I am reading "Modelling Count Data" by Hilbe and I feel I am missing something fundamental about Poisson Regression.  $\hat{\mu} = \exp(\alpha + \sum\beta_ix_i)$  One of the requirements for using it is that the underlying distribution generating my data is capable of producing counts of zero.  What I don't understand: how can such a model predict a count of zero? If it can't, how is this a useful model of my data?  Example (in R)  library("ggplot2") library("COUNT")  # Simulation weights b0 = 1 b1 = 0.5 b2 = 0.01  # Simulation variables and observations obs.num = 10000 x1 = rnorm(obs.num) x2 = rnorm(obs.num) py = rpois(obs.num, exp(b0 + b1*x1 + b2*x2))  # Poisson Regression model.poisson = glm(py ~ x1 + x2, family=poisson)  # Inspect Results summary(model.poisson) ggplot() + aes(py) + geom_histogram(bins=120) ggplot() + aes(predict(model.poisson, type="response")) + geom_histogram(bins=120)   The summary looks good in-so-far as it gets the estimates:  Call: glm(formula = py ~ x1 + x2, family = poisson)  Deviance Residuals:      Min       1Q   Median       3Q      Max   -3.3435  -0.8094  -0.1061   0.5842   3.8852    Coefficients:             Estimate Std. Error z value Pr(&gt;|z|)     (Intercept) 1.002306   0.006376 157.205   &lt;2e-16 *** x1          0.501053   0.005659  88.535   &lt;2e-16 *** x2          0.012516   0.005675   2.205   0.0274 *   --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  (Dispersion parameter for poisson family taken to be 1)      Null deviance: 18964  on 9999  degrees of freedom Residual deviance: 11070  on 9997  degrees of freedom AIC: 37494  Number of Fisher Scoring iterations: 5   But the plot of the predictions shows that no 0 predictions were made:
A Tweedie distribution can model skewed data with a point mass at zero when the parameter $p$ (exponent in the mean-variance relationship) is between 1 and 2.   Similarly a zero-inflated (whether otherwise continuous or discrete) model may have a large number of zeros.  I'm having trouble understanding why it is that when I do prediction or calculate fitted values with these kinds of models, all of the predicted values are non-zero.  Can these models actually predict exact zeros?  For example  library(tweedie) library(statmod) # generate data y &lt;- rtweedie( 100, xi=1.3, mu=1, phi=1)  # xi=p x &lt;- y+rnorm( length(y), 0, 0.2) # estimate p out &lt;- tweedie.profile( y~1, p.vec=seq(1.1, 1.9, length=9)) # fit glm fit &lt;- glm( y ~ x, family=tweedie(var.power=out$p.max, link.power=0)) # predict pred &lt;- predict.glm(fit, newdata=data.frame(x=x), type="response")   pred now does not contain any zeros.  I thought the usefulness of models such as the Tweedie distribution comes from its ability to predict exact zeros and the continuous part.  I know that in my example the variable x is not very predictive.
Replace arbitrary characters in the middle of an IP address string with sed I need to find and replace either one or two numerical characters in strings in a file.  The strings are IP addresses of the form:   10.xx.y.z    Where xx can be one or two characters.    I want to replace the xx with the single character 0, so I have  10.0.y.z    preserving the values of y and z.   The string may appear multiple times in the file.  What is the sed invocation to do this? Why, with Springer's  svmono template, do the letters written with the \mathcal font change? It seems that \mathcal becomes \mathscr.  Edit: Look at this image:    With the svmono template \mathcal returns the first alphabet and not the (classical) latter.  Here the packages I use in my document:  \documentclass[envcountsame,envcountchap]{svmono}  \usepackage{subfiles} \usepackage[utf8]{inputenc}  \usepackage{mathptmx} \usepackage[bottom]{footmisc} \usepackage{microtype} \usepackage{stmaryrd}    \usepackage{amsmath} \usepackage{courier} \usepackage{mathrsfs}  \usepackage{amssymb}  \usepackage[all,cmtip]{xy} \usepackage{faktor} \usepackage{graphicx} \usepackage{mathdots} \usepackage[colorlinks={true},linkcolor={blue},citecolor={blue}]{hyperref} \usepackage[frame,width=15truecm,height=23.5truecm,center]{crop}   With this settings I have the above strange behavior of \mathcal. Is there a program to mount all of my drives automatically? Will having multiple domains improve my seo? Lets say I have a domain already, for example www.automobile4u.com (not mine), with a website fully running and all.  The title of my "Website" says:    &lt;title&gt;Used cars - buy and sell your used cars here&lt;/title&gt;   Also, lets say I have fully SEO the website so when people searching for the term buy used cars, I end up on the second or first page.  Now, I want to end up higher, so I go to the google adwords page where you can check how many searches are made on specific terms.  Lets say the term "used cars" has 20 million searches each month.  Here comes the question, could I just go and buy that domain with the search terms adress, in this case www.usedcars.com and make a redirect to my original page, and this way when people search for "used cars", my newly bought domain name comes up redirecting people to my original website (www.automobile4u.com)?  The reason I believe this benefits me is because it seems search engines first of all check website adresses matching the search, so the query "used cars" would automatically bring www.usedcars.com to the first result right?  What are the downsides for this?  I already know about google spiders not liking redirects, but there are many methods of redirecting...  Is this a good idea generally? Is there a name for an element $z$ such that $\,zx = z = xz\,$ for all $x$? Is there a general name for the following properties, (similar to the properties of existence of an additive identity, existence of multiplicative identity etc):   For any given set, the intersection with the empty set results in the empty set. For any real number, multiplication with zero results in zero. Converting *.tif file into headerless (flat) binary file? I am using NDVI files (value range -1 to +1) created from Landsat CDR images to produce a timeseries in TIMESAT software.   My  .tif file has following characteristics.  File type  TIFF,Data Type  Double Precision, Byte Order Host (Intel), Interleave BSQ  As per the requirement of TIMESAT, the image should be headerless(flat) binary file, and values can be stored as 8 bit integer(0-255), 16 bit signed integer(-32767 to +32768) or 32 bit real.   Now i need to change my data type into any of these 3 format and .tif file into headerless binary files.   Any idea? I am trying to solve:  $$\int_{-\infty}^{\infty}\frac{x\sin{x}}{x^2 + a^2}dx$$  and show that it equals $\pi e^{-a}$ for all $a &gt; 0$.  I translate it to its complex equivalent:  $$lim_{R \rightarrow \infty} \int_{-R}^{R}\frac{z\sin{z}}{z^2 + a^2}dz = \int_{C}\frac{z\sin{z}}{z^2 + a^2}dz - \int_{\gamma}\frac{z\sin{z}}{z^2 + a^2}dz$$  where C is a half circle with radius R, above the real axis, and $\gamma$ is only the curved (top part) of the half circle.  I've shown that $$\int_{\gamma}\frac{z\sin{z}}{z^2 + a^2}dz$$ tends to 0 as $R \rightarrow \infty$.  So now:  $$lim_{R \rightarrow \infty} \int_{-R}^{R}\frac{z\sin{z}}{z^2 + a^2}dz = \int_{C}\frac{z\sin{z}}{z^2 + a^2}dz$$  By residue theorem,   $$\int_{C}\frac{z\sin{z}}{z^2 + a^2}dz = 2\pi i \cdot res_{ai}f$$  as $ai$ is the pole of $f$ that lies above the real axis.  $$2\pi i \cdot res_{ai}f = 2\pi i \cdot lim_{z \rightarrow ai} (z-ai)\frac{z sin{z}}{z^2 + a^2}$$  By L'Hospital's rule, this is equivalent to:  $$2\pi i \cdot lim_{z \rightarrow ai} (z-ai)\frac{z^2\cos{z} + 2z\sin{z} - zai\cos{z} - ai\sin{z}}{2z} = 2\pi i \cdot \frac{\sin{ai}}{2} = \pi i \sin{ai}$$  But how is $\pi i \sin{ai}$ equivalent to $\pi e^{-a}$? Did I make a mistake? Find $x$ in   $$ \Large 2 = x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}}$$   A trick to solve this is to see that $$\large 2 = x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}} \quad\implies\quad 2 = x^{\Big(x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}}\Big)} = x^2 \quad\implies\quad x = \pm \sqrt{2} $$  Are these solutions correct? If not, why? If yes, are there other solutions?    PS: An extension of this discussion can be found in Why avoid increment ("++") and decrement ("--") operators in JavaScript? How to install XAMPP? Hi all im a noob on Ubuntu/Linux World,  So i need some that give a full tutorial to How to install  from apachefriends.org correctly on Ubuntu 11.10 + all beyond Ubuntu for 32 bit and also 64 bit Desktop Version.. and also i need this:   Make a Folder on Your Home Folder and Linked to htdocs from Apache Web Server Make a GUI interface for Xmapp Start Xampp when Ubuntu Boot Up or Start Ubuntu   (Note: i ask it for both X86 and X64 so people in the further can see the tutorials)    New Data:  What i did was i download from  for now and i also what to say that I'm currently running Ubuntu 11.10 X64 bit for Dell Studio 1558 processor intel i3  i will let you know guys which solution was the best, and it is for a Desktop Version of Ubuntu 11.10 (Laptop 15 inch screen ^_^ ) not Server Ubuntu Why does 1366x768 resolution exist? I know that there's  but it doesn't have any real answers despite having been viewed 12,400 times, and the fact that it's been closed. With that in mind...  Why in the world is 1366x768 resolution a real thing? It has an aspect ratio of 683:384, which is the weirdest thing I've ever heard of while living in a 16:9 world.   All screens and resolutions I've been familiar with have been 16:9 aspect ratio. My screen, 1920x1080, is 16:9. The 720p that I'm familiar with is 1280x720, also 16:9. 4K that I'm familiar with, 3840x2160, is also 16:9. Yet 1366x768 is 683:384, a seemingly wild break from the standard.  I know there are plenty of other resolutions all over the place, but 1366x768 seems to dominate most of the mid priced laptop world and also seems unique to the laptop world. Why don't laptops use 1280x720 or something else as a standard? Remove default ID attribute from HTML helpers in ASP.NET MVC Is there a word to describe a highly desirable cursed treasure? Is MacBook Pro warming during gaming normal? I have a 2010 MacBook Pro MC371 (Core i5, GeForce 320M, 4Gb RAM).   When I launch a game either new one (i.e. Starcraft 2) or rather old (Unreal Tournament 2004, bootcamped) my MacBook gets rather warm, even hot in the top left corner, around the place where magsafe charger is plugged in. The temperature is more than 40C. The fact that confuses me is that this warming occures even when I play old games.  Is that OK? Does every linearly independent set of n vectors in $R^n$ forms a basis in $R^n$? Basically does a vector set that is linearly independent in $R^n$ automatically span $R^n$?  My initial thought is yes, but is there some counterexample that can disprove this? Spanning Trees: Prove if $e_1$ is an edge in $X$ that isn't in $Y$, then there exists an edge ... Say $X$ and $Y$ are two different spanning trees of a simple and connected and undirected graph $G$. Prove that if $e_1$ is an edge in $X$ that isn't in $Y$, then there exists an edge $e_2$ in $Y$ that isn't in $X$... so the graph $(X − e_1) + e_2$ (obtained from $X$ on replacing $e_1$ by $e_2$) is also a spanning tree of the original graph, $G$. Navigation to section/subsection from Beamer headline titles Beamer infolines themes, like CambridgeUS, insert the titles of the current section and subsection in the headline. These titles appear to be clickable (the screen pointer changes as if they were so) but nothing happens when one clicks them.   Is there a way to link the headline titles to the first frame of the corresponding section or subsection? Something like this already works on the theme footline: clicking on the presentation title takes you to the title page.   Edit: MWE  \documentclass{beamer} \usetheme{CambridgeUS}  \setbeamertemplate{navigation symbols}{} \title{Click on Headline} \author{A.~U.~Thor} \institute{X-University} \date{2015} \begin{document} \begin{frame}   \titlepage \end{frame} \begin{frame}[t]{Contents}   \tableofcontents[subsectionstyle=hide]  \end{frame} \section{Section 1} \begin{frame}{Section 1}   \centering \Large Section 1 \end{frame} \begin{frame}[t]{Section 1: Contents}   \tableofcontents[currentsection,hideothersubsections] \end{frame} \subsection{Subsection 1.1} \begin{frame}{Frame 1.1.1}   A frame of subsection 1.1 \end{frame} \begin{frame}{Frame 1.1.2}   Another frame of subsection 1.1 \end{frame}   \subsection{Subsection 1.2} \begin{frame}{Frame 1.2.1}   A frame of subsection 1.2 \end{frame} \begin{frame}{Frame 1.2.2}   Another of subsection 1.2 \end{frame} \section{Section 2} \begin{frame}{Section 2}   \centering \Large Section 2 \end{frame} \begin{frame}[t]{Section 2: Contents}   \tableofcontents[currentsection,hideothersubsections] \end{frame} \subsection{Subsection 2.1} \begin{frame}{Frame 2.1.1}   A frame of subsection 2.1 \end{frame} \end{document} I'm having trouble understanding Cantor's diagonal argument.  Specifically, I do not understand how it proves that something is "uncountable".  My understanding of the argument is that it takes the following form (modified slightly from the  article, assuming base 2, where the numbers must be from the set $ \lbrace 0,1 \rbrace $):  \begin{align} s_1 &amp;= (\mathbf{0},1,0,\dots)\\ s_2 &amp;= (1,\mathbf{1},0,\dots)\\ s_3 &amp;= (0,0,\mathbf{1},\dots)\\ \vdots &amp;= (s_n \text{ continues}) \end{align}  In this case, the diagonal number is the bold diagonal numbers $(0, 1, 1)$, which when "flipped" is $(1,0,0)$, neither of which is $s_1$, $s_2$, or $s_3$.  My question, or misunderstanding, is: When there exists the possibility that more $s_n$ exist, as is the case in the example above, how does this "prove" anything?  For example:  \begin{align} s_0 &amp;= (1,0,0,\mathbf{0},\dots)\ \ \textrm{ (...the wikipedia flipped diagonal)}\\ s_1 &amp;= (\mathbf{0},1,0,\dots)\\ s_2 &amp;= (1,\mathbf{1},0,\dots)\\ s_3 &amp;= (0,0,\mathbf{1},\dots)\\ s_4 &amp;= (0,1,1,\mathbf{1},\dots)\\ s_4 &amp;= (1,0,0,\mathbf{1},\dots)\ \ \textrm{ (...alternate, flipped } s_4\textrm{)}\\ s_5 &amp;= (1,0,0,0,\dots)\\ s_6 &amp;= (1,0,0,1,\dots)\\ \vdots &amp;= (s_n \text{ continues}) \end{align}  In other words, as long as there is a $\dots \text{ continues}$ at the end, the very next number could be the "impossible diagonal number", with the caveat that it's not strictly identical to the "impossible diagonal number" as the wikipedia article defines it:     For each $m$ and $n$ let $s_{n,m}$ be the $m^{th}$ element of the $n^{th}$ sequence on the list; so for each $n$,      $$s_n = (s_{n,1}, s_{n,2}, s_{n,3}, s_{n,4}, \dots).$$      ...snip...      Otherwise, it would be possible by the above process to construct a sequence $s_0$ which would both be in $T$ (because it is a sequence of 0s and 1s which is by the definition of $T$ in $T$) and at the same time not in $T$ (because we can deliberately construct it not to be in the list). $T$, containing all such sequences, must contain $s_0$, which is just such a sequence. But since $s_0$ does not appear anywhere on the list, $T$ cannot contain $s_0$.      Therefore $T$ cannot be placed in one-to-one correspondence with the natural numbers. In other words, it is uncountable.   I'm not sure this definition is correct, because if we assume that $m = (1, \dots)$, then this definition says that "$s_n$ is equal to itself"&mdadsh;there is no "diagonalization" in this particular description of the argument, nor does it incorporate the "flipping" part of the argument, never mind the fact that we have very clearly constructed just such an impossible $T$ list above.  An attempt to correct the "diagonalization" and "flipping" problem:  $$s_n = (\lnot s_{m,m}, \lnot s_{m,m}, \dots) \quad \text{where $m$ is the element index and} \quad\begin{equation}\lnot s_{m,m} = \begin{cases}0 &amp; \mathrm{if\ } s_{m,m} = 1\\1 &amp; \mathrm{if\ } s_{m,m} = 0\end{cases}\end{equation}$$  This definition doesn't quite work either, as we immediately run in to problems with just $s_1 = (0),$ which is impossible because by definition $s_1$ must be $ = (1)$ if $s_1 = (0)$, which would also be impossible because...   Or more generally, with the revised definition there is a contradiction whenever $n = m$, which would seem to invalidate the revised formulation of the argument / proof.  Nothing about this argument / proof makes any sense to me, nor why it only applies to real numbers and makes them "uncountable". As near as I can tell it would seem to apply equal well to natural numbers, which are "countable".  What am I missing? "going to" definition, does it imply intent? I have had a debate with one of my friends about this little game:  "1 rabbit saw 9 elephants while going to the river. Every elephant saw 3 monkeys going to the river. Each monkey had 1 tortoise in each hand. How many animals are going to the river?"  Answers:   4 - if you could rabbit and monkeys (which are described as "going to" the river)  10 - if you are counting tortoises in monkeys' hands 19 - if you assume all   my argument is that the tortoises are not "going to", but are being either "taken to" or "move towards" river. That's what I would say if someone holds me and goes to the river.  my friend's argument is that because they move towards the river, they are "going to" the river. he gave example of me being in the car.  Me: If I don't intend to go there, I'm being "taken to", even if in the car.  Question: does "going to" implies intent of the subject ? Show that: $\lim\limits_{r\to\infty}\int\limits_{0}^{\pi/2}e^{-r\sin \theta}\text d\theta=0$ I would like to show $\lim\limits_{r\to\infty}\int_{0}^{\pi/2}e^{-r\sin \theta}\text d\theta=0$.  Now, of course, the integrand does not converge uniformly to $0$ on $\theta\in [0, \pi/2]$, since it has value $1$ at $\theta =0$ for all $r\in \mathbb{R}$.   If $F(r) = \int_{0}^{\pi/2}e^{-r\sin \theta}\text d\theta$, we can find the $j$th derivative $F^{(j)}(r) = (-1)^j\int_{0}^{\pi/2}\sin^{j}(\theta)e^{-r\sin\theta}\text d\theta$, but I don't see how this is helping.  The function is strictly decreasing on $[0,\pi/2]$, since $\partial_{\theta}(e^{-r\sin\theta})=-r\cos\theta e^{-r\sin \theta}$, which is strictly negative on $(0,\pi/2)$.  Any ideas?