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

learn more… | top users | synonyms (1)

0
votes
0answers
12 views

Different quantiles of a fitted GPD in different R packages?

I am performing an extreme value analysis for meteorological data, to be precise for precipitation data available in mm/d. I am using a threshold excess approach for estimating the parameters of a ...
4
votes
1answer
56 views

Best method to create growth charts

I have to create charts (similar to growth charts) for children of ages 5 to 15 years (only 5,6,7 etc; there are no fractional values like 2.6 years) for a health variable which is non-negative, ...
2
votes
1answer
32 views

Finding predictors of upper level of a variable

I am analyzing data on a health variable and its relation to age, gender, height etc. I am more interested in 90th percentile of the health variable, which can be called upper limit of 'normal'. How ...
1
vote
0answers
59 views

Estimating the 95th percentile of nitrate data using non-parametric Weibull method, with associated confidence intervals in R

I am currently involved in a project where I have to estimate the 95th percentile of nitrate data from different sample points, using the non-parametric Weibull method, to see if it breaches the ...
-1
votes
1answer
31 views

Sum of percentile rank scores of two or more variables

I need to sum some variables that are on different scales to make a new one. I'm wondering If it's correct to calculate the percentile scores first, and then to sum them up. Imagine I have to ...
3
votes
0answers
57 views

How to evaluate similarity of datasets based on summary data?

I have summary data that I want to compare to my own data. For the summary data I do not have access to the underlying data, however, I know the percentiles as shown below (A). I also calculated ...
3
votes
2answers
45 views

How to determine overlap of two empirical distribution based on quantiles?

I'm looking for a method to calculate "threshold" at which the $\alpha^{th}$ quantile of one empirical distribution is equal to the 1-$\alpha^{th}$ quantile of another empirical distribution. I had ...
5
votes
0answers
80 views

Limits on conditional expectation with normal margins and specified (Pearson) correlation

I saw the following question on another forum: "Suppose that both height and weight of adult men can be described with normal models, and that the correlation between these variables is 0.65. If a ...
1
vote
1answer
24 views

quantile regression with e.g. gamma distribution and log link

I have a basic question about quantile regression (I'm new to it): Why doesn't it seem possible to do a quantile regression with a specified family (e.g. gamma) and link function (e.g. log), as in a ...
0
votes
1answer
50 views

Approximating any percentile from 1st, 5th, and 9th decile

1) If I have the values for the 10th percentile, 50th percentile, and 90th percentile, can I find the value of any individual percentile? If not what assumptions would I need to make to determine ...
1
vote
0answers
20 views

Unique matching for quantiles from one half of the density to a subset of the other half?

I am interested in finding the median absolute distance to quantiles. So, for $Q_\alpha$ the $0 \le \alpha \le 1$ quantile, I would like to find $Q_\gamma^*$ such that $Q_\gamma^*$ satisfies ...
1
vote
1answer
49 views

calculating percentiles for transformation into standard normal quantiles

I'm trying to hand calculate a standard normal quantile plot. The first step involves transforming the data into percentiles. That sounded like the easy part, but apparently there are several ...
1
vote
0answers
49 views

z scores, highest percentile ranking, different distributions

Let a value $x$ have a z-score of (say) $+0.10$. With respect to which distribution(s) can $x$ have the highest percentile ranking: normal, positively skewed, or negatively skewed?
0
votes
0answers
52 views

What is the multivariate analog of the median?

There is a univariate mean: sum the points and divide by the count. There is a multivariate mean analog - the centroid, a point in a multidimensional space. (1). For the median one sorts the list ...
3
votes
2answers
97 views

Using bootstrap to obtain sampling distribution of 1st-percentile

I have a sample (of size 250) from a population. I do not know the distribution of the population. The main question: I want a point estimate of the 1st-percentile of the population, and then I want ...
3
votes
1answer
29 views

Quantiles written as the expectation of a transformation?

Consider a continuous random variable $X$, with finite defined mean $E[X]=\mu$ and variance $E[X^2]=\sigma^2$. Notice that the variance of $X$ can be written as the expectation of a transformed ...
0
votes
0answers
22 views

How to quantify the similarity between two samples using quartiles only?

I have several sets of samples I would like to compare. Each set is comprised of two samples, for which I only have the quartiles, min/max values and sample size for each sample. I would like to ...
2
votes
1answer
43 views

Empirical Distributions

I am working with a small data set that is clearly non-Gaussian. This data is bound within a fairly narrow range. I have been asked to estimate the quantiles of the population that this data is from. ...
3
votes
0answers
29 views

Quantile estimation based on non-random sample points

This is my first post. I am curious to understand that what is the effect of using non-random sample to estimate the population quantile with sample quantile? Let say, I need to measure the 10th ...
2
votes
1answer
56 views

Partial sorting: select at most N elements including for sure the top T elements

To whom it may concern. My "population" with known size P is a landscape and has not more than 4 peaks with about same high. Naturally top elements group locally within the population. I seek the top ...
3
votes
1answer
68 views

Find the degrees of freedom of a F distribution given its 97.5th percentile

Let's suppose I have a F distribution $f$ with unknown degrees of freedom $df_{numerator}=df_{denominator}=df$. If I know the 97.5th percentile $f_{0.975}$ such that $P(f>f_{0.975})=0.025$, is it ...
3
votes
1answer
67 views

Difference between the forecast and simulate functions in the {forecast} package in R

I have been using the forecast package in R to make forecasts based on an ARIMA model and have noticed a difference in the output of the forecast and simulate functions when calculating confidence ...
2
votes
1answer
89 views

Quantiles of a compound gamma/negative binomial distribution

Are there any formulae for the quantiles of a compound gamma/negative binomial distribution? That is, suppose we have $$N \sim \text{NegBin}(\alpha, \lambda)$$ and conditional on $N$, $$Y = ...
1
vote
1answer
49 views

When to report proportions and when to report median + IQR for ordinal variable

A colleague brought to my attention documentation for a standardised questionnaire which recommended using the median and interquartile range to describe summary variables created by combining ...
0
votes
1answer
65 views

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 ...
2
votes
1answer
97 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 ...
1
vote
1answer
23 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, ...
4
votes
1answer
121 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 ...
0
votes
0answers
25 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 \ \ \ = ...
2
votes
1answer
105 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 ...
2
votes
1answer
34 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 ...
7
votes
3answers
205 views

Top scoring students across a series of tests

I have a number of students and their scores across a series of tests, all of which have equal importance in my model. I would like to identify the top scoring students (e.g. top 10%). My first idea ...
1
vote
1answer
33 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 ...
2
votes
0answers
108 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 ...
1
vote
0answers
47 views

expected shortfall and value-at-risk

I once read a R example of computing Value-at-Risk and expected shortfall as follows ...
2
votes
1answer
81 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 ...
3
votes
1answer
139 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 ...
1
vote
1answer
79 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 ...
2
votes
1answer
99 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 ...
0
votes
0answers
29 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 ...
1
vote
1answer
38 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 ...
0
votes
0answers
52 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 $a$. ...
1
vote
0answers
106 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 ...
0
votes
1answer
53 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 ...
0
votes
0answers
32 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 ...
1
vote
1answer
39 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 ...
1
vote
0answers
52 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) ...
1
vote
0answers
19 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 ...
3
votes
2answers
122 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 ...
0
votes
1answer
55 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