Linked Questions

5
votes
1answer
912 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 ...
57
votes
5answers
17k views

Central limit theorem for sample medians

If I calculate the median of a sufficiently large number of observations drawn from the same distribution, does the central limit theorem state that the distribution of medians will approximate a ...
14
votes
3answers
24k views

Standard error of the median

Is the following formula right if I want to measure the standard error of the median in case of a small sample with non normal distribution (I'm using python)? ...
8
votes
2answers
3k views

Confidence interval for the median

I have a set of values ${x_i}, i=1, \dots ,N$ of which I calculate the median M. I was wondering how I could calculate the error on this estimation. On the net I found that it can be calculated as $1....
4
votes
1answer
3k views

Reporting quartiles in bar plots

I have some non parametric data and my supervisor wants me to use bar plots to visualise it. He said because I'm using the median, that my error bars should be the 1st and 3rd quartiles....I get that ...
2
votes
1answer
3k views

How much sense does median of one number make?

Median of one number = the number itself. I am calculating the median price sq ft of properties of different areas based on the different data entries I have got that include their ID, area and ...
2
votes
2answers
657 views

How to estimate high end percentile (e.g. >90%)

Say my dataset is of size $N$, and I want to calculate the 90th percentile. Suppose $N$ is too large that I can't compute the percentile by going through the entire dataset, what is the best way to ...
5
votes
1answer
85 views

Basic calculations with Order Statistics

I've come across the following problem, and I am tempted to delve into order statistics to solve this. I would greatly appreciate any help! Suppose you draw 6 independent samples from a continuous ...
3
votes
1answer
146 views

Confidence interval for quantiles: distribution-free, asymptotic and assuming a normal distribution

An acquaintance of mine has been using this wrong inference formula for years: given a i.i.d. sample $\mathbf{X}={X_1,\dots,X_N}$ for a continuous RV $X$, sample mean $\bar{X}=\frac{\sum X_i}{N}$ ...
1
vote
0answers
49 views

Seeking a general solution to confidence intervals around ranks

Often test takers are ranked based on their test scores (e.g., people taking a civil service exam) and often those test scores are rounded before being ranked, producing many ties). How might I go ...
1
vote
0answers
27 views

Confidence on the median for a weighted empirical distribution

I have observation data $x_1, \dots, x_n$ with associated positive weights $w_1, \dots, w_n$ such that $\sum_i w_i = 1$, representing a "weighted" empirical distribution with CDF $$ \hat{F}(x) = \sum_{...