in Wikipedia, it is said that: The Quantile function is $Q(p)=\inf\{x\in R:p\le F(x)\}$ for $F:R\to(0,1)$, for a probability $0<p<1$, the ...
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76 views

Error bars on a logarithm

I'm plotting the following point using python (a and b have are non gaussian): x=np.log10(a) y=np.log10(b) xmedian=np.median(x) ymedian=np.median(y) and I ...
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How to accurately track the 75% quantile in a non-stationary timeseries?

I have a non-stationary timeseries with a mean (µ) and standard deviation (SD) which both vary across time. The distribution of the timeseries is skewed, so the left and right sides of the ...
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52 views

How to get the quantiles by simulations?

I would like to find the quantiles of a random variable $X$ by simulations. I plan to do it in the following way, however, I do not know which one should be more correct though the results look very ...
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113 views

Which quantile type (quantile calculation method) is best for small samples?

The R help page of the quantile function lists 9 types of quantiles, i.e. 9 methods to calculate sample quantiles. Which method suits small sample sizes best? Which method will give the most similar ...
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205 views

Percentiles of a distribution

I'm measuring error on the median of my data using bootstrapping. I would like to obtain I sigma error bars on my data, so I'm measuring the 16th and 84th percentiles of my data. Should I divide these ...
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85 views

Best estimate for a decile or quintile mean from a known distributional family?

Suppose you have a population drawn from a known distributional family f with a vector of unknown parameters θ. You may also assume that the distribution is strictly non-negative and skewed, with a ...
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135 views

VaR in case of ARMA-GARCH?

How do I calculate the VaR in case of using an ARMA-GARCH approach? I am not good at time series, so I am more or less confused with the different possible notations of an ARMA-GARCH process. I hope ...
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What do people call the groups into which quantiles divide the population?

Is there a correct technical name for the group of observations between two quantiles? For example, if you have the values of the four cut-points that divide a population into five groups of equal ...