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 do I find the range? Details below

"The average mark in a grade 9 math class is 75.5% with a standard deviation of 9.5%. If Grade 9 math marks have a normal distribution: b) Within what range of marks are 99.7% of all students?" In ...
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Relationship Between Percentile and Confidence Interval (On a Mean)

This question came up at work when someone asked me what the relationship was between a percentile and a confidence interval, and I had a very hard time articulating my thoughts. The context was a ...
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Estimating quantiles by bootstrap

It's known that one shouldn't use bootstrap to estimate minimum and maximum of the distribution which are quantiles. I have heard the reasoning that quantiles cannot be bootstrapped because quantile ...
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Hypothesis testing for quantiles

Suppose we want to test $H_0: q_\tau=q$ vs. $H_a: q_\tau>q$, where $q_\tau$ is the quantile of order $\tau$ of a certain population. A popular test for this hypothesis is the sign test, which ...
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Error estimation from resampling

In my data analysis I must always keep the errors (or uncertainties). In physics, a result without an error estimate is worthless. Take this trivial example: I measure $x$ and convert it to the ...
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Estimate value of dependent variable such that P(Y>y|X=x) = p

I want to model a dependent variable Y on an independent variable X (and possibly some covariates as well). In my situation, it is safe to assume that the relationship is monotonically increasing. ...
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Sparsity estimators

I've recently started to read about sparsity estimation. Let's recall that the sparsity function is defined as $s(\tau)=f(Q(\tau))$, where $f$ is the population density and $Q$ is its quantile ...
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Is it possible estimating Conditional Skewness with Quantile Regressions?

I am studying Quantile Regressions (Koenker, R. and Bassett, G. (1978)). But i cant find a work that uses Quantile Regressions to estimate Conditional Skewness. There is some work/article who did ...
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Tobit distribution QQplot

I have data where a tobit model (based on normal distribution and censored at zero) would fit quite well, e.g.: d <- rnorm(200, 1, 2) d[d < 0] <- 0 I ...
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What does quantile parameter represent in estimate_bandwidth during Mean Shift Clustering?

I was doing Mean Shift clustering in a set of data with Python Scikit learn.We need to estimate bandwidth during Mean shift clustering.But what does the parameter quantile in the function "...
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Calculating percentile conditional on continuous variable

I have a collection of datasets with (x,y) - pairs where the value of y is conditional on x. Neither the distribution of x nor of y is known, n is ranging from 1000 to 10000. Here is the scatterplot ...
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Percentile rank for list of event freqencies.

I have a global list of event frequencies and then another list of local event frequencies for another population of the same type. The objective is to compare the local frequencies with the global ...
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sum of quantile for GEV distribution

Let $q_x$ and $q_y$ be $p$-quantiles for $\text{GEV}_X$ and $\text{GEV}_Y$, where $\text{GEV}_V$ stands for the Generalized Extreme Value distribution associated with sequence of r.v. $(V)_1^n$. That ...
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Power calculation - categorised continuous exposure in case-control study

I have a continuous exposure that I would like to catagorise it into quantiles according to the distribution of control (i.e. 25% controls in each exposure level group). From pilot study, I know that ...
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Convergence of the distribution of 0.05 quantiles through Monte-Carlo simulation

I am trying to get admitted to a masters in quantitative finance (I come from a computer science background), so next week I will have 3h to solve an exam in statistical computing using my favourite ...
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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 -0....
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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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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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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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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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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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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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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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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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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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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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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 $(\tau-1)\int_{-\infty}^\hat{x}(x-\hat{...
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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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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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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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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} + \frac{...
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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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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: http:/...
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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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321 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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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 ...