Cum Hazard | Clipmarks


	Cum Hazard

abailart

12-9-2007 6:06 AM

168 views

tags:

cum hazard, probability

2 Comments |

Add a Comment

12-9-2007 7:01 AM

debbyski

POP for the title.

12-9-2007 7:50 AM

katsteevns

I knew that!

Login to Comment. Not a member yet? Sign up

View the Top Clips from December 9, 2007

Embed This Clip In Your Site...

<div style="margin: 12px 0px; font-family: arial; color: #333333; background: #ffffff; border: solid 4px #e5e5e5; width: 100%; clear: left;"><div class="CM_CTB_Content_Wrap" style="margin: 0px; padding: 0px;background-color: #ffffff;"><div style="border-bottom: solid 1px #dcdcdc; white-space: nowrap; margin-bottom: 8px; background-color: #eeeeee ;background-image: url(http://www.clipmarks.com/images/source-bg.gif); background-repeat: repeat-x; height: 24px; line-height: 24px; vertical-align: middle; padding-bottom: 4px; color: #666666; font-size: 10px;" ><a href="http://clipmarks.com/clip-to-blog/" title="see clips that are hot right now"><img src="http://content.clipmarks.com/blog_embed/ce152daf-4a64-45fd-9d85-790b0454fdc1/C7362C69-A7B2-4674-BD4D-1D93B38A30FA/" alt="" width="19" height="19" border="0" style="vertical-align: middle; margin: 0px 4px; display: inline; border: none; float:none;" /></a>clipped from <a title="http://www.itl.nist.gov/div898/handbook/apr/section2/apr222.htm" href="http://www.itl.nist.gov/div898/handbook/apr/section2/apr222.htm" style="font-size: 11px;">www.itl.nist.gov</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.itl.nist.gov/div898/handbook/apr/section2/apr222.htm"><P>The cum hazard for the <A href="../section1/apr161.htm#Formula's and Plots">exponential</A>
is just <I>H(t) = <IMG align="absbottom" alt="lambda" src="http://www.itl.nist.gov/div898/handbook/apr/section2/gifs/lambda.gif" />t</I>,
which is linear in <I>t</I> with a 0 intercept. So a simple linear graph
paper plot of <I>y</I> = col (6) vs <I>x</I> = col (1) should line up as
approximately a straight line going through the origin with slope <IMG align="absbottom" alt="lambda" src="http://www.itl.nist.gov/div898/handbook/apr/section2/gifs/lambda.gif" />
if the exponential model is appropriate. The Dataplot commands and graph
of this are shown below:
</P><P>LET X = DATA 37 73 132 195 222 248
<BR />LET Y = DATA .1 .225 .391 .591 .924 1.424
<BR />PLOT Y X</P></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.itl.nist.gov/div898/handbook/apr/section2/apr222.htm"><div align="center"><img src="http://content8.clipmarks.com/blog_cache/www.itl.nist.gov/img/B06B27D9-5FC6-4D65-8A4E-AE6917DCAE51" alt="Exponential cumulative hazard plot" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.itl.nist.gov/div898/handbook/apr/section2/apr222.htm"><P>The cum Hazard for the <A href="../section1/apr162.htm#Formula'sand">Weibull</A>
is <IMG width="94" height="26" align="absmiddle" alt="H(t) = (t/alpha)**gamma" src="http://www.itl.nist.gov/div898/handbook/apr/section2/eqns/weicumhaz.gif" />,
so a plot of <I>y</I> vs<I> x</I> on log log paper should resemble a straight
line with slope <IMG width="13" height="17" align="absbottom" alt="gamma" src="http://www.itl.nist.gov/div898/handbook/apr/section2/gifs/gamma.gif" />,
if the Weibull model is appropriate. The Dataplot commands and graph of
this are shown below:
</P></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.itl.nist.gov/div898/handbook/apr/section2/apr222.htm"><P>XLOG ON
<BR />YLOG ON
<BR />PLOT Y X
<BR /><IMG width="456" height="383" alt="Plot of Weibull cumulative hazard" src="http://www.itl.nist.gov/div898/handbook/apr/section2/gifs/chazweib.gif" />
</P></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.itl.nist.gov/div898/handbook/apr/section2/apr222.htm">The Weibull fit looks better, although the slope estimate is 1.27, which
is not far from an exponential model slope of 1. Of course, with a sample
of just 10, and only 6 failures, it is difficult to pick a model from the
data alone.</blockquote></div><div style="margin: 0px 6px 6px 4px;"><table style="font-size: 11px;border-spacing: 0px;padding: 0px;" cellpadding="0" cellspacing="0" width="100%"><tr><td style="background:transparent;border-width:0px;padding:0px;">&nbsp;</td><td align="right" style="background:transparent;border-width:0px;padding:0px;width:107px" width="107"><a href="http://clipmarks.com/share/C7362C69-A7B2-4674-BD4D-1D93B38A30FA/blog/" title="blog or email this clip"><img src="http://content9.clipmarks.com/images/c2b-foot.png" border="0" alt="blog it" width="107" height="17" style="border-width:0px;padding:0px;margin:0px;" /></a></td></tr></table></div></div>

Clipmarks: Home; New Clips; Top Clips; Dashboard

Popular Topics: News; Life; Science; Technology; Entertainment

Get Started: Sign Up; Install Clipping Tool; How Clipping Works; Clip-to-Blog™; ClipSearch

Tools and Resources: FAQ; ClipWeek; Top Clippers; Top Tags; Site Map

About Clipmarks: About Us; Contact; Blog; Copyright; Privacy; EULA

Search Options

Related Clips

More clips from abailart

Today's Top Clips