Linked Questions

5
votes
0answers
236 views

The Central Limit Theorem in Quantile Estimation [duplicate]

I don't have a very strong background in statistics so I have a few conceptual questions and there is a strong possibility I'm missing something obvious. Suppose I'm interested in estimating the 99th ...
4
votes
0answers
167 views

Is there a statement for the median like the central limit theorem for the mean? [duplicate]

According to the Central Limit Theorem (CLT) in statistics, the distribution of the average of randomly sampled n observations tends to follow normal distribution as the sampling size n becomes larger,...
1
vote
0answers
21 views

Showing p-th sample quantile is asymptotically normal [duplicate]

I'm working through van der Vaart to improve my knowledge on asymptotic statistics, and I'm attempting the following problem. Let $F_n^{-1}(p)$ be the p-th sample quantile of a sample from a ...
1
vote
0answers
13 views

How to find approximation of variance of $i^{th}$ order statistic [duplicate]

Given PDF and CDF of a distribution, how does one find an approximation of $(\operatorname{Var}(X_i))$ using a normal approximation of $(X_i)$? According to "Mathematica Laboratories for ...
8
votes
2answers
2k 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....
8
votes
2answers
3k views

Confidence intervals for median

I have a distribution of samples with a small number of values in each one (less than $10$). I have calculated the median for each sample, which I want to compare with a model and obtain the ...
7
votes
2answers
1k views

Beta as distribution of proportions (or as continuous Binomial)

Beta distribution is related to binomial being also the distribution for order statistics. Probability mass function of binomial distribution is $$ f(k) = {n \choose k} p^k (1-p) ^{n-k} \tag{1} $$ ...
13
votes
3answers
975 views

What distribution does the inverse normal CDF of a beta random variable follow?

Suppose you define: $$X\sim\mbox{Beta}(\alpha,\beta)$$ $$Y\sim \Phi^{-1}(X)$$ where $\Phi^{-1}$ is the inverse of the CDF of the standard normal distribution. My question is: Is there a simple ...
4
votes
4answers
3k views

Does a sample have the same statistics as another sample taken from the same population?

Let's say I take a sample from a population and find the statistics of it like the mean, variance, minimum and maximum. Then, I take another sample from the same population and find its statistics. ...
7
votes
1answer
1k views

What is the mean and variance of the median of a set of i.i.d normal random variables?

Let $X_1$, ..., $X_n$ be identically independently distributed random variables with $N(\mu, \sigma^2)$ It is easy to show that sample mean $\bar{X} = \frac{1}{n}\sum^n_{i = 0}{X_i}$ is a random ...
2
votes
1answer
2k 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 ...
1
vote
1answer
1k views

variance of sample median of normal distribution

Does anyone tell me how to find the variance of sample median when random samples are normally distributed?? I know that I need to use the order statistics, but actually I don't understand how to ...
3
votes
2answers
304 views

Expectation of Median of Absolute Random Variables

Let $X_1, X_2,..., X_n$ from $N(0,\sigma^2)$. What I want to get is not $E(median(|X|))$ , but $E(median(|X_1|,|X_2|,...,|X_n|))$ Reason why I need it is because I'm studying LOWESS, and in using ...
2
votes
2answers
466 views

Meta-analysis: Estimating the population median

The Borenstein (2008) textbook I'm using doesn't make any references to estimating a population median. Searching the internet I find lots of references to using the median and range to estimate the ...
2
votes
1answer
679 views

distribution of 'median difference' in permutation test

Recently, I want to apply the permutation test to find out if the difference of median for sample1 and sample2 has difference. Sample1 variance is 3.225248, and Sample2 variance is 0.1451835. In my ...

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