# Questions tagged [quantiles]

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

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### Can we write $P(A > B)$ in terms of their quantile functions?

Suppose $A$ and $B$ are two independent, continuous random variables with bounded supports $[min, max]$ and densities $f_A(a), f_B(b)$ and CDFs $F_A(a), F_B(b)$. Can we write $P(A > B)$ in terms of ...
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1 vote
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### Prediction interval for continuous positive data including zeros

I am trying to figure out given a set of positive continuous numbers (including zeros) what would be the most appropriate way to calculate a prediction interval, or a normal range, i.e. a range in ...
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### Should I treat these data points as outliers?

Currently, I am building my analytics portfolio as part of the Google Data Analytics course. I chose the option to analyze Divvy Bike Sharing data for the year 2021. But now I'm currently stuck in the ...
1 vote
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### Combining distribution stats of multiple populations

I have the following statistics of two independent populations: First population: ...
• 51
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### Will taking mean of sample quantiles be an unbiased estimate the population quantile?

Say I have $N$ samples of 100 numbers all drawn IID from the same distribution $\mathcal{D}$. For each sample, I take the 95th quantile to get $N$ sample quantiles $\hat{q}_n$. Will taking the average ...
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### qBCCGo function in GAMLSS package (quantile function)

I am working with GAMLSS technique and I use LMS (with three parameters of mean,variation and skewness) method. I found the follwoing formula to calculate the lower limit of normal as the link ...
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1 vote
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### Correcting for sample size in skewed data

Empirically I have noticed that when data is skewed, and when for example interested in the 99th percentile of latencies, that it is difficult to compare experiments with different sample sizes ...
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### Estimates of the Quantile Regression

In the Quantile regresion model we assume that$$y_i=x_i^T\beta +\epsilon_i,\ i=1, 2, 3, ....,n$$ such that the conditional quantiles of the error terms are zero and for the OLS model we assume that ...
1 vote
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### Does the zeroth and 100-percentile exist and do the minimum and maximum of the data belong in those respective sets?

Does the zeroth and 100-percentile exist and do the minimum and maximum of a set of data belong in those respective sets?
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### Observation in Quantile Regression

i have 30 observations of yearly data and i try to do quantile but results is all of my variables is not significant. im wondering if we can use quantile regression on yearly data? or is there any ...
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### Best practice for estimating values between 5% and 95% CIs for multimodal distribution

How can I improve my quantile estimation method for estimating values between the 5% and 95% confidence intervals for a multimodal distribution (as a mixture of gaussians) ? Where the CI are only for ...
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### How to average multiple non-normal distributions?

I have the following statistics of two independent random variables: First random variable: ...
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### The best way to determine what percentile a range of numbers closely aligns with?

I have a table of ~600 numbers and percentiles like below: Data 40th 50th 60th 70th 80th 90th 71 53 55 57 60 63 68 101 78 81 83 88 92 102 121 89 94 98 105 110 123 209 146 153 163 171 176 189 68 ...
1 vote
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### Asymmetries in the DKW bound

Suppose I have $n$ i.i.d. samples $X_1,...,X_n$ drawn from a distribution with CDF $F$. We use the samples to form the empirical CDF: $$F_n(x)=\frac{1}{n}\sum_{i=1}^{n} \mathbb{1}_{X_i\leq x}$$ The ...
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