similar to: Math characters in column heading using latex() in Hmisc

I would like to code the following in R: a1(b1+b2+b3) + a2(b1+b3+b4) + a3(b1+b2+b4) + a4(b1+b2+b3) or in summation notation: sum_{i=1, j\neq i}^{4} a_i * b_i I realise this is the same as: sum_{i=1, j=1}^{4} a_i * b_i - sum_{i=j} a_i * b_i would appreciate some help. Thank you. -- View this message in context: http://r.789695.n4.nabble.com/summation-coding-tp4646678.html Sent from the R

...as promised. This describes the mdct used in my d.m.l patch. I think it is the same as the Lee fast-dct. I typed it in a kind of pseudo-TeX, 'cause the ascii art would kill me. Hope you can read TeX source; if not, ask someone who can to make a .ps/.gif/.whatever of the TeX output, and put it on a webpage or something. I'm to lazy to do it (and besides, I don't have access to TeX,

Dear R experts I need to write a function that incorporates double summation, the problem being that the upper limit of the second summation is the index of the first summation, i.e: sum_{j=0}^{x} sum_{i=0}^{j} choose(i+j, i) where x variable or constant, doesn't matter. The following code obviously doesn't work: f=function(x) {j=0:x; i=0:j; sum( choose(i+j,i) ) } Can you help? Thanks

I need to refresh my memory on Probability Theory, especially on conditional probability. In particular, I want to solve the following two problems. Can somebody point me some good books on Probability Theory? Thank you! 1. Z=X+Y, where X and Y are independent random variables and their distributions are known. Now, I want to compute E(X | Z = z). 2.Suppose that I have $I \times J$ random number

Hi all, I have a problem using rdirichlet{gtools}. For Dir( a1, a2, ..., a_n), its mode can be found at $( a_i -1)/ ( \sum_{i}a_i - n)$; The means are $a_i / (\sum_{i} a_i ) $; I tried to study the above properties using rdirichlet from gtools. The code are: ############## library(gtools) alpha = c(1,3,9) #totoal=13 mean.expect = c(1/13, 3/13, 9/13) mode.expect = c(0, 2/10, 8/10) #

Dear helpers in this forum, I have the following question: Suppose I have the following data set: id x y 023 1 2 023 2 5 023 4 6 023 5 7 412 2 5 412 3 4 412 4 6 412 7 9 220 5 7 220 4 8 220 9 8 ...... and i want to calculate sum_{i=1}^k sum_{j=1}^{n_i}x_{ij}*y_{ij} is there a simple way to do this within and between subject summation in R?

Hi, I'm bit confused about ecdf (read the help files but still not sure about this). I have an analytical expression for the pdf, but want to get the empirical cdf. How do I use this analytical expression with ecdf? If this helps make it concrete, the pdf is: f(u) = \sum_{t = 1}^T 1/n_t \sum_{i = 1}^{n_t} 1/w K((u - u_{it})/w) where K = kernel density estimator, w = weights, and u_{it} =

Dear helpers in this forum, This is a clarified version of my previous questions in this forum. I really need your generous help on this issue. > Suppose I have the following data set: > > id x y > 023 1 2 > 023 2 5 > 023 4 6 > 023 5 7 > 412 2 5 > 412 3 4 > 412 4 6 > 412 7 9 > 220 5 7 > 220 4 8 > 220 9 8 > ...... > Now I want to compute the

Dear R users, I?m a graduate students and in my master thesis I must obtain the values of the parameters x_i which maximize this Multinomial log?likelihood function log(n!)-sum_{i=1]^4 log(n_i!)+sum_ {i=1}^4 n_i log(x_i) under the following constraints: a) sum_i x_i=1, x_i>=0, b) x_1<=x_2+x_3+x_4 c)x_2<=x_3+x_4 I have been using the ?ConstrOptim? R-function with the instructions

I wrote some functions for multiway CANDECOMP, i.e. for least squares fitting of a_{i_1\cdots i_m}\approx\sum_{s=1}^p x^1_{i_1s}x^1_{i_1s}\cdots x^m_{i_ms} with arrays of arbitrary dimension. Reminded me of the good old APL days. I could not find this in the archives, but if it's already there, I would appreciate if someone let me know.

Dear R Users, I have 12 data frames, each of 12 rows and 2 columns. e.g. FeketeJAN MEAN SUM_ AMAZON 144.4997874 68348.4 NILE 5.4701955 1394.9 CONGO 71.3670036 21196.0 MISSISSIPPI 18.9273250 6511.0 AMUR 1.8426874 466.2 PARANA 58.3835497 13486.6 YENISEI 1.4668313 592.6 OB 1.4239179 559.6 LENA 0.9342164

Hi all; I recently have been used 'maxLik' function for maximizing G2StNV178 function with gradient function gradlik; for receiving this goal, I write the following program; but I have been seen an error  in calling gradient  function; The maxLik function can't enter gradlik function (definition of gradient function); I guess my mistake is in line ******** ,that the vector  ‘h’ is

Dear List: I am working to understand some differences between the results of the svymean() function in the survey package and from code I have written myself. The results from svymean() also agree with results I get from SAS proc surveymeans, so, this suggests I am misunderstanding something. I am never comfortable with "I did what the software" does mentality, so I am working to

Hi Firstly , happy Christmas to R-Help! Secondly, I wonder if anyone can help me with the following query: I am trying to reproduce some explicit probability calculations performed in APPL (a Maple extension for computational probability). For instance, in APPL, to compute the probability that the sum of 10 iid uniform variables [0,1] will be between 4 and 6, (i..e Pr( 4 < \sum_{i=1}^{10}X_i

I am using both nlminb and optim to get MLEs from a likelihood function I have developed. AFAIK, the model I has not been previously used in this way and so I am struggling a bit to unit test my code since I don't have another data set to compare this kind of estimation to. The likelihood I have is (in tex below) \begin{equation} \label{eqn:marginal} L(\beta) = \prod_{s=1}^N \int

Full_Name: Jerry W. Lewis Version: 2.6.1 OS: Windows XP Professional Submission from: (NULL) (24.147.191.250) pchisq(0,0,ncp=lambda) returns 0 instead of exp(-lambda/2) pchisq(x,0,ncp=lambda) returns NaN instead of exp(-lambda/2)*(1 + SUM_{r=0}^infty ((lambda/2)^r / r!) pchisq(x, df + 2r)) qchisq(.7,0,ncp=1) returns 1.712252 instead of 0.701297103 qchisq(exp(-1/2),0,ncp=1) returns 1.238938

Hello, I noticed that feeding 'clang -O3' with functions like: int sum1(int x) { int ret = 0; for(int i = 0; i < x; i++) ret += i; return ret; } int sum2(int x) { int ret = 0; for(int i = 0; i < x; i++) ret += i*i; return ret; } ... int sum20(int x) { int ret = 0; for(int i = 0; i < x; i++) ret +=

Hi everybody I have a questionnaire with a lot of questions that allow for more than one option to be chosen (like a tickbox in a html form). The data captured on a mobile device and is supplied in a format where every option is a separate variable (logical). I want to develop a generic function to process these questions. As part of the analysis I want make a matrix of the p-value from the

Is there a weighted median function out there similar to weighted.mean() but for medians? If not, I'll try implement or port it myself. The need for a weighted median came from the following optimization problem: x* = arg_x min (a|x| + sum_{k=1}^n |x - b_k|) where a : is a *positive* real scalar x : is a real scalar n : is an integer b_k: are negative and positive scalars

Well, I could argue that it's not *completely* OT since my question is motivated by an enquiry that I received in respect of a CRAN package "Iso" that I wrote and maintain. The question is this: Given observations y_1, ..., y_n, what is the solution to the problem: minimise \sum_{i=1}^n (y_i - y_i^*)^2 with respect to y_1^*, ..., y_n^* subject to the "isotonic"