The quantiles of a distribution refer to points on its cumulative distribution function. Some common quantiles are quartiles and percentiles.
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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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1answer
24 views
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 ...
3
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1answer
42 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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1answer
49 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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3answers
93 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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0answers
32 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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0answers
24 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 ...
2
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0answers
39 views
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 ...
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1answer
160 views
1sigma error on the mean
My x and y data (n) have a non normal distribution. I'm measuring the mean of the distribution (I'm using Python):
x_m=np.mean(x)
y_m=np.mean(y)
I would like to ...
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2answers
69 views
Compute cdf and quantile of a specific distribution
I want to calculate a quantile of a specific distribution. Therefore I need the cdf. My distribution is a standardized Student's-t distribution, this can be written as
\begin{align*}
f(l|\nu) =(\pi ...
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2answers
82 views
Is there a smooth probability density function with finite moments and a closed form quantile function?
I am looking for a smooth probability density function with finite moments and closed form quantile function. As one knows, an example of smooth probability density function with finite moments is the ...
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0answers
72 views
Is there a quick way to convert z-scores into percentile scores?
Does anyone know of a function or R package that can help me turn z scores into percentile scores?
The final goal is to classify or rank a group of respondents into four categories based on the ...
5
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0answers
107 views
VaR calculation
I am refering to this article:
RiskMetrics Technical Document - Fourth Edition 1996, December
One of their model is called RiskMetrics-GED and given by (p. 238-239):
on p. 242 they say
My ...
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0answers
21 views
R: Assigning variable to quintile on monthly basis [closed]
I am trying in R to indicate in which quintile a value of a variable is for every month of my data frame in this case based on volatility. For each month I want to know for each stock if it is in the ...
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0answers
72 views
Ftting a mixture of two Gaussians
I want to fit a mixture of two gaussian densities to my financial data. The data can be found here: http://uploadeasy.net/upload/2a7mw.rar the variable is called dat.
The probability density of a ...
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1answer
54 views
quantile transformation with t distribution
I'm wondering about the monotonic quantile transformation in case of a t distribution. First, for explanation, lets consider a normal distribution:
\begin{align*}
f(l | \mu , \sigma ...
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1answer
70 views
quantile threshold of t distribution and normal distribution
I want to calculate the quantiles of a t distribution and a normal distribution fitted to my data (can be found here: http://uploadeasy.net/upload/nk0f.rar).
The t distribution is leptokurtic, ...
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1answer
80 views
Quantile of a non standardized t distribution?
I have a non standardized t distribution with parameters $\nu$,$\beta$ (or sometimes also denoted by $\sigma^2$) and $\nu$. Now I want to get the quantiles of it. qt just calculates the quantile of a ...
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0answers
19 views
Grouping observations based on variables that sum to one
I have a problem where I am trying to group observations (most likely using k-means or a similar unsupervised learning tool) where each observation includes n-variables, with the total sum of these ...
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2answers
78 views
Compute Quantiles [closed]
I have a question about quantiles in medical statistics. I think it best to explain my question in an example.
Let's assume we have a population of mice. Some of these will get a disease of interest. ...
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1answer
76 views
Rank data from 1 to N (N may not be equal to number of elements in the dataset)
I calculate percentile ranks based on the method at http://www.psychstat.missouristate.edu/introbook/sbk14m.htm
I need to assign ranks to a dataset where ranks are ...
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1answer
35 views
How to assign ranks given the distribution above mean?
Say I have the following data,
% students below average in math: S1
% of students at proficient level in math: S2
% of students at above proficient level: S3
S1 + S2 + S3 = 100%
If I have this ...
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1answer
236 views
Finding gaussian distribution given 15th and 50th percentile.
My knowledge of statistics are small so I need a little bit of help.
I have some data showing the relationship between age and walking speed. The numbers of walking speed are presented only as the ...
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1answer
198 views
How to calculate median of distributed data?
How to find the median (or approximate median) of n chunks of values. The values in each chunk can be assumed to have been sorted if it helps. In addition, the existence of a histogram for each chunk ...
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0answers
79 views
Quantile regression analyzing the conditional quantiles of one of the regressors?
Given response $Y_t$ and predictor $X_t$, we can use OLS to analyze the conditional mean; $E[Y_t | X]$. Quantile regression can be used to analyze the conditional quantile function; $Q(Y_t(\tau)|X)$. ...
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1answer
368 views
quantile in scipy library
I am confused what is quantile in scipy.stats.norm.pdf function.
Definition of quantile says that k-th of q-quantile is essentially value which divides population into k/q and (q-k)/q parts. But if I ...
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1answer
84 views
terminology question: Is there a generic name for the set of probabilities corresponding to quantiles
Given a set $P_i$ of probabilities and a Cumulative Distribution Function of $X$ you can find the set $X_i$ of values of $X$ corresponding to $P_i$. The $X_i$ are the "quantiles". Is there an ...
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1answer
54 views
Average of rate of change in a set of independent change events
What is the right method for computing average of percentage values? Arithmetic average, geometric average, or something else?
Here's an example of problems I'm talking about. Suppose for years 2009, ...
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1answer
207 views
Percentile Ranks in Matlab
I have 2 vectors of raw values. I need to do a percentile rank correlation and an ordinal rank correlation between them in Matlab.
...
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1answer
184 views
(Quantile regression) Which standard error for heteroscedasticity & serial correlation
I have heteroscedastic and autocorrelated residuals in my multivariate quantile regression model.
What's the quantile regression standard error estimator that's robust to this? Something hopefully ...
5
votes
1answer
300 views
Beta distribution from mean and quantile
Suppose I'm given the mean and one quantile (e.g. the 20% 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 ...
5
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1answer
316 views
Is it possible to interpret standardized beta coefficients for quantile regression?
Is it possible to interpret coefficients from a quantile regression on standardized data?
Suppose I standardize the dependent variable $y$ and the independent variable $x$ (subtract the mean and ...
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2answers
377 views
Solving a simple integral equation by random sampling
Let $f$ be a nonnegative function. I am interested in finding $z \in [0,1]$ such that
$$ \int_0^{z} f(x)\,dx = \frac{1}{2}\int_0^1 f(x)\,dx$$ The caveat: all I can do is sample $f$ at points in ...
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0answers
63 views
Power Calculations for Median in a Clustered Trial
I'm currently performing power calculations for an NGO wanting to evaluate a sanitation program. They've asked us to look at the distributional effects of their intervention. I know that I can appeal ...
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1answer
93 views
Are $\sigma_{70\%} = cte * \sigma /\sqrt{N}$, & $\sigma_{\bar x_{70\%}} = cte * \sigma /\sqrt{N}$ valid with non-normal distributions?
My working population is non normally distributed and from time to time I need to take a sample of it. Sometimes my sample exists of 100 units, at other times of 150 units. Of my sample I calculate ...
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1answer
309 views
Is it possible for quartiles to have uneven groups?
If I have a data set with many values repeated (example below) how would it be divided into quartiles? I assumed at first that the quartiles would be uneven, but every single definition I've read ...
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1answer
95 views
Estimating ratios of quantile means for sorted data
In studying the relationship between income and consumption, it is common to sort the observations by income and observe that high-income households have lower levels of consumption per dollar of ...
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votes
1answer
122 views
Are sample means for quantiles of sorted data unbiased estimators of the true means?
In studying income inequality, it is very common to look at sample means for deciles or quintiles of the sample, and to assume that the sample means are good estimators of the true means. In this ...
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0answers
43 views
Estimating the quantiles of a latent variable
I am trying to estimate the quantiles of the function $f(x_i)$ in the equation:
$$
y_{it} = \alpha_i + f(x1_{it}, x2_{it}) + \epsilon_{it}
$$
My current, probably naive, approach is to run the ...
3
votes
1answer
495 views
How to interpret the results of the R pnorm and analogous functions?
The help for the pnorm function states:
It says that pnorm gives the "distribution function", but it seems that it gives the quantile,
for example, ...
4
votes
2answers
315 views
How does Cornish-Fisher VaR (aka modified VaR) scale with time?
I have already posted this question in the quant section, maybe the statistics community is more familiar with the topic:
I am thinking about the time-scaling of Cornish-Fisher VaR (see e.g.page 130 ...
5
votes
1answer
240 views
Is there a method to estimate distribution parameters given only quantiles?
is there a way to fit a specified distribution if you are only given a few quantiles?
For example, if I told you I have a gamma distributed data set, and the empirical 20%, 30%, 50% and ...
5
votes
2answers
134 views
Risk assesment and non-statistician's perception of percentages
I'm planning on doing quantile regression for estimating pain relief after hip surgery. My aim is to construct for my patients information in this format:
4 out of 5 patients experience with your ...
2
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0answers
163 views
Univariate- Variance preserving, order reversing transformation
This is a soft question: How can the order of a sample univariate data be reversed while preserving the variance?
7
votes
4answers
4k views
Quartiles in Excel
I am interested in the definition of quartile that is usually used when you're in basic statistics. I have a Stat 101 type book and it just gives an intuitive definition. "About one quarter of the ...
2
votes
2answers
665 views
Tool to draw normal QQ-plot with 45 degree reference line
I have some data (a set of numbers) and I want to compare them with the normal distribution using QQ-plot. The only statistical tool that I am aware of is Octave but Octave doesn't draw the reference ...
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0answers
155 views
Percentile calculation for the combined group
I was struggling to find some solution of my problem which is as below:
Let say, I have 20 groups and for each group I have say 10the percentile value. Then is it anyway possible to calculate the ...
4
votes
2answers
836 views
Quantile intervals vs. highest posterior density intervals
I am reading a bit about Bayesian analysis, but I cannot understand the difference between the classic quantiles and the Highest Posterior Density Intervals. What is the difference between the two? I ...
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1answer
213 views
Quantiles for non-normal cdf
When I compute the five-number summary on my sample, I obtain quantiles that differ from the quantiles I got from the empirical cdf, since they are not normally distributed data.
Can you help me in ...
4
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1answer
219 views
How much does quantizing continuous data affect power?
Background/how this came up:
A student has numeric ratings on a variety of items in questionnaires and sports performance data and would like to model the performance on questionnaire scores. He ...
