Linked Questions

5 votes
0 answers

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 ...
user27606's user avatar
  • 109
4 votes
0 answers

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,...
Arjun's user avatar
  • 73
0 votes
0 answers

Median for Normal Distribution [duplicate]

Please can someone explain the steps for deriving the probability density function of median for Normal Distribution
Srishti Batra's user avatar
1 vote
0 answers

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 ...
TotalFailure's user avatar
1 vote
0 answers

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 ...
blamp05's user avatar
  • 11
284 votes
11 answers

How would you explain covariance to someone who understands only the mean?

...assuming that I'm able to augment their knowledge about variance in an intuitive fashion ( Understanding "variance" intuitively ) or by saying: It's the average distance of the data ...
PhD's user avatar
  • 14.7k
19 votes
5 answers

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)? ...
mary's user avatar
  • 211
18 votes
2 answers

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 ...
Py-ser's user avatar
  • 451
10 votes
2 answers

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....
shamalaia's user avatar
  • 285
6 votes
3 answers

"Weighted Median": statistical properties and connection to the sample variance

Suppose we only have the following information: A set of sample means : $\bar{x_1}$, $\bar{x_2}$ ... $\bar{x_k}$ The sample size used to calculated each sample mean: $n_1$, $n_2$ ....$n_k$ The ...
stats_noob's user avatar
10 votes
2 answers

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 $$ f(k) = {n \choose k} p^k (1-p) ^{n-k} \tag{1} $$ ...
Tim's user avatar
  • 138k
16 votes
3 answers

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 ...
David Robinson's user avatar
4 votes
4 answers

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. ...
needshelp's user avatar
9 votes
1 answer

Distribution of half-life from radioactive decay

Suppose that $X$ measures the half-life of a radioactive element, with decay rate $\lambda$ (per unit of time). Starting from a population of $N$ particle, I believe you can model the number of ...
FZS's user avatar
  • 395
9 votes
1 answer

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 ...
Nicolas De Jay's user avatar

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