Linked Questions

5 votes
0 answers
336 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 ...
user27606's user avatar
  • 109
4 votes
0 answers
281 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,...
Arjun's user avatar
  • 73
0 votes
0 answers
37 views

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
34 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 ...
TotalFailure's user avatar
1 vote
0 answers
26 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 ...
blamp05's user avatar
  • 11
284 votes
11 answers
167k views

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
34k 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)? ...
mary's user avatar
  • 211
18 votes
2 answers
24k 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 ...
Py-ser's user avatar
  • 451
10 votes
2 answers
7k 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....
shamalaia's user avatar
  • 285
6 votes
3 answers
2k views

"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
4k 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 $$ f(k) = {n \choose k} p^k (1-p) ^{n-k} \tag{1} $$ ...
Tim's user avatar
  • 138k
16 votes
3 answers
2k 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 ...
David Robinson's user avatar
4 votes
4 answers
10k 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. ...
needshelp's user avatar
9 votes
1 answer
1k views

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
3k 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 ...
Nicolas De Jay's user avatar

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