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

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How to perform quantile transformation with missing values?

Given are an input vector $I$ with missing values and a target/reference distribution ${T}$. For example: $I$: 0.215 NA 0.103 0.649 0.057 0.292 NA 0.433 0.521 NA $T$: -0.996 -0.606 -0.394 -0.090 ...
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Top Percentile Definition

Suppose I am in the top 10 percentile of a particular test. (I know what it means to be in the tenth percentile, but not the top tenth percentile) Does this mean I am in the top 10% of all ...
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34 views

Help with intuition about Chi-Squared distribution and its relation to Normal Distribution

At $\alpha = 0.05$, the significance cutoff of a Chi-squared distribution with 1 df is approximately 3.84, and that if we take the square root of 3.84, it's approximately 1.96, which is the 97.5 ...
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Why the quartile of daiky stock returns are different to the estimated normal model [on hold]

Explain why the empirical quantiles of a daily stock returns series are unlikely to correspond to the quantiles of an estimated normal model with constant mean and constant variance fitted to the same ...
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1answer
19 views

Non-central t-distributions with different degrees of freedom

I have two non-central t distributions with CDF given by $t_{n,a}$ and $t_{m,a}$ with $n>m$ degrees of freedom respectively and the same non-centrality parameter $a$. The question is: for which ...
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quantile of standardized t distribution

How to show that, for any given left tail probability, the corresponding quantile of standardized t distribution is increasing in degree of freedom for left tail probability less than 0.5? This is ...
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7 views

How do I determining the exact percentile among a sample given the 10, 25, 50, and 90 percentiles

Background: I'm trying to provided employees or decision makers with comparative wages analysis based on national or regional wage estimates. I'm developing a tool to provide employees and clients an ...
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2answers
63 views

Why is the QQ Plot for Normal Distribution a Straight Line?

Pardon my basic question on this, but I could not find why the QQ Plot for normal distribution is a straight line. Also, according to the accepted answer here: Percentile vs quantile vs quartile ...
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23 views

How do I calculate quantiles for groups containing infinity?

I am looking at prescribing of drug A versus prescribing of drug B. I have the following A/B ratios: ...
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9 views

Ergodicity and percentiles

The mean ergodicity of a homogeneous/stationary random field/process is such a property under which given a sufficiently long realization, the mean of the realization converges to the mean of the ...
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46 views

Calculate the mid-60% range

I need some help please! I am not too sure how to answer question 1.3 regarding the "mid-60& range". Are they looking for 60th percentile? Thanks for the assistance!
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Ranking districts (on basis of % cahnge) after controlling initial conditions

We want to rank Indian districts as good/bad/average performer on the basis of change in access to latrine between 2001 and 2011. We calculate the percentage point change in access to latrine ...
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26 views

How many samples do I need to compute long tail percentiles (99.99th)

I have a time series data set and I would like to compute a moving percentiles starting from median, 95th, up to 99.99th. My question is, what should be the size of my window, i.e. how many samples ...
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33 views

Calculating 25th/75th Percentiles

If I know the minimum, maximum, mean and median is there an approximation which will enable me to calcultate the 25th and 75 percentiles? Thanks.
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1answer
24 views

Calculating “distances” from quantiles

I am trying to compare the measurements from two different methods, A and B, that have each reported 16%, 50%, and 84% quantiles for a measurement X. How can I capture in a number how far away A and B ...
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Computations of Durbin-Watson quantiles

For some educational reasons I am currently trying to re-compute Durbin and Watsons (1951, Paper II) critical values of the lower and upper bounds of their Test-Statistic (dL and dH), and also table ...
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Derivative of a Riemann-Stieltjes integral (quantile regression)

(Moved from the mathematics site as I didn't receive any response there) In pp. $5−6$ of Roger Koenker's Quantile Regression, the author minimizes the function ...
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24 views

Is it valid to instrument endogenous variables one at a time?

I am a Stata user and am attempting to implement the IV Quantile regression method of Chernozhukov and Hansen (2008), for my model, which has two endogenous variables, call them "GD" and "ED". I am ...
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28 views

Calculate the non centrality parameter (ncp) for non central chi squared distribution

I have the 0.975-quantile value (0.191) and the degree of freedom (k=1). How can i calculate the non centrality parameter ? in R if possible. Q0.975(k=1, ncp= ??) = 0.191
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Using quantiles for correlation

Here's hoping that people don't get irritated if this was a repeat question, or perhaps not the best place to post this question -- I'm new to the community. My stats skills are basic, but I will ...
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Equivalence of definitions of quantiles

Let us define the concept of quantile of order $\tau$ of a random variable $X\in F$ in two different ways: Definition $1$: $c_\tau$ is said to be a quantile of order $\tau$ if and only if $lim_{x\to ...
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1answer
10 views

Calculating age-adjustments for column percents

I am having trouble understanding how SUDAAN calculates adjusted column percents and I'm hoping someone can explain. Let's say I have 3 variables, gender(M/F), happyness (binary happy/sad), and age ...
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Calculate percentile from ranks

I am trying to come up with a formula to calculate my percentile finish in fantasy sports games while also learning some statistics along the way. Rather than trying to work with the complete list of ...
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Analytical properties of sample quantiles in statistical packages

When studying and proving properties of sample quantiles, such as its consistency or its asymptotic normality, every text I have seen uses the standard definition of this estimators. This is, given a ...
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1answer
48 views

Understanding The Algorithms Behind Quantile() in R

So I was trying to compute the quantiles from a dataset in R: c(3,5,7,8,12,13,14,18,21) using the quantile() function, and I realised that it was returning ...
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How to calculate theoretical quantiles of an odd dataset?

In order to calculate a set of theoretical quantiles I usually apply the following method: $\frac{1}{2. N} + \frac{x}{N}$ so here this makes: $\frac{1}{24} + \frac{6}{12}$ $\frac{1}{24} + ...
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Normaldistribution function of quantile [closed]

Im looking for an upper bound (not just 1) of the following $$ \Phi(\alpha_1 \Phi^{-1}(\alpha_2)) $$ where $\Phi$ is the distribution function of the standard normal and $\alpha_1$ and $\alpha_2$ are ...
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Meaning of a plot obtained by 'quantile' function of R

I have a following plot that is obtained by using the quantile function of R: Could anyone explain me what the plot means? The input X to the quantile function QUANTILE(X, P) is a '180x100 'matrix. ...
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45 views

How to calculate quantiles?

Could someone please show(!) and explain step-by-step how to calculate the theoretical quantiles for the following normally distributed dataset: {1,1,2,2,2,3,3,5,8,14,24,40} Given this table: ...
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How is $\beta$ of the $\beta$-Quantile called?

I was often wondering how to call $\beta$ of the $\beta$-quantile of a distribution. Of course, $\beta$ is a probability or proportion. But is there an official name for it? So instead of saying ...
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178 views

How can I calculate the mean and standard deviation given three percentiles using Matlab?

I have the percentiles of 3 values. The percentiles are 5th, 50th and 95th. The values respectively are 340, 365 and 385. How can I find the median and the standard deviation given that data follow a ...
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40 views

Calculating actual quantile from poorly defined lognormal distributions

I have a dataset in which the uncertainties in various parameters are modelled with a lognormal distribution. After the experiment I get a single number result. As part of a lookback to understand how ...
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Quantiles of big areas to calculate the associated quantiles of small areas

I have this question to solve and i don't understand it: How can i use quantiles of big areas to calculate the associated quantiles to small areas and construct a table that gives me the 0.05, 0.025 ...
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Asymptotic normality of order statistic of heavy tailed distributions

Background: I have a sample which I want to model with a heavy tailed distribution. I have some extreme values, such that the spread of the observations are relatively large. My idea was to model this ...
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How to compute the VaR(a) of the following cdf

I have to compute the mean value, the variance, the VaR and ES of the CDF F(x)= 1- (3/2x)^(-3) if x>= 3 F(x)=0 if x< 3 The mean and variance I have computed, but what about computing the value at ...
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Combine multiple Monte-Carlo estimates

I use a Monte Carlo simulation (say 100.000 runs) to estimate parameter in R. I have memory problems and my first thought is to run multiples times my estimation program (say 500 times) . My ...
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Linearly scaling a distribution (X) to have the same 5th and 95th percentile of distribution (Y)

As done in this paper here: I would like to linearly scale a distribution such that it has the same 5th and 95th percentile (0.05 and 0.95 quantile) as another distribution. That is, given two ...
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References on how to calculate quantile of a population from a small sample

I'm a novice in statistics. I need to study a problem that basically consists in checking if the 5% quantile of a population (that can be assumed normally distributed) is above or below a given value ...
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72 views

Linear Properties of the Quantile Function

Suppose $X$ is a random variable with continuous distribution function $F(x)$ and quantile function $Q_X(p)$ and let $Y = aX + b$ for some constants $a > 0$ and $b$. How can I prove that $Q_Y(p) = ...
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Asymptotic Distribution of Sample Quantile

My question is related to the proof below. Why can we say that $F^{-1}(Y_n(x))=X_{[np]}$? I would like to understand better the reason for that. Any help would be appreciated. I've also asked ...
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170 views

Relation between Quintiles and the Arithmetic Mean

I have a set of final exam grades for an entire year of students, and I need to calculate quintiles from them. How should I go about it? Also, is the range from the arithmetic average and the top of ...
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cdf based bias correction

I have three sets of climate data: obs, baseline (model) and future (model) data. I have calculated the cdf for all series of above data sets, I have also calculated the cdf of projected future. But I ...
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Quantile regression on non linear data

R and statistics beginner here, trying to do a quantile regression on a non-linear dataset. I want to identify datapoints that have a higher y axis value that expected given their value on the x ...
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2answers
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Using quantile in predict for survival

I am working on survival analysis and fit a model: ...
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56 views

How does anova.rq compare estimates from quantile regression in the quantreg package for R

I am using the quantreg package in R to develop quantile estimates at different taus, then using anova to test whether the Beta ...
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117 views

Uncertainty of PDF quantile estimated from empirical PDF [duplicate]

I want to determine the quantile of a probability density function (PDF). I do not know the distribution, but I have a sample that was generated from it. I estimate the quantile of the distribution ...
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Quantile aggregation for a sum of dependent variables

I am currently working with a sum of dependent variables following complex laws. For these laws I have a vector of means, $\mu$ and a linear correlation matrix $\Sigma = \rho_{i,j})_{i=1..n,j=1..n}$. ...
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What are the consequences of removing the tails of a distribution?

I would like to know the consequences of removing the tails of a distribution by deleting observations above and below certain thresholds. For instance, if one were to calculate the percentiles of a ...
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176 views

Removing outliers and calculating percentiles with highly variable data

I want to be able to rank and get percentiles for groups of scores from a range of organisations. These percentiles will be used to judge other organisations. The organisation's scores are an average ...
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111 views

Estimation of quantile given quantiles of subset

Let's say we have sets $X=\{x_1, x_2, \ldots, x_m\}, Y=\{y_1, y_2, \ldots, y_n\}$ and we have some estimate (or exact) quantile information about them at some level $a$. How could we approximate the ...