All Questions
774 questions
2
votes
0
answers
184
views
Posterior distribution
Suppose $X1,..,X4$ be iid from pdf $f(x|\theta)=\frac{1}{\theta}$ ,for $0<x<\theta$.
The prior distribution is
$\pi(\theta)=\frac{2}{\theta^3}$ , for $\theta>1$
I have to obtain:
a)...
- 851
1
vote
0
answers
115
views
Long tail of pareto vs. pearson IV distribution
I am told that wealth follows a Pareto distribution, and that IQ follows a Pearson IV distribution (http://www.abelard.org/burt/burt-ie.asp). Both Pareto and Pearson IV distributions have long tails. ...
- 11
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
2
votes
1
answer
57
views
Testing hypothesis about the location of the maximum point on a curve
I have data from an experiment on the relationship between PPI (the dependent variable, a measure of startle reflex attentuation by weak stimuli) and SOA (the main independent variable; it's the time ...
- 21
2
votes
1
answer
78
views
Modelling the tail only
I'm trying to model a real-world random variable that behaves approximately as a Gaussian, so a Normal distribution fit is reasonable but far from perfect.
However, I only care about its tail, that ...
- 451
1
vote
1
answer
43
views
What statistic to use to measure effectiveness of treatment on fluctuating process
I have a process $R$ that normally does something like a random walk between 0 and 1. I have a set of treatments. I believe that some of the treatments will bias the process $R$ in such a way that, ...
- 1,108
1
vote
0
answers
99
views
Fitting of bivariate data to a self-defined probability density function
I have a bivariate set of data points which I want to fit to a self-defined distribution (i.e. not standard normal or chi-square or like that, a different, let's say "new" density function). I would ...
- 11
1
vote
0
answers
171
views
What is the meaning of McFaddens Axiom: Irrelevance of Alternative Set Effect?
On page 110 of McFadden,1973 - Conditional logit analysis of Qualitative Choice Behavior, Frontiers in Economics, ed Zarembka, New York: Academic Press, pp. 105-142 the following three Axioms are ...
- 1,113
1
vote
0
answers
19
views
Good predictive models for a linear minimum bound?
Are there any good predictive models for a pattern like the left plot of the first figure? I'm trying to predict how long a file transfer takes (in seconds) according to its package size (in bytes). I'...
- 379
2
votes
1
answer
185
views
Meaning of return period on extreme events
If the distribution of the periods between an extreme event to another is a power law (as for example can be the return period of extreme earthquakes or flooding), the existence of the mean value is ...
- 2,098
1
vote
1
answer
52
views
Distribution of value closest to 0
Consider $K$ independent Laplace variables $X_i$ ($1 \leq i \leq K$) with mean 0 and scale $\lambda$. Let $X′$ be the variable taking the value of the Laplace variable whose absolute value is the ...
- 13
2
votes
1
answer
51
views
Estimating costs with extreme values
I am trying to estimate health care costs and I was wondering what the standard practice is for extreme values?
By extreme values I mean I have a large portion of my costs being zero and a small ...
- 979
3
votes
0
answers
142
views
Distribution of variable
How to find the distribution of $$\sum_{i=1}^n (X_i - X_{1:n}),$$ where $X_i$ are i.i.d. random variables and $X_{1:n} = \min(X_1,X_2,...,X_n)$?
I need to find the distribution in a particular case, ...
- 31
1
vote
0
answers
74
views
Mode of Joint Posterior - Maximization Problems
I have a problem whereby I get two different answers if I try to maximize a function.
let
$ \begin{bmatrix} Y_{o}\\ Y_{a} \end{bmatrix}|\phi\sim N (0,\phi^{-1}A^{-1}) $
$\pi(\phi)=\frac{1}{\phi}$,
...
- 121
1
vote
0
answers
15
views
How to write the set of indexes of Pareto optimal reward set in formal methods
I denote that a reward vector of an item $a$ as $r_a$. Say there is a set of items denoted as $A_t$. I want to get a set $A^\prime_t$ of items from $A_t$ that has non-dominated reward vectors. For a ...
- 123
1
vote
0
answers
26
views
Get level set from 3D dataset obtained exploring a 2D space parameter
I am exploring a 2 parameter space performing simulations. As a result I get a surface as a function of these 2 parameters. I know this is probably simple but I don't know how to look for it.
Now I ...
- 111
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
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
4
votes
0
answers
114
views
fitting the tail of a distribution in a regression tree
I have 3 integer valued time series $a_t$, $b_t$ and $y_t$ with $k$ observations. I want to fit $y_t$ with the 2 first, and for that purpose I use a regression tree like this:
test all combinations ...
- 141
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
4
votes
0
answers
79
views
Non-Analytic extrapolation
I have some samples of a stable real-world process. Its is polymodal, and does not cleanly fit any of the "textbook" analytic distributions. I need to make very accurate estimates of the maximum ...
- 9,853
1
vote
1
answer
41
views
How to test the significance of increase in sample interval range(s)?
Suppose we have two samples of a variable taken under different conditions: e.g. A1 without medical treatment and A2 after medical treatment. These are not necessarily normally distributed. Suppose A1 ...
0
votes
0
answers
30
views
Accounting for minimum dependent measure in data when fitting a distribution
I have what is possible a naive question. I am current comparing various models (i.e. distributions). And the comparisons do not involve different distributions but rather how the model is fed the ...
- 43
1
vote
0
answers
24
views
Newton Raphson Algorithm: negative semi definiteness [duplicate]
I would like to minimise the function $l(\theta|Y)$.
Given the Newton's method below
$$\theta^{(t+1)} = \theta^{(t)} - \left[l''(\theta\;|\;Y)\right]^{-1} l'(\theta^{(t)}\; | Y)\quad t = 0,1,...$$
...
- 1,893