Template:Exponential Distribution Example: Likelihood Ratio Bound for Time: Difference between revisions

Latest revision as of 08:42, 10 August 2012

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-====Example 6: Likelihood Ratio Bound for Time====
+#REDIRECT [[The Exponential Distribution]]
-For the data given in Example 5: Likelihood Ratio Bound for <math>\lambda </math>, determine the 85% two-sided confidence bounds on the time estimate for a reliability of 90%. The ML estimate for the time at <math>R(t)=90%</math> is <math>\hat{t}=7.797</math>.
-=====Solution to Example 6=====
-In this example, we are trying to determine the 85% two-sided confidence bounds on the time estimate of 7.797. This is accomplished by substituting <math>R=0.90</math> and <math>\alpha =0.85</math> into the likelihood ratio bound equation. It now remains to find the values of <math>t</math> which satisfy this equation. Since there is only one parameter, there are only two values of <math>t</math> that will satisfy the equation. These values represent the <math>\delta =85%</math> two-sided confidence limits of the time estimate <math>\hat{t}</math>. For our problem, the confidence limits are:
-::<math>{{\hat{t}}_{R=0.9}}=(4.359,16.033).</math>