g****g
发帖数: 1828 | 1 In probability theory, the normal (or Gaussian) distribution, is a
continuous probability distribution that is often used as a first
approximation to describe real-valued random variables that tend to cluster
around a single mean value. The graph of the associated probability density
function is “bell”-shaped, and is known as the Gaussian function or bell
curve:[nb 1]
f(x) = \tfrac{1}{\sqrt{2\pi\sigma^2}}\; e^{ -\frac{(x-\mu)^2}{2\sigma^2}
},
where parameter μ is the mean (location of the pe... 阅读全帖 |
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t******g
发帖数: 2253 | 2 如果X和Y是joint normal,那么两个marginal都是normal，如果X和Y marginal是normal
，joint不一定是normal。举个很简单的例子，X是normal(0,1),Z equals to 1 with
probability 1/2, equals -1 with probability 1/2. Let Y=XZ, then Y is still
standard normal, but X and Y are not jointly normal. |
|
s******u
发帖数: 21 | 3 degenerate normal is still normal? has the same characteristic function of
the ordinary normal? 但是density function能表示出来吗？ 因为 inverse (sigma)不
存在？
如果degenerate normal is normal too， 那么 能找到反例吗？ all pairs are
normal,
but joint (x1,x2,x3) is not normal?
有现成的关于low dimension 和 high dimension distribution 的关系的理论吗？
谢谢:) |
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f**********g
发帖数: 107 | 4 如果这两个normal随机变量X and Y 可以组成一个multivariate normal，当然choose
L=(1, 1)，the sum is a normal. 但问题是是不是随便两个normal随机变量的joint
ditribution都是multivariate normal。我记得LX is univariate normal好像是一个
必要条件。 |
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n***p
发帖数: 7668 | 5 我从来没有“认为S的法向量经过f一定是变成了S'的法向量”，而且推导结果也不是
法向量变成了法向量。
我的推导里面有一个假定就是S是嵌入在一个高一维的空间里，这是为什么我把它写成
一个Zero Level Set. 而这个变换 y=f(x) 根本就是在这个高一维的空间里。
In the previous post, I did not say n' was a unit vector. And
it is in fact not in most cases. You need to normalize it if
you want the unit normal. But for LZ's original question, since
he was dealing with a surface integral, it may not be necessary
to normalize it, as it is just a change of variable, unless he
need to use other tricks like divergence theorem,... 阅读全帖 |
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f*******w
发帖数: 6 | 6 可以把Normal值 当作颜色值传入, 那么normal值就会被 rasterize 到 屏幕上.
glColor3f( normal.x, normal.y, normal.z)
glVertex3f( ..., ..., ... );
然后用 glReadPixels 可以读取他们.
BTW:
如果其实你想做的是per-pixel lighting, 可以把normal值当作3d texture coordinates
,
rasterization之后interpolated value会传给fragment program使用.
如 |
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d****r
发帖数: 135 | 7 independent 的话一定是normal。你可以随便设出两个normal distribution r.v.，然
后利用independence得到两个r.v.的乘积density function，进一步用积分计算他们的
和的density function，你会发现还是一个normal的density function。这个计算不难。
楼上给出的例子不是一个反例。因为nomarl distribution 有一个极限情况，可以被认
为是variance趋向无穷的情况。而那个反例恰好就是这样子的，它的density function
是在0点blow up，其它点值为0，这个在一些讲广义函数的书里被叫做delta 函数。因
为正规normal distribution实际上是热方程在一维情况下，初值为delta函数的基本解
的图像（似乎差个scalar），因此delta 函数恰好就是一个极限状态的normal
distribution。 |
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p*****e
发帖数: 15 | 8 We treat the 0 variance/covariance case as normal.
X is a random vector with n components.
Then X is multivariate normal if and only if
LX is univariate normal, for every 1 x n vector L.
See any general multivariate statistics textbook.
Therefore, the sum of two normals (indep. or not) is still normal if
we choose L=(1, 1). |
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s***e
发帖数: 267 | 9 Shiloh,
If X and Y are jointly normal, here is one easy way to solve your problem:
Define Z1=X-Y and Z2=2X+Y then they are jointly normal as well. So you write
down their joint Normal mean and variance. The conditional distribution of
normal is still normal, and here you only need the mean. Its formula is not
hard to derive, and you can easily google its answer. |
|
L*****k
发帖数: 327 | 10 如果X和Y是joint normal，那么这道题目很容易。在joint-normal下，condition
distribution还是normal，因此计算可以大大简化
如果joint不是normal，但是其他的给定分布，还是可以做的。只不过没有了condition distribution还是normal的这个特性，计算可能变难，很可能没有close form（可能某些指数分布族会简单些）
而如果joint的分布不告诉你，那就是题目有问题，没有joint，怎么可能求condition，那就是一个个joke题目 |
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s******u
发帖数: 21 | 11 x1, x2 are normal respectively normal, (x1,x2)不一定是normal;
但是如果(x1,x2),(x1,x3),(x2,x3)都是 normal, 那么(x1,x2,x3)一定是 normal 吗?
这是在看另一个Topic的论文中，突然想到的一个问题，很困惑。。。
谢谢了 |
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n*****n
发帖数: 3123 | 12 The statement is not correct. I didn't take a look at your proof, but it
should be wrong in somewhere.
Consider the case, X,Y,Z are all standard normal. Y is independent of X and
Z, but X and Z are not independent. So (X, Y) are bivariate normal, (Y,Z)
are bivariate normal, but (X,Z) may not be bivariate normal. Any examples
showing that marginal normal does not imply joint normal can be used here as
counterexample. |
|
b******n
发帖数: 4559 | 13 Shonda Rhimes Says She Isn't 'Diversifying' Television, She's 'Normalizing'
It -- There's A Difference
Shonda Rhimes proved long ago that she is a force to reckon with.
The growing influence she has had in television has not gone unrecognized
and has resulted in a major boost for ABC’s Thursday night network ratings.
However, more importantly, Rhimes -- who is the mastermind behind shows
like "Scandal," "Grey's Anatomy" and "How To Get Away With Murder" -- has
increased onscreen representation o... 阅读全帖 |
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h***i
发帖数: 3844 | 14 What is true is that if the random variable pair (X,Y) follows the bivariate
normal distribution, and Cov(X,Y) = 0, then X and Y must be independent.
But what is not true is that if each of X and Y is normally distributed, and
Cov(X,Y) = 0, then X and Y must be independent.
two random variables are each normally distributed, that does not
necessarily mean that they jointly follow a bivariate normal distribution
bell |
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L*****k
发帖数: 327 | 15 X是Normal R.V., Y是Normal R.V.，两个R.V.自然会有一个correlation \rho，这个条
件没有任何意义
2个Normal R.V.的joint当然不一定还是Normal
反之，如果joint是，那个两个margin(X or Y)都是 |
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t***l
发帖数: 3644 | 16 这种面试题去年申请的时候在版上看得多了。
简单的说，就是你不假设joint-normal就没法做。我的猜测是出这些面试题的人中有一
部分都不知道两个Normal RV可以不joint-normal的，所以两边就纠结了。一方刚从学
校出来的追求着是不是得加个假设什么的，另一方在墙街工作多年的面试官早就忘了什
么joint-normal（或者从来也没知道过）之类的事情。在实际模型上，很多时候都可以
假设这个条件的。 |
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j*****e
发帖数: 182 | 17 1. The performance of normality test is not that great. Simulate a large
sample from normal distribution and check it out yourself.
2. T-test is a robust test. Robust means even if the distribution is not
normal, as long as it is not very skewed, t-test still has great power. This
is mentioned in any intro stat book.
3. Checking normality is better said than done. I remember someone actually
simulated sample from normal distribution in SAS and plot the qq-plot. It
turned out that naked eyes can |
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w*******y
发帖数: 60932 | 18 AT&T Black Friday Sale: Refurbed iPhone 4 for $99
posted by Trey Trawick on Wednesday, November 24, 2010 at 7:04 pm.
If you dont mind purchacing a refurbished phone, then AT&T has a pretty
sweet Black Friday deal for you: 16GB iPhone 4s for just $99 on a 2-year
contract (A full 50 percent off the price of a brand new onewhich is not too
shabby). 32GB models will run you double that, (which is also a $50
discount from the regular refurbished price of $249.
For those who dont care about th... 阅读全帖 |
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l****z
发帖数: 29846 | 19 By Mark Rogers 12/28/2013 ·
This statement from GLAAD, a collection of gay and lesbian members:
“Phil Robertson should look African American and gay people in the eyes and
hear about the hurtful impact of praising Jim Crow laws and comparing gay
people to terrorists. If dialogue with Phil is not part of next steps then A
&E has chosen profits over African American and gay people – especially its
employees and viewers.”
The utter nonsense of that statement accusing Robertson of comparing gay
peop... 阅读全帖 |
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h*******r
发帖数: 1083 | 20 自己招过postdoc工作，也找过tenure track，不过都只找过很少几次。我一直以为自
己找工作的方式是在美国自古皆然的，可是看了莫宗坚教授最近的妙文，有点糊涂了。
基于我极为有限的经验，adviser／mentor总是要给学生／博后写推荐信的，如果不写
，就是表明对这个学生／博后的相当程度的不认可，等价与一封负面推荐信。
我找博后工作的时候，当然是自己投简历申请的，不是靠老板的条子；不过老板跟我说
，他还是跟他的一些朋友写信打招呼过，希望他们对我的申请多留意些。
我找博后工作，需要老板之外的外部推荐信。老板很费了些心思帮我选择推荐人：水平
差的自然不行，太牛的大牌教授也不好，因为他们不会给我认真写，并且还要把人品不
可靠的人排除在外。至于谁人品不可靠，我一个学生怎么知道，全靠老板几十年的革命
经验。
我的推荐信，基本都是（在老板帮我选定名单后）我自己请求的；不过其中一个比较大
牌的教授，是老板自己写信帮我请的，怕我自己请请不动。
如果说我是不是靠自己努力找的工作？某种程度上是的：自己写statement，自己找人
写推荐信，自己投简历。可是每一步，都有我老板不可忽视，并且是关... 阅读全帖 |
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w*******e
发帖数: 285 | 21 正在做intern,有一个关于normalization的问题。假设在一个物理机器上有两台虚拟机
，分别有两个程序A,B同时运行，然后我测量到了一系列参数，假设为v1-vk,然后对于
不同的A和B构造一个矩阵。
A1 A2 ... An
B1 v1,v2...vk v1,v2...vk v1,v2..vk
B2
B3
B4
...
Bm
我的目的是用不同行向量(n*k维）代表不同的B，然后对不同的B1到Bm进行分类。现在
的问题是不同的行有不同的range,比如A1:v1的方差跟A2:v1,A1:v2或者A2:v2都不同，
比较距离的时候如果用euclidean或者mahattan什么的都是方差大的列占便宜。我的意
见是对每行单独进行normalize,这样每行都有相同的方差和平均值。但是跟我一组的别
人坚持说要把同样的参数放在一起normalize,比如A1:v2,A2:v2 ... An:v2要放在一次
进行一次normalize,然后再放回各个列去，理由是它们 |
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n******7
发帖数: 12463 | 22 审一个算是领域内主流的杂志
一篇烂稿子，从写作到方法到组织都没法看
好像是几个美国拉丁裔投的
我要求也不高，可以你放几个正文里面都没提过的图是什么意思？
英语烂的我这外国人都看不下去了
结果其他reviewer几乎没意见，于是就修回了
一般修回的稿子，哪怕装模作样回应一下，我也就给过了
这个稿子还是很烂，最不能接受的是
他们有个图，大致是说normal细胞有两种sub-group，然后改变一下两者的比率，就可
以变成tumor细胞
我评论说这是错的
他们回复，对，我们写错了，不是normal/tumor细胞，是normal/tumor组织
我擦，这还是不可能啊。tumor组织肯定得有normal组织里面没有的tumor细胞啊
要不要放水呢？再放水要闹笑话吧 |
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p*****e
发帖数: 15 | 23 It is true that normal marginals do not imply the joint normal or
dependence structure. Feedback has given the counter example.
The condition that every linear combination is univariate normal
is sufficient and necessary.
See http://en.wikipedia.org/wiki/Multivariate_normal_distribution
choose |
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i**w
发帖数: 71 | 24 short rate model里，最简单的Ho-Lee model:
dR(t) = mu*dt + vol*dW(t)
为了缓解负利率的问题，加上mean reversion就得到了Vasicek model:
dR(t) = k*(b-R(t))*dt + vol*dW(t)
面试就可能会问:把上面这个R(t)解出来，是什么distribution?mean和variance是什么
之类的。bond price呢？(记得shreve上有general affine model下discount bond
price的例子)
如果想再扩展，就把参数都变成时间的函数。
到这儿，R(t)始终是个normal variable。我的理解，大家说normal model的时候都是
说distribution是normal的。
如果再扩展，让vol依赖于R(t): vol=sigma*sqrt(alpha+beta*R(t)),就到了affine
model.R(t)就应该不是normal的了。 |
|
i**w
发帖数: 71 | 25 short rate model里，最简单的Ho-Lee model:
dR(t) = mu*dt + vol*dW(t)
为了缓解负利率的问题，加上mean reversion就得到了Vasicek model:
dR(t) = k*(b-R(t))*dt + vol*dW(t)
面试就可能会问:把上面这个R(t)解出来，是什么distribution?mean和variance是什么
之类的。bond price呢？(记得shreve上有general affine model下discount bond
price的例子)
如果想再扩展，就把参数都变成时间的函数。
到这儿，R(t)始终是个normal variable。我的理解，大家说normal model的时候都是
说distribution是normal的。
如果再扩展，让vol依赖于R(t): vol=sigma*sqrt(alpha+beta*R(t)),就到了affine
model.R(t)就应该不是normal的了。 |
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w**********y
发帖数: 1691 | 26 First, you have to know or follow a standard definition of (Multivariate)
Normal Distribution.
Refer to the Definition 1.2.1 on Page 5 in the book “Plane Answers to
Complex Questions: The Theory of Linear Models”:
There is no requirement of the positive definition of AA’. So degenerate
normal is definitely a Normal distribution following the definition above.
of
sigma)
不 |
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w**********y
发帖数: 1691 | 27 As for your question, suppose we don’t consider the degenerate situation.
My intuition is “No”.
A counterexample is: (similar as the exercise 4.47 in Casella's
"Statistical Inference")
Let Z1,Z2,Z3 be iid Standard Normal Random Variable.
Let A=Z1, B=Z2.
C=Z3 if Z1Z2Z3>0; C=-Z3 if Z1Z2Z3<0.
Then it is not hard to prove that (A,C) is joint normal (In hurry…Didn’t
do strict prove…u can check by urself.). (B,C) is similar.
But (A,B,C) is not joint Normal. Cuz P(ABC<0)=0, which is impossible for
non- |
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s******u
发帖数: 21 | 28 Thanks:)
But, in my opinion, even for the degenerate normal, it should satisfy
that any non-zero linear combination of x1, x2 ,x3,
a*x1+b*x2+c*x3= (a+c)x1+(b+c)x2 is normal; but in tamuer's exampl, when
c=-a=-c， it is 0. Does this prove (x1, x2, x3) is not normal.
situation. |
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D*********2
发帖数: 535 | 29 重学回来了，那个jt normal确实是俺的错～ 反正人也丢了，干脆继续，再请教一下啊～
Fixed Effect应该没错吧，error~ Normal, Y ~ Normal, 所以in practice, 就直接测
Y。
Random Effect
1. in practice 这么验证 normality? Y|X 具体咋implement?
2. 我看wiki上其实写的是 error|X 的一系列 assumption
楼主，great question! 但您问的是simple linear regression呢，还是ordinary
least
square?
X
X) |
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z**********i
发帖数: 12276 | 30 我用PROC CAPABILITY来CHECK NORMALITY.
看图形很NORMAL,但PVALUE 很小.这个到底是NORMAL DISTRIBUTION吗?
多谢!
Variable: RBMI
Moments
N 37667 Sum Weights
37667
Mean 0.05291262 Sum Observations 1993.
05967
Std Deviation 0.00865415 Variance 0.
00007489
Skewness -0.3560206 Kurtosis 0.
79177021
Unc... 阅读全帖 |
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s*****b
发帖数: 106 | 31 看图的感觉：真实分布跟Normal 差别不大（长得很像），
但是由于样本很大，所以这很小的差别(例如，左尾部
比Normal 分布要厚尾一些) 也被检测出来了。
问题在于：你需要它是Normal的原因是什么？
虽然它的真实分布不是Normal 也许它也能满足很多好的性质。 |
|
u******e
发帖数: 60 | 32 I have a score with missing value. The score is on a 0-70 scale and measured
at 4 time points. The missing pattern is not monotonic. The score is not
normally distributed in the sample. it is right skewed with a lot of
subjects having score 0.
Subjects with disease A are likely to have high score. The distribution of
score is close to normal distribution when separating subjects with and
without disease A.
The purpose of the study is to assess relation between disease A and change
of score durin... 阅读全帖 |
|
|
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e**t
发帖数: 29 | 35 Software Engineering Institute of East China Normal University is currently
recruiting several full-time academic staffs.
Positions: Lecturers/Associate Professors/Full Professors
Areas: Formal Methods, Highly Dependable Systems, Information Security,
Embedded System Design Method and Tools,
Co-design of Software and Hardware Systems,
Computer Algebra Algorithms and Applications,
Web Search and Web Mining, Large Scale Data Management
Institute: Software Engineering Institute,... 阅读全帖 |
|
G***G
发帖数: 16778 | 36 for a camry 2000, what is the normal parasitic drain?
Is 56.6mA normal?
what is the parasitc drain for your car?
when door open, the drain reaches to 260mA, is this normal? |
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f*******0
发帖数: 508 | 37 求助：左下腹疼痛一个月（B超，CT, Urine test normal）
大概从一个月前发现左下腹疼痛，就是和肚脐平行靠近腰的位置，有时还放射到相同位
置的背侧疼。不分时候，白天晚上都会时不时的疼，没有规律。刚发现是站起来走路时
加重。这几天几乎一直疼。
• 疼痛一周后去见obgyn，给physically 检查了子宫什么的，说正常。
• 一周后疼痛不减，就给做了妇科的B超，也都正常。
• 又过了一周，做urine test排除肾结石，也negative.
• 当时obgyn说他能想到的一个可能是endometriosis, but need to use
laprascopy to confirm. 因为是创伤性的检查，不建议马上做。 所以先做了个之后又
做了腹部CT （oral and IV contrast）, 结果总的说也正常。具体内容如下。我怀疑
是不是liver cyst 造成的？上周我没有觉得特别不舒服。可是从周六开始，腹部疼痛
厉害。用了热敷，有点帮助。今天上班扛不住了，吃了2颗Advil 200... 阅读全帖 |
|
B******y
发帖数: 110 | 38 Neuroscience Post-doc Position Available
Beijing Normal University
Applicants are invited for a postdoctoral position in Dr. Haidong Lu's lab
at Beijing Normal University. Dr. Lu’s lab uses optical imaging,
electrophysiology, and histological methods to study the neural mechanisms
underlying vision in non-human primates. Ongoing research projects include:
1. Anatomical connections among functional architectures in the monkey
visual cortex; 2. Functional roles of the motion sensitive neurons in t... 阅读全帖 |
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D*A
发帖数: 1169 | 39 I like to play online tournament, but i can not afford the normal speed of
15 minutes blind period, one MTT can take a whole night,
So i always choose turbo, which is much fast, but turbo are not stable as
normal.
in normal MTT, i almost always can get in money circle
but for Turbo MTT, i always been wiped out out of circle,
so i can choose SNG, in which case i can get in money 1 out of 3 or more
but i can not get much profit. |
|
c****n
发帖数: 1488 | 40 是啊。
不要直接查normal这个词得意思。
请查norm得含义。
由名次衍生成形容词normal，此意引申有现在normal下得常用词条。 |
|
B******y
发帖数: 110 | 41 Neuroscience Post-doc Position Available
Beijing Normal University
Applicants are invited for a postdoctoral position in Dr. Haidong Lu's lab
at Beijing Normal University. Dr. Lu’s lab uses optical imaging,
electrophysiology, and histological methods to study the neural mechanisms
underlying vision in non-human primates. Ongoing research projects include:
1. Anatomical connections among functional architectures in the monkey
visual cortex; 2. Functional roles of the motion sensitive neurons in t... 阅读全帖 |
|
f**********g
发帖数: 107 | 42 I mean that if X & Y normal, and X = -Y, then Z=X+Y=0 is still a normal. |
|
A*******r
发帖数: 768 | 43 http://www.springerlink.com/content/x453xu/?p=b2b422921b154f5c8a9974cb3c6b0e66&pi=1
Statistical Physics
Including Applications to Condensed Matter
Publisher Springer New York
DOI 10.1007/b106783
Copyright 2005
%%%%%%%%%%%%%%%%%%%%%%%%%%
Page 33
%%%%%%%%%%%%%%%%%%%%%%%%%%
Hence, the sum of two normal random variables is always (even if they are
mutually
dependent) another normal random variable. |
|
b******k
发帖数: 58 | 44 The sum of two normally distributed R.V. is still normal, and the
correlation is integrated to the variance of the sum. HTH. |
|
g****e
发帖数: 1829 | 45 A lot of people have posted their answers. I think there is a point that one
should always bear in mind, (my personal opinion):
If X & Y are not independent and both are Normal distribution, we can draw a
conclusion: it must be LINEAR dependence, which means you can represent Y
~~~~~~
per follow up posts, this could be wrong (and I didn't really prove it).
in a linear form of X. the question then reduces to:
If X & Y are linearly dependent, is their sum still a normal? An |
|
A*******r
发帖数: 768 | 46 懒得看
X+Y is normal if the disjoint distribution of X and Y is normal |
|
q*******n
发帖数: 1334 | 47 Assume X = [X1, X2]^t is bivariate normal distributed with mean vector m = [
m1, m2]^t and covariance matrix C = [c1, r; r, c2].
1. Define s = [s1, s2]^t as the dumb variable vector for MGF, then the MGF
of the vector X is
M_X(s) = E[exp(s^t * X)] = exp(m^t s + 1/2*s^t*C*s). (eqn. 1)
2. Set s1 = s2 = u in (eqn. 2), then we can get the MGF of X1+X2
M_{X1+X2}(u) = E[exp( (X1+X2)u ) = exp((m1+m2)u + 1/2*(c1+c2+2r)*u^2) (eqn.
2)
3. Eqn. 2 is in the form of the MGF for Normal RV. Therefore, X1+X2 is |
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h***i
发帖数: 3844 | 48 第一步就错了，两normal， joint不一定是bivariate normal
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p****l
发帖数: 23 | 49 【 以下文字转载自 Statistics 讨论区 】
发信人: propel (fitness water), 信区: Statistics
标 题: question about the sum of truncated normal rv
发信站: BBS 未名空间站 (Fri Jan 15 23:52:00 2010, 美东)
x and y are i.i.d normal, left-truncated at 0, with mean \mu and variance \
sigma. Is x+y normally distributed with mean 2\mu, variance 2\sigma and left
-truncated at 0?
thanks. |
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A*****s
发帖数: 13748 | 50 到底啥样是normal model啊？
dS = u dt + vol dW?
normal model会造成负数的价格。。。至少比起lognormal来说完全不valid吧。。。
lognormal的challenge也就是在fitting的层面上
normal的challenge都在本质特性上的inconsistency了 |
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