All Questions
774 questions
3
votes
2
answers
26k
views
Given P(A) and P(B), what would be the minimum probability of the intersection?
Like if I was given a P(A) of .5 and a P(B) value of .4 how would I get the minimum of the P(A∩B)?
- 41
2
votes
2
answers
618
views
Predicting a maximum value with little data
My problem is i'm trying to figure out how many servers might be required to handle a theoretical maximal load of data requests. To do that I need to know what the maximum number of requests in a ...
- 123
12
votes
2
answers
3k
views
Order statistics (e.g., minimum) of infinite collection of chi-square variates?
This is my first time here, so please let me know if I can clarify my question in any way (incl. formatting, tags, etc.). (And hopefully I can edit later!) I tried to find references, and tried to ...
- 696
5
votes
1
answer
1k
views
How to apply Mahalanobis weighted regression in R?
Some research has shown that in linear regression applications the Mahalanobis distance approach can be used to perform regressions that lower the influence of outliers. The idea is that in the ...
- 3,091
2
votes
1
answer
209
views
The min draw from F(x), where the max is an order statistic of the max draws from different, yet overlapping distributions?
Consider $m$ independent draws from each of $n$ distributions. $X_{i,j}$ the $i_{th}$ draw from cdf $F_{j}(x)$. where $1 \leq i \leq m$ and $1 \leq j \leq n$. Therefore we have $m\cdot n$ total ...
- 1,049
9
votes
2
answers
932
views
What is the distribution of maximum of a pair of iid draws, where the minimum is an order statistic of other minima?
Consider $n\cdot m$ independent draws from cdf $F(x)$, which is defined over 0-1, where $n$ and $m$ are integers. Arbitrarily group the draws into $n$ groups with m values in each group. Look at the ...
- 1,049
1
vote
1
answer
27k
views
How to get expectation (E-value) for a dataset? [closed]
For an examination, scores for 10 students (all from class 4B) were obtained. I want to convert each score to E-value.
If I understand correctly, to calculate E-value I have to determine an ...
- 611
3
votes
2
answers
2k
views
Is my data fit "extreme value distribution" or "normal distribution"?
I have a large data.frame in R. I would like to double if its distribution fit normal distribution or extreme value distribution better
Here is my simplified data.frame.
...
- 31
5
votes
2
answers
1k
views
Calculating the distribution of maximal value of $n$ draws from a normal distribution [duplicate]
According to normal probability distribution theory which says that for $n$ independent,
identically distributed, standard, normal, random variables $\xi_j$ the expected absolute maximum is
$E(\max|\...
- 505
7
votes
1
answer
190
views
Estimate the nearest of N random points in a box in E^d?
I have N uniform-random points $p_j$ in a box in $E^d$,
$a_i \le x_i \le b_i$,
and want to estimate the expected distance of the point nearest the origin in $L_q$:
$\quad$ nearest( points $p_j$, box $...
- 3,297
14
votes
4
answers
1k
views
Unbiased estimator for the smaller of two random variables
Suppose $X \sim \mathcal{N}(\mu_x, \sigma^2_x)$ and $Y \sim \mathcal{N}(\mu_y, \sigma^2_y)$
I am interested in $z = \min(\mu_x, \mu_y)$. Is there an unbiased estimator for $z$?
The simple estimator ...
- 141
2
votes
0
answers
354
views
Understanding the Pareto distribution as applied to wealth
The Pareto distribution can be used to give a pdf for the wealth of a person chosen randomly from a population. (In fact, this was its origin. See, for instance, http://en.wikipedia.org/wiki/...
user3463
12
votes
3
answers
5k
views
How to estimate parameters for Zipf truncated distribution from a data sample?
I have a problem with the estimation parameter for Zipf. My situation is the following:
I have a sample set (measured from an experiment that generates calls that should follow a Zipf distribution). ...
- 375
9
votes
1
answer
3k
views
The code variable in the nlm() function
In R there is a function nlm() which carries out a minimization of a function f using the Newton-Raphson algorithm. In particular, that function outputs the value of the variable code defined as ...
- 22.4k
30
votes
7
answers
21k
views
How to calculate Zipf's law coefficient from a set of top frequencies?
I have several query frequencies, and I need to estimate the coefficient of Zipf's law. These are the top frequencies:
...
- 319
7
votes
3
answers
1k
views
How do extreme values scale with sample size?
Assume I have a random vector $X = \{x_1, x_2, ..., x_N\}$, composed of i.i.d. binomially distributed values. If it would simplify the problem substantially, we can approximate them as normally ...
- 8,879
6
votes
1
answer
483
views
Quantile extrapolation?
Suppose you wanted to estimate the $q$ quantile of a distribution by observing $n$ independent draws from that distribution, but with $q < \frac{1}{n}$. What methods are available, and for what ...
- 15k
3
votes
1
answer
182
views
Basics of extreme values / high-water marks?
With real-valued $X_1, X_2, \ldots$, define
$Max_n := \max(X_1,\ldots,X_n)$ record value or high-water mark
$NextMax_n :=$ the next greater high water, $Max_{n+m} > Max_n$
$Up_n := NextMax_n - ...
- 3,297
5
votes
2
answers
836
views
Is there an analytical expression for the distribution of the max of a normal k sample?
For example:
k <- 100
R <- 10000
max.g <- numeric(R)
for(i in 1:R) max.g [i] <- max(rnorm(k))
hist(max.g) # We can see it's right tailed...
I ...
- 21.9k
7
votes
1
answer
2k
views
Tangency portfolio in R
I am trying to solve for an efficient portfolio in R. How do I translate my constraints for a tangency point for 2 risky asset portfolio, and a given risk free rate to R solve.QP function? So ...
- 2,799
9
votes
3
answers
10k
views
What is the expected MINIMUM value drawn from a uniform distribution between 0 and 1 after n trials?
Assume you draw a uniformly distributed random number between 0 and 1 n times. How would one go about calculating the expected minimum number drawn after n trials?
In addition, how would one go ...
- 597
7
votes
1
answer
449
views
How can I apply a Pareto tail to a truncated distribution?
Many income surveys (especially older ones) truncate key variables, such as household income, at some arbitrary point, to protect confidentiality. This point changes over time. This reduces inequality ...
- 71
9
votes
4
answers
855
views
Why is the average of the highest value from 100 draws from a normal distribution different from the 98th percentile of the normal distribution?
Why is the average of the highest value from 100 draws from a normal distribution different from the 98% percentile of the normal distribution? It seems that by definition that they should be the ...
- 19k
83
votes
3
answers
105k
views
How is the minimum of a set of IID random variables distributed?
If $X_1, ..., X_n$ are independent identically-distributed random variables, what can be said about the distribution of $\min(X_1, ..., X_n)$ in general?
- 941