I've been studying the Cox Proportional Hazards model, and this question is glossed over in most texts.  Cox proposed fitting the coefficients of the Hazard function using a partial likelihood method, but why not just fit the coefficients of a parametric Survival function using the maximum likelihood method and a linear model?  In any cases where you have censored data, you could just find the area under the curve. For example, if your estimate is 380 with standard deviation of 80, and a sample is censored >300, then there is an 84% probability for that sample in the likelihood calculation assuming normal error.
I've been studying the Cox Proportional Hazards model, and  this question is glossed over in most texts.    Cox proposed fitting the coefficients of the Hazard function using a partial likelihood method, but why not just fit the coefficients of a parametric Survival function using the maximum likelihood method and a linear model?    In any cases where you have censored data, you could just find the area under the curve.  For example, if your estimate is 380 with standard deviation of 80, and a sample is censored >300, then there is an 84% probability for that sample in the likelihood calculation assuming normal error.
How to evaluate $\int_{0}^{+\infty}\exp(-ax^2-\frac b{x^2})\,dx$ for $a,b>0$ How to send email from MySQL 5.1 I am drawing some graphs with tangents. I calculated the tangent should be centered at x=57/27 which is approximately x=2.11. I'm currently using the pos and sloped keys for nodes to draw tangents, but I'm not happy about the result; the tangents don't really align.   I think this is because the pos key calculates the actual length of the graph while the graphs don't have the same length.  I'm sure I can somehow let LaTeX do the calculations for me so as to align the slopes vertically at an x value of my choice. But how?  PS: The below document requires a working installation of gnuplot to compile.    \documentclass{standalone}   \usepackage{pgfplots} \pgfplotsset{compat=1.10} \usetikzlibrary{arrows, decorations.markings,intersections}  \makeatletter \tikzset{     nomorepostaction/.code=\makeatletter\let\tikz@postactions\pgfutil@empty,      my axis/.style={         postaction={             decoration={                 markings,                 mark=at position 1 with {                     \arrow[ultra thick]{latex}                 }             },             decorate,             nomorepostaction         },         thin,         -,         every path/.append style=my axis     } } \makeatother  \definecolor{headtitle}{RGB}{167,63,63}  \begin{document} \begin{tikzpicture}   \begin{axis}[%       axis line style={my axis},       xlabel = $U_A$,       ylabel = $S$,       xmin = 0, xmax = 3.25,       ymin = 0,       xtick={1,1.5},       xticklabels={$U_{B,\mathrm{initial}}$,$U_{A,\mathrm{initial}}$},       xticklabel style={             inner sep=0pt,             anchor=north east,             rotate=35         },       ytick=\empty,       height=.66\linewidth, width=\linewidth-4.5\tabcolsep,       axis lines*=left,       every axis y label/.style={at=(current axis.above origin),anchor=east},       every axis x label/.style={at=(current axis.right of origin),anchor=west}]%     \addplot+[mark={},draw=headtitle] gnuplot[raw gnuplot] {%       set samples 51;       plot [0:3] log(3*(3-x)+1);       } node[sloped,above,pos=.63333,       minimum height=1cm,minimum width=1cm] (SB) {} node[pos=0.6,pin=45:{\color{black}{$S_B$}}] {};      \addplot+[mark={},draw=headtitle] gnuplot[raw gnuplot] {%       set samples 51;       plot [0:3] log(9*x^2+6*x+1);       } node[sloped,above,pos=.83333,       minimum height=1cm,minimum width=1cm] (SA) {} node[pos=0.25,pin=-15:{\color{black}{$S_A$}}] {};       \addplot+[mark={},draw=headtitle] gnuplot[raw gnuplot] {%       set samples 51;       plot [0:3] log(9*x^2+6*x+1)+log(3*(3-x)+1);       } node[sloped,above,pos=.775,       minimum height=1cm,minimum width=1cm] (St) {} node[pos=0.525,pin=165:{\color{black}{$S_\mathrm{total}$}}] {};      \path (SB.south east) edge[headtitle,very thick] node {} (SB.south west);      \path (SA.south east) edge[headtitle,very thick] node {} (SA.south west);      \path (St.south east) edge[headtitle,very thick] node {} (St.south west);   \end{axis}% \end{tikzpicture}% \end{document} How to prove this $\pi$ formula? I am hoping to find out where the formula  $$\frac{\pi}{2}=\sum_{k=0}^{\infty}\frac{k!}{\left(2k+1\right)!!}$$ comes from. I can't see how one could begin to prove it. Finitely generated projective module Why don't self-closing script elements work? How can one motivate the relativistic momentum? Motivating the non-relativistic momentum $$\mathbf{p} = m\mathbf{v}$$ is quite easy: it is meant to represent the quantity of motion of the particle, and since the mass is one measure of quantity of matter it should be proportional to mass (how much thing is moving) and should be proportional to velocity (how fast and to where it is moving). Now, in Special Relativity the momentum changes. The new quantity of motion becomes $$\mathbf{p} = \dfrac{m\mathbf{v}}{\sqrt{1-\dfrac{v^2}{c^2}}}$$ Or, using $\gamma$ the Lorentz factor $$\mathbf{p} = \gamma(v) m\mathbf{v}$$ where I write $\gamma(v)$ to indicate that the velocity is that of the particle relative to the frame in which the movement is being observed. The need for this new momentum is because the old one fails to be conserved and because using the old one in Newton's second law leads to a law which is not invariant under Lorentz transformations. So the need for a new momentum is perfectly well motivated. What I would like to know is how can one motivate that the correct choice for $\mathbf{p}$ is the $\gamma(v)m\mathbf{v}$. There are some arguments using the mass: considering a colision, requiring momentum to be conserved, transform the velocity and then find how mass should transform. Although this work, it doesn't seem natural, and it is derived in one particular example. On my book there's even something that Einstein wote saying that he didn't think it was a good idea to try transforming the mass from $m$ to $M = \gamma(v)m$, that it was better to simply keep $\gamma$ on the new momentum without trying to combine it with the mass. So I would like to know: without resorting to arguments based on transformation of the mass, how can one motivate the new form of momentum that works for special relativity? There are many cases in maths where doing the same thing over and over again will bring you closer to a value. Derivation of polynomials is the striking example: no matter what you start with, you end up with 0. In a series expansion, the longer you continue the sequence the closer you get to the real value.  This concept applies in areas other than math (Wikipedia's everything-leads-to-philosophy phenomenon, for example). It's a little unrelated but it just proves the concept.  Hashing algorithms are just special math. Following logically, hash entropy supposedly decreases the more you hash a value. So is there a point at which any input value will give the same hash as any other?  (Let me just specify that we're not re-injecting any new data every time we hash, as if we're trying to increase the security of the hash by salting and re-hashing. It's strictly a matter of md5(md5(md5(... if that's the algorithm we're using.  I can see some problems with this already. Algorithms like md5 are designed to change their output radically when the input changes only by one bit of information. So even if a common hash for two values appears along the way, it itself will start changing. But then, does the fact that the output appears to be very different actually mean the possibilities are still many? I am looking for a way to delete all files older than 7 days in a batch file.  I've searched around the web, and found some examples with hundreds of lines of code, and others that required installing extra command line utilities to accomplish the task.  Similar things can be  in just a couple lines of code. It seems that something at least remotely easy could be done for batch files in Windows. I'm looking for a solution that works in a standard Windows command prompt, without any extra utilities. Please no PowerShell or Cygwin either. What kind of capacitor could build up, and maintain a charge acquired from lightning? "Which" vs. "what" — what's the difference and when should you use one or the other? Literal @YES not working in iOS 5 / Xcode 4.4 What is the default root password? Is it possible to prevent an NSURLRequest from caching data or remove cached data following a request? On iPhone, I perform a HTTP request using NSURLRequest for a chunk of data. Object allocation spikes and I assign the data accordingly. When I finish with the data, I free it up accordingly - however instruments doesn't show any data to have been freed!  My theory is that by default HTTP requests are cached, however - I don't want my iPhone app to cache this data.   Is there a way to clear this cache after a request or prevent any data from being cached in the first place?  I've tried using all the cache policies documented a little like below:  NSMutableURLRequest *theRequest = [NSMutableURLRequest requestWithURL:[NSURL URLWithString:url]]; theRequest.cachePolicy = NSURLRequestReloadIgnoringLocalCacheData;   but nothing seems to free up the memory! memoryless property of exponential distributions with random variables It is true that $P(X&gt;t+s|X&gt;t)=P(X&gt;s)$ for certain values $t$ and $s$.  However, how can I show that this still holds if:   $T$ is a continuous random variable. That is $P(X&gt;T+s|X&gt;T)=P(X&gt;s)$ Both $T$ and $S$ are continuous RVs: $P(X&gt;T+S|X&gt;T)=P(X&gt;S)$   All the random variables are independent. Why did the descriptive "Orientals" shift into a pejorative? Why can't I catch Pokemon in Pokemon Go anymore? I have a statement,     Either p or q   and I have to write it in terms of logical connectives but I don't get which logical connector should I be using? Here is what I did (I think there could have been a better way to do this)     $(p \lor q ) \land (\neg((p \Rightarrow q) \land (q \Rightarrow p)))$ read only access to all files in a specific sub-folder I have got a specific folder located in "/home/.../reboot/".  I have a series of users that require read-only access to the ever changing files within.  My problem is that the same users are not authorized to view any of the parent directory files.  Right now, the only thing I have in place is that their starting folder is at "/home/.../reboot/" by changing the etc/passwd file; and I need to block all access to other folders.  How could I only give them access to this directory? Not enough reputation - wanting to answer/comment I've seen a few questions I'd like to comment on or give a different answer, but seeing how I don't have 50 reputation (I've been a lurker for years, finally decided to participate) do I really need to ask a few questions before I can comment/answer other people's stuff? Or am I missing something here?  Sorry if this has been answered before, but with a few search tries I couldn't find any similar stuff, even tried google just for "50 reputation stackoverflow" but that didn't give me anything either.