m******e
发帖数: 45 | 1 How to generate uniform [0,1] distributed random numbers with correlation
rho?
generating correlated gaussian r.vs are trivial, but it seems there is no
clean way
for uniform r.v. , any idea? thanks. |
|
c******s
发帖数: 90 | 2 Please see this link below.
http://www.noise.cz/sbra/sibram02/2-Ses/Fegan.htm
In this paper, the author present a way to generated correlated uniform R.V.
Another result you may be able to use is:
If X and Y are bivariate-normal with correlation rho,
Let Ux=normcdf(X) and Uy=normcdf(Y), then
Ux and Uy are bivariate-uniform with correlation
(6/pi)*arcsin(rho/2). |
|
c******s
发帖数: 90 | 3 Essentially the correlated bi-variate uniforms generated
by the second method can be viewed as a Gaussian copula with marginal
uniform distribution. You can calculate the spearman's rho, which
is given by that formula. |
|
b***k
发帖数: 2673 | 4 ☆─────────────────────────────────────☆
littletshirt (小仙鹤) 于 (Tue Oct 28 16:58:17 2008) 提到:
a) how to simulate uniformly distriuted portfolio weight w_i, i=[1,N], given the
constraints sum(w_i) = 1, and w_i >=0. N is constant.
b) now assume each holding in the portfolio has an attribute x_i, and x_i is
uniformly distributed in [0,1] and independent of w_i. What's the
distribution of sum(w_i*x_i).
many thanks.
☆─────────────────────────────────────☆
littletshirt (小仙鹤) 于 (Tue Oct 28 17:1 |
|
j******n
发帖数: 271 | 5 Assume U1, U2 are independent, uniform distributed in (0,1). Define
V1 = min(U1, U2)
V2 = max(U1, U2)
Prove that V1 conditional on V2 is uniformly distributed in (0, V2), i. e.,
P{V1 < x | V2 = y} = x/y |
|
o**o
发帖数: 3964 | 6 如果p是uniform, 上面曲线的积分等于2／3。可是凭啥假定p有prior而且是uniform?
★ 发自iPhone App: ChineseWeb - 中文网站浏览器 |
|
D**u
发帖数: 204 | 7 Is there a link (or name of the theorem) that the limiting distribution does
not exist (or is not uniform)?
., a Brownian motion, it does not have a limiting distribution (for BM, it's
simply diffusion on a closed surface, thus uniform). so i would naively
think the answer to (2) is no. i will try (1) when i get more time. |
|
a***s
发帖数: 616 | 8 首先有点confused，这个rand产生的是啥样的distribution? Uniform的？
要求产生1…7也是uniformly？
如果是这样的话，可以取25个不同正数，保证任意两个之和不等于其他两个。然后call
一次rand(5)，映射到前5个数中的一个；再call一次rand(5)，映射到后5个数中的一个
，然后取和。
把25个可能的和分成8组，前7组每组3个，最后一组4个。比较所得的和与组，若落在前
7组中的一组，取组号为rand7的结果，若为第8组中数，重新执行上述步骤，直到产生所
得结果为止。
理论上来讲这个program可能不终止，但实际上很容易就终止了。我试了运行这一程序1
00000次，最大的loop数是6，也就是说6次就能产生结果。而绝大多数则是1，平均loop
数是1.135。
这是我的matlab code
function [value, counter] = rand7_BY_rand5 ()
value = 0;
t = 22; %group sorter
counter = 0; %loop counter |
|
w********0
发帖数: 1211 | 9 其实最简单的方法（当然多半不是最高效的）是：
Call这个1-5的随机数7次，如果第一次得到的数最大，结果就是1，第二次最大就是2，
。。。，第七次最大就是7。
如果有并列最大的，比如有3个并列最大的，就再call三次分别对应这三个，选最大的
，直到选出来为止。
只要原来的那个1-5的随机数是i.i.d.的，那最后得到1-7的概率肯定是uniform的，（
甚至原来1-5的分布都不必uniform） |
|
s***t
发帖数: 49 | 10 I think, here the 31, 32 is the bit number.
If the assumption is that, both of them are uniformly distributed,
I think we can combine two 31bits to one 62bis, and just take 32 of them,
because each bit is uniformly
distributed as well. |
|
p*****k
发帖数: 318 | 11 assume uniform prob distribution for each process, i.e., each digit
is chosen uniformly from 0-9, then completely random permutation of
these 6 digits for the second step.
say for digit i, there are ni>=0 of them, with
n0 + n1 + ... + n9 = 6 (*)
easy to see, once given (n0,...n9) for the 2nd step, the prob of
getting the same number as the original is (n0)!*(n1)!*...*(n9)!/6!
originally there are total of 100,000 different numbers and for
each (n0,...n9), there are 6!/[(n0)!*(n1)!*...*(n9)!] of |
|
|
s*****i
发帖数: 93 | 13 2 independent random variables uniformly distributed in [0,1]. How do you
transform them, so that they stay uniformly distributed in [0,1], but the
correlation between them becomes \rho. |
|
b***k
发帖数: 2673 | 14 One question on the following solution I copied from wilmott.
let Z be an independant uniform variable
and
Y2 = X if Z< rho
Y2 = Y if Z > rho
Cov(X,Y2) = cov(X,X) * rho
and Y2 is uniform
(X,Y2) is our solution.
对于上面构造的Y2，如何计算E(Y2),Var(Y2),
为什么Cov(X,Y2)=cov(X,X)*rho?
是从公式Cov(X,Y2)=E(X*Y2)-E(X)*E(Y2)得到的吗？我推不出来啊。 |
|
w******g
发帖数: 67 | 15 【 以下文字转载自 JobHunting 讨论区 】
发信人: wyizhang (MM), 信区: JobHunting
标 题: 一道概率题目
发信站: BBS 未名空间站 (Thu Aug 26 19:53:59 2010, 美东)
A,C are iid random numbers uniformly distributed in (0,1)
B is random number uniformly distributed in (1/2,1)
What is the probability P(A>B,A>C)?
My answer is (1/2)*(3/8)=3/16. Is it correct? Thanks. |
|
d*e
发帖数: 843 | 16 Good point, it's not a martingale, and thanks a lot for all your
thoughts on this question. I'm not very familiar with Girsanov Theorem
though.
A second thought: $I(t)$ is still a supermartingale if we choose $c(s)$
non-negative and satisfyingall the conditions such that $I(t)$
converge in $L^2$ to 0.
Now that $I(t)$ is $L^2$-bounded implies that $I(t)$ is uniformly
integrable. By the MCT, a uniformly integrable supermartingale can be
closed and so $I(t)$ has an almost sure limit. ... 阅读全帖 |
|
T*****w
发帖数: 802 | 17 Two independent random variables uniformly distributed in [0,1]. How do you
transform them, so that they stay uniformly distributed in [0,1], but the
correlation between them becomes \rho.
不知道如何用copula的方法去解?
(另外：类似的题目是如果是两个 normally distributed z1, z2 ~N(0,1),（independently）
可以用 cholesky decomposition 的方法得到
x1=z1
x2=pz1 + sqrt(1-p^2) z2 |
|
i**w
发帖数: 71 | 18 背景:fresh physics PhD
还没offer,但年前基本上不会再折腾了。
有重复。基本上都是很标准的题。
简单的题如果人家想问倒你也是很容易的。
面试书recruiter推荐
1) Mark Joshi: "Quant Job Interviews: Questions and Answers". I have
heard very good things about this book.
2) Xinfeng Zhou, "A Practical Guide to Quantitative Finance Interviews"
个人觉得非常有用， 大部分问题都在这两本上。
算法，C++, stochastic calculus 就看比较标准的几本。
- sqrt(i)=?
- You and me roll a dice,first one gets a six wins. You roll first. what
is the probability of you winning?
- A stair of n steps. Each time you st... 阅读全帖 |
|
w**********y
发帖数: 1691 | 19 多谢分享.大概做了做..欢迎补充和指正.
- sqrt(i)=?
e^{\pi/4 i} or - e^{\pi/4 i}
- You and me roll a dice,first one gets a six wins. You roll first. what
is the probability of you winning?
P(I win) = P(Y !win and I win) = 6/11
- A stair of n steps. Each time you step up 1 or 2 steps. How many
different ways are there to reach the top? what is the asymptotic limit?
Fibonacci sequence ..limF(n)/F(n-1)==x for n>2, solve x, and F(n) ~ x^{n-1}
- Moment generating function of standard model.
statistic book…
- Write a si... 阅读全帖 |
|
t*******y
发帖数: 637 | 20 第二题应该是6/11吧
能讲讲这个吗? - X1 and X2 are independent random variable with pdf f and g.
what is what is the pdf of X=X1+X2
Jacobian matrix for X1+X2 and X1-X2..
多谢分享.大概做了做..欢迎补充和指正.
- sqrt(i)=?
e^{\pi/4 i} or - e^{\pi/4 i}
- You and me roll a dice,first one gets a six wins. You roll first. what
is the probability of you winning?
P(I win) = P(Y !win and I win) = 5/6*1/6
- A stair of n steps. Each time you step up 1 or 2 steps. How many
different ways are there to reach the top? what is the asymptotic... 阅读全帖 |
|
c****o
发帖数: 1280 | 21 They are from different companies, including hedge fund and IB.
1.How to find out first K biggest number in an array efficientely, time
complexity.
2. How to find out the memory layout of a class without initiate the class
3x_i are independent uniform distribution,let s_\tao denoted the first time
the sum exceed 1, what the expectation of \tao(answer:e)
4.A matrix which is ordered each row (left to right)and column(up to dowm),
how to find an element in the matrix?
5.Assume the temperature on th... 阅读全帖 |
|
w******i
发帖数: 503 | 22 Thanks for the post.
1.How to find out first K biggest number in an array efficientely, time
complexity.
2. How to find out the memory layout of a class without initiate the class
3 x_i are independent uniform distribution,let s_\tao denoted the first time
the sum exceed 1, what the expectation of \tao(answer:e)
4.A matrix which is ordered each row (left to right)and column(up to dowm),
how to find an element in the matrix?
5.Assume the temperature on the earth is continuous, prove that there e... 阅读全帖 |
|
f***u
发帖数: 32 | 23 话说小明家住Uptown，从GS下班坐地铁回家。他到地铁站的时间介于七点到八点之间，
uniformly distributed。去Uptown 和 Downtown的地铁这段时间到来的时间也是
uniformly distributed。小明由于刚从玉米地来到NYC，不知道uptown 和 downtown地
铁的区别，所以到了地铁站逮到最近的一班地铁就上。结果他郁闷地发现被地铁到
downtown的次数多于uptown的次数。
问：在什么情况下会出现这种情况。
Any idea? 在此替小明谢谢大家。 |
|
A**u
发帖数: 2458 | 24 不是的
他要的是 uniform [0,1]
X+Y不是uniform
所以原来的那个用在正态分布上的 decomposition不顶用了 |
|
k*****y
发帖数: 744 | 25 那我觉得大概是：
假设我们有一个(X, Y)，marginal是uniform，使得correlation是r != 0。我们就能定
义(X', Y') = (X, 1-Y)，这时(X', Y')同样有marginal是uniform，但是correlation
是-r。所以假设参数空间的measure保持这个对称性的话，E(r) = 0。 |
|
l******i
发帖数: 1404 | 26 Transformation Method and Accept-Reject Method
are two basic ways to generate random variables.
To summarize:
1. To generate iid uniform firstly:
Most programming languages have the ability to generate pseudo-random
numbers which are effectively distributed according to the standard
uniform distribution.
For instance, In C++, use srand().
2.
Given \rho to generate two N(0,1) with correlation \rho:
From 1, we can easily generate two iid U(0,1)
random variables P and Q;
Use Box-Muller transformati... 阅读全帖 |
|
h**********y
发帖数: 41 | 27 You are waiting for a bus at station. If the buses have an average arrival
time of 10 minutes and you arrive at the bus station at a random time. What
is your expected waiting time if the buses arrive according to a uniform
distribution? If you have waited for 2 minutes, how many more minutes do you
expect to wait?
绿书里给出了Poisson process的解法，但我想知道这类题目更一般的解法，如果换成
是uniform distribution 或其他将怎么解呢？ |
|
k*****y
发帖数: 744 | 28 请问如何定义buses arrival according to a uniform distribution?
Poisson process是从N(t) = # of arrivals at t开始定义，然后可以推出based on任
意时刻a，下一辆车到达的时间差是exponetial分布，跟时刻a无关，相当于memoryless
。所以expected waiting time可以make sense。
反过来定义的话，如果要得到memoryless的uniform似乎不是well defined的。
What
you |
|
r******n
发帖数: 4522 | 29 http://www.sec.state.ma.us/sct/sctlic/licidx.htm
上面：
Examination or Certification Requirements
Each investment adviser representative submitting an application for
registration must have met the requirements of either (a) or (b) below:
(a) Currently hold the professional designation of
Certified Financial Planner (CFP),
Chartered Financial Analyst (CFA),
Chartered Financial Consultant (ChFC),
Chartered Investment Counselor (CIC), or
Personal Financial... 阅读全帖 |
|
g***e
发帖数: 577 | 30 我的理解是这样的：首先假设两个车的时刻表是相互独立的均匀分布。
bus1 timetable: 12m,
bus2 timetable: 30n+t, t is uniformly distributed in 0-12,
now, Lets consider 0-12, 12-24, 24-36, 36-48, 48-60, 5 intervals ( 60 is the
common multiple
of 30 and 12 ).
if passenger arrives in 0-12 at x, then the waiting time is ( 12 - x ) if t
< x, ( t-x ) if t > x,
so it is double integral on a square,
if passenger arrives in 12-24 at x, then the waiting time is 6 on average
because no bus2 in this interval.
if passenger arrives in 24-36 at x... 阅读全帖 |
|
g***e
发帖数: 577 | 31 我的理解是这样的：首先假设两个车的时刻表是相互独立的均匀分布。
bus1 timetable: 12m,
bus2 timetable: 30n+t, t is uniformly distributed in 0-12,
now, Lets consider 0-12, 12-24, 24-36, 36-48, 48-60, 5 intervals ( 60 is the
common multiple
of 30 and 12 ).
if passenger arrives in 0-12 at x, then the waiting time is ( 12 - x ) if t
< x, ( t-x ) if t > x,
so it is double integral on a square,
if passenger arrives in 12-24 at x, then the waiting time is 6 on average
because no bus2 in this interval.
if passenger arrives in 24-36 at x... 阅读全帖 |
|
g***e
发帖数: 577 | 32 我的理解是这样的：首先假设两个车的时刻表是相互独立的均匀分布。
bus1 timetable: 12m,
bus2 timetable: 30n+t, t is uniformly distributed in 0-12,
now, Lets consider 0-12, 12-24, 24-36, 36-48, 48-60, 5 intervals ( 60 is the
common multiple
of 30 and 12 ).
if passenger arrives in 0-12 at x, then the waiting time is ( 12 - x ) if t
< x, ( t-x ) if t > x,
so it is double integral on a square,
if passenger arrives in 12-24 at x, then the waiting time is 6 on average
because no bus2 in this interval.
if passenger arrives in 24-36 at x... 阅读全帖 |
|
y****n
发帖数: 60 | 33 给的答案是：
int num = 5*(rand5()-1) + (rand5()-1);
if(num<21) return ( num%7+1);
不明白为什么第一行代码要两个相加？前面一个不就是0 到20 的uniform
distribution 了吗？两个random number 加之后并不是uniform 的distribution 啊？
谢谢。 |
|
s***e
发帖数: 267 | 34 For 1 you can use an algorithm similar to random sorting, i.e. pick a
uniform number S1 between 1..N, swap X[1] and X[S1], then pick S2 uniform
from 2..N, swap X[2] and X[S2], .., until you get N/2 done.
For 2 you can decompose C into things like C = U S U^T and the rest should
be easy to compute. |
|
d******e
发帖数: 17 | 35 The first question is simple. Fix one point. Then clockwise there are three
arcs with total length 1. Denote the the length of the three arcs as a,b,c.
Then we have a+b+c=1, a>0, b>0, c>0. Use c=1-a-b, then 0
Now we know the density for a and b is uniform in the triangle area (0
0
the triangle ABC, Denote points A=(0,0), B=(1,0), C=(0,1),D=(1/2,0), E=(0,1/
2), F=(1/2,1/2). See the following figure.
C|\
| \... 阅读全帖 |
|
H******i
发帖数: 4704 | 36 MIT牛人解说数学体系（推荐~）来源： 彭成的日志
数学如何一步步从初级向高级发展，更高级别的数学对于具体应用究竟有何好处。
集合论：现代数学的共同基础现代数学有数不清的分支，但是，它们都有一个共同的基
础——集合论——因为 它，数学这个庞大的家族有个共同的语言。集合论中有一些最
基本的概念：集合(set)，关系(relation)，函数(function)，等价 (equivalence)，
是在其它数学分支的语言中几乎必然存在的。对于这些简单概念的理解，是进一步学些
别的数学的基础。我相信，理工科大学生对于 这些都不会陌生。
不过，有一个很重要的东西就不见得那么家喻户晓了——那就是“选择公理” (Axiom
of Choice)。这个公理的意思是“任意的一群非空集合，一定可以从每个集合中各拿出
一个元素。”——似乎是显然得不能再显然的命题。不过，这个貌似平常 的公理却能
演绎出一些比较奇怪的结论，比如巴拿赫-塔斯基分球定理——“一个球，能分成五个
部分，对它们进行一系列刚性变换（平移旋转）后，能组合成两个一样大小的球”。正
因为这些完全有悖常识的结论，导致数学界曾经在相当长时间里对... 阅读全帖 |
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b***n
发帖数: 6 | 37
F=-dE/dz
E=-M.B for uniform material, E=-M.dB/dz
M can be calculated from the shape of object, you can assume
it is uniform. |
|
m********r
发帖数: 811 | 38 【 以下文字转载自 Physics 讨论区 】
发信人: miniplayer (mplayer), 信区: Physics
标 题: ion source
发信站: BBS 未名空间站 (Mon Aug 31 16:59:23 2009, 美东)
For an ion source, the maximum half-angle of ion emission from the source
is 18 milliradians. The source is biased to 10.5 kV and the aperture radius
is 2 mm. Assuming uniform emission of the aperture and uniform distribution
of particles over this range, what is the normalized emmitance from the
source if the beam consist of ions 40 Ar 9+? |
|
x******n
发帖数: 173 | 39 *the question might not be the exact
In which situation, SELECT is more efficient than IF/THEN ELSE?
A. In the small amount selected data which is randomly distributed for
numeric variables.
B. In the small amount selected data which is uniformly distributed for
numeric variables.
C. In the large amount selected data which is randomly distributed for
character variables.
D. In the large amount selected data which is uniformly distributed for
character variables.
Thanks |
|
B*********B
发帖数: 37 | 40 Can anyone tell me what is the correct answer for the following question?
In which situation, SELECT is more efficient than IF/THEN ELSE?
A. In the samll amount selected data which is randomly distributed for
numeric variables.
B. In the samll amount selected data which is uniformly distributed for
numeric variables.
C. In the large amount selected data which is randomly distributed for
character variables.
D. In the large amount selected data which is uniformly distributed for
character variabl |
|
w**********a
发帖数: 6 | 41 yes it is D.
When the data set is small, or the criteria is not uniformly distributed,
use IF/THEN-ELSE is more efficient.
If the data is large and the criteria is uniformly distributed, use
SELECT is more efficient. |
|
x***x
发帖数: 3401 | 42 If U is a random variable from uniform (0, 1) and V is random variable
from uniform (-1, 1); also, U^2+V^2<=1. It is said X=V/U is a cauchy
distribution. I tried to prove this by let X=V/U and Y=U. Using bivariate
transformation, I get f(X, Y)=Y/2. Also, I get the constraint
0
which has the cauchy form, but not exactly a cauchy distribution. The Pie
is missing, but i can't figure out where i went wrong. Any help will be
apprec |
|
|
e****o
发帖数: 690 | 44 how to find 4 highest and mean, median, I don't know to get median by
industry as grouping except using proc means. Any good coding?? 3X for your
reply.
data temp;
do i=90 to 107;
xx=abs(i/i**2 -100*uniform(7));
industry = 10;output;
end;
do i=108 to 130;
xx=abs(i/i**2 -100*uniform(7));
industry = 20; output;
end;
run;
proc sort data=temp; by industry descending xx;
data t1;
set temp;
id + 1;
if first.industry then id =1;
run;
data t2 ;set t1 ;
if id<5;
run;
proc |
|
z**********i
发帖数: 12276 | 45 Posting Date: November 17, 2010
Position: Population Analysts
Company: SRA International, Aurora, CO
SRA has 2 openings for population analysts on its team that provides
consultative, data quality management, analytical, and education services
for DOD health care clients. The team provides health policy and data
analysis; performs market, utilization and efficiency analyses; documents
problems, concerns and areas for improvement in military health care data;
and performs other evaluative functio... 阅读全帖 |
|
g*****k
发帖数: 623 | 46 原话是 A stick of unit length is broken randomly in two places.
我应该怎么理解这句话，我可以这么理解吗？
假设断在x_1, x_2上，且0
Can I assume that X_1 is uniformly distributed on [0,1] and
X_2 is uniformly distributed on [x_1, 1] conditional on that X_1=x_1?
这样的话，joint density function is 1/(1-x_1)
这肯定是不对的，希望指教是什么地方我混淆了概念。本人蔡鸟，请轻拍！
谢谢 |
|
a***r
发帖数: 420 | 47 嗯哪，懂了
主要在这个概念上当时没转过弯：
uniformly sampling from a finite population without replacement
marginal distribution of samples is still uniform
谢啦~ |
|
I*****a
发帖数: 5425 | 48 This question can be potentially useful. I don't know the answer.
A much simplified and somehow similar problem may be as follows:
We have a single continuous predictor x from some uniform distribution and a
response variable EY = b0 + b1*x. Instead of ranking x into bins, we round
x to w, which is usually assumed in real situations where exact measurement
is difficult.
a) we estimate b1-hat
b) we estimate d1-hat from EY = d0 + d1 * w
In this case, I think the predictor effect is less significan... 阅读全帖 |
|
s**********8
发帖数: 25265 | 49 Good Laboratory Practice
In the experimental (non-clinical) research arena, the phrase good
laboratory practice or GLP specifically refers to a quality system of
management controls for research laboratories and organizations to try to
ensure the uniformity, consistency, reliability, reproducibility, quality,
and integrity of chemical (including pharmaceuticals) safety and efficacy
tests.
GLP was instituted following cases of animal test fraud by pharmaceutical
and industrial chemical (mainl... 阅读全帖 |
|
s**********8
发帖数: 25265 | 50 Sterilization (microbiology)
http://en.wikipedia.org/wiki/Sterilization_(microbiology)
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