r****y
发帖数: 1437 | 1
Define Hamilton function
H(p, q, t)=Summation(p(i) d(q(i))/dt)-L
d p(i)/dt = - partial(H)/partial(q(i))
d q(i)/dt = partial(H)/partial(p(i))
in Poisson bracket
d p(i)/dt =[p(i), H]
d q(i)/dt =[q(i), H] |
|
f******k
发帖数: 297 | 2 W. Fischer, K. Meier-Hellstern,
"The Markov-modulated Poisson process (MMPP) cookbook",
Performance Evaluation 18 (1992) 149-171 |
|
F******n
发帖数: 160 | 3 2. Origin -- How Did The Problem Arise?
As discussed in previous article (article series #8288, this board), by taking
time as a physical observable, we have to perform the quantization procedure
on "time" variable, such as the canonical quantization method given below:
In classical mechanics, we have canonical variables (H,T) which satisfy the
Hamiltonian equation:
dT/dt={H,T} = 1
where:
H is the system hamiltonian and T its conjugate variable;
"{ }" is the Poisson bracket).
By following the co |
|
D**u
发帖数: 204 | 4 Great. Here is a "probabilistic" solution assuming that we do not notice to
use f_j(t) := exp(-x_j*t) right away.
Assume Y_i is a Poisson arrival process with arrival rate x_i, then we know
that
E(Y_i) = 1/x_i, and E(min(Y_i,Y_j)) = 1/(x_i+x_j). Suppose the CDF of Y_i
and Y_j are P_i(t) and P_j(t), then easy to see the CDF of min(Y_i,Y_j) is
1-(1-P_i(t))*(1-P_j(t)). Then with a little computation, we see that
E(min(Y_i,Y_j)) = \int_0^{\infty} (1-P_i(t))*(1-P_j(t)) dt
= \int_0^{\infty} exp(-x_ |
|
b*******n
发帖数: 605 | 5 比如说我有一个categorical data, and the assumption is: cell counts have
Poisson distributions. 用的是log-linear model. Sometimes we can get formulas
of MLE for parameters in the log-linear model. But sometimes we can't. In SAS,
the MLE can be calculated numerically. (The formulas are to get parameter
estimates from the categorical cell counts, let's call them functions of cell
counts for parameters). Here is my question:
In Birch's Theorem, one of the conditions is: parameters should be able to be
written |
|
|
p********a
发帖数: 5352 | 7 ☆─────────────────────────────────────☆
asdfghi (asdfgghi) 于 (Wed May 9 17:56:55 2007) 提到:
想产生10个x_j，并打印出来：
data x_j;
call streaminit(rand('POISSON', 5/3));
do i=1 to 10;
x1=rand('Binomial',0.5,1);
output;
end;
proc print data=x_j;
run;
用do能搞么？
用macro怎么搞呢？
谢谢啦-:）
☆─────────────────────────────────────☆
asdfghi (asdfgghi) 于 (Wed May 9 18:44:11 2007) 提到:
有没有哪位高手教我一下啊？
☆─────────────────────────────────────☆
oloolo (山村老尸之不腐传说) 于 (Wed May 9 19:38:47 2007) |
|
s********e
发帖数: 2 | 8 In a series of mine 108 explosions in England, the time interval between
the first and 54th accidents
was 8,042 days, whereas the interval between the 55th and 108th accidents
was 16,864 days. If it is
assumed that mine explosions followed a Poisson process in each period, and
that they did so at constant
rates λ1 and λ2 respectively, set up and carry out a test of the
hypothesis λ1=λ2 based on an F-statistic.
这个假设检验怎么建立咧？？？？ |
|
j********g
发帖数: 44 | 9 I think your problem is a two sample mean comparison.
You may find this article helps. I am not sure.
Some Simple Approximate Tests for Poisson Variates
D. R. Cox
Biometrika, Vol. 40, No. 3/4. (Dec., 1953), pp. 354-360. |
|
|
h**l
发帖数: 4883 | 11 Thanks. So basically students can fail maximally 5 tests and then they'll be
kicked out.
So the study will have 12 tests, most of the students will fail less than 5
tests so the odds ratio would be # of failed tests/ 12. But for those who're
kicked out, the odds ratio would be 5/# tests they take. In this case, it's
negative binomial?
well, so I think I should use proc GENMOD? how do you perform logistic
regression of negative binomial variables?
Thanks a lot.
to |
|
s*********e
发帖数: 1051 | 12 what exactly is the objective of your study?
with binomial, you are trying to predict the probability to pass all 12 exams.
with poission / nb, you are trying to predict the number of exams passed. |
|
h**l
发帖数: 4883 | 13 The objective of the study is to compare the academic performance of 2
groups of students. The tricky part is that there are students who failed 5
tests and dropped out immediately after they failed 5. We don't want to
exclude these students who didn't have chance to take all 12 exams.
exams. |
|
|
h**l
发帖数: 4883 | 15 well, each test can only have two outcomes: pass and fail... it's just that
the students can have different number of tests depending on if they pass or
not, and the number has a minimum of 5 and maximum of 12. |
|
x*******i
发帖数: 1791 | 16 这个不难，用classical方法，做一个link function 就可以了。 |
|
h**l
发帖数: 4883 | 17 no...
Multinomial has k outcomes. When k=2, multinomial=binomial.
So binomial is like flipping a coin
and multinomial is like throwing a die. |
|
n*******m
发帖数: 101 | 18 BTW, if a student quits whenever he fails 5 times, it's no longer a binomial
distr or multinomial. Use the negative binomial as the link will work. |
|
h**l
发帖数: 4883 | 19 Does negative binomial have infinite tests until the students fail 5 test?
binomial |
|
n*******m
发帖数: 101 | 20 樓上正解。log(mu_i/t_i)=X*beta->mu_i=t_i*exp（X*beta),把t_i帶入就行了。 |
|
x*******i
发帖数: 1791 | 21 没明白为什么是5-12之间的数？ 1-4为什么不行？说中文吧。说实话就没明白你想干啥。
multinomial 和binomial一回事。 |
|
d******e
发帖数: 7844 | 22 一共3个参数.
1个lambda,Poisson本身的参数
1个Pi,是Finite Mixture的参数
还有一个theta是什么玩意? |
|
l********s
发帖数: 430 | 23 两个poisson的参数分别是theta和lambda |
|
d******e
发帖数: 7844 | 24 theta是干什么的?
一元Poisson只有一个lambada啊.
而且我发现那个lambda和Theta是以乘机形式出现的.
那不本就应该是Possion的Mean么? |
|
l********s
发帖数: 430 | 25 X ~ Pi * Pois(lambda) + (1-Pi) * Pois(theta)
所以有Pi, lambda, 和 theta 三个参数。
不知道我理解错误了没有 - 是mixture of two poisson distribution么？ |
|
d******e
发帖数: 7844 | 26 我说得lambda theta都是向量啊.而且怎么可能只有两个component?
Mixture Poisson的ith component是mean是lambda(i),每个componnent的比例是Pi(i). |
|
o******6
发帖数: 538 | 27 ☆─────────────────────────────────────☆
sissialice (cecilia) 于 (Fri Mar 7 13:07:47 2008) 提到:
In a series of mine 108 explosions in England, the time interval between
the first and 54th accidents
was 8,042 days, whereas the interval between the 55th and 108th accidents
was 16,864 days. If it is
assumed that mine explosions followed a Poisson process in each period, and
that they did so at constant
rates λ1 and λ2 respectively, set up and carry out a test of the
hypothesis λ1=λ2 based on |
|
o******6
发帖数: 538 | 28 ☆─────────────────────────────────────☆
whatsummer (不理猫@冥王星) 于 (Mon May 5 16:23:31 2008) 提到:
谢谢
☆─────────────────────────────────────☆
sotough (天马行空) 于 (Mon May 5 17:41:00 2008) 提到:
proc genmod can run poisson model also. I don't think proc logistic can run
poission.
☆─────────────────────────────────────☆
himalaya (Tea) 于 (Mon May 5 18:45:47 2008) 提到:
genmod的参数很多的 distribution可以是possion, negative binomial, normal之类
的, link可以是logit probit identity等等
http://www2.stat.unibo.it/M |
|
|
|
w******g
发帖数: 313 | 31 P(y>a)=P(x1>a)P(x2>a)...P(xn>a)
对a求导即可 |
|
z*****n
发帖数: 95 | 32 Thank you very much. very useful information. |
|
z*****n
发帖数: 95 | 33 thank you very much. Really helpful. |
|
d******e
发帖数: 7844 | 34 ... ...你是来恶搞的，还是你不知道Poisson啊 |
|
|
o****o
发帖数: 8077 | 36 universal syntax?
in any domain, there are symbols universally assumed to refer to certain subjects
Poi(\lambda) indicates poisson distribution ah |
|
z****e
发帖数: 2024 | 37 I have to say, the pdf expression needs an explicit definition or else even 1/\lambda and \lambda for a Poisson could make difference. lots of books out there using different notations for the same pdf.
guys, please focus on lz's question. if not 0, i'd like to learn.
subjects |
|
a*********r
发帖数: 108 | 38 赞“思维”
even 1/\lambda and \lambda for a Poisson could make difference. lots of
books out there using different notations for the same pdf. |
|
z****e
发帖数: 2024 | 39 which 级数? thanks.
since poi() is defined as Poisson, it is not continuous,so the answer should
not be zero. |
|
C******y
发帖数: 1997 | 40 The Skellam distribution is the discrete probability distribution of the
difference n1 − n2 of two statistically independent random variables
n1 and n2 each having Poisson distributions with different expected values
μ1 and μ2. |
|
p******c
发帖数: 83 | 41 Thanks for your reply.
The problem is:
Let X be a Poisson random variable with parameter: lambda.
Assume lambda is big enough such that Pr(X=0) can be ignored
Let Y = ln(X), find the mean and variance of Y
E{Y}=?
Var{Y}=? |
|
D******n
发帖数: 2836 | 42 u can model it as a poisson process |
|
h*****5
发帖数: 14 | 43 谢谢！
貌似GLIMMIX只能做MIXED EFFECT MODEL USING RANDOM STATEMENT，没有REPEATED
STATEMENT.
想找一个GEE macro，然后改写CODE， 插入一个TRUNCATED POISSON 分布。能否用SAS
实现？ |
|
|
l*********s
发帖数: 5409 | 45 Rare discrete events can be assumed to follow Poisson distributions. |
|
s*********e
发帖数: 1051 | 46 follow is copied from one of my paper and hope it helpful.
"
To evaluate the goodness-of-fit of a regression for count data, the most
popular but somewhat problematic practice is to compare the predicted and
observed values of the dependent variable. However, a measure of
goodness-of-fit solely based upon the expected value is unable to address
the improvement achieved by a model with less restrictive variance
assumption. A better alternative is to compare the predicted and observed
prob |
|
|
w**********y
发帖数: 1691 | 48 有人发信询问.实在才疏识浅,写点愚见,请大家一起讨论.
统计最传统用到金融中的当然就是time series的东西了.经典教科书是Analysis of Financial Time Series (Wiley Series in Probability and Statistics) - Ruey S.Tsay.
time series处理的是discrete time,对应到continuous time下,就是stochastic
process.这个,任何一本关于quantitative finance的书都有介绍. 经典教科书是john hull的'Options, Futures And Other Derivatives'和shreve的'Stochastic Calculus for Finance'的.
真正的统计的东西,真的都是零零散散的应用,比如PCA,copula,VaR.而正规的统计model
,比如GLM之类的,华尔街好像极少极少用到.
保险公司倒是用的比较多,比如DGLM(double glm)/tweedie's compound poisson
有兴趣 |
|
|
n******y
发帖数: 192 | 50 Proc TSCS and Proc panel能做泊松么？ |
|
