Template:Two parameter exp distribution: Difference between revisions

Latest revision as of 10:10, 9 August 2012

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-===The Two-Parameter Exponential Distribution===
+#REDIRECT [[The Exponential Distribution]]
-The two-parameter exponential ''pdf'' is given by:
-::<math>f(T)=\lambda {{e}^{-\lambda (T-\gamma )}},f(T)\ge 0,\lambda >0,T\ge 0\text{ or }\gamma </math>
-where <math>\gamma </math> is the location parameter.
-Some of the characteristics of the two-parameter exponential distribution are [19]:
-#The location parameter, <math>\gamma </math>, if positive, shifts the beginning of the distribution by a distance of <math>\gamma </math> to the right of the origin, signifying that the chance failures start to occur only after <math>\gamma </math> hours of operation, and cannot occur before.
-#The scale parameter is <math>\tfrac{1}{\lambda }=\bar{T}-\gamma =m-\gamma </math>.
-#The exponential <math>pdf</math> has no shape parameter, as it has only one shape.
-#The distribution starts at <math>T=\gamma </math> at the level of <math>f(T=\gamma )=\lambda </math> and decreases thereafter exponentially and monotonically as <math>T</math> increases beyond <math>\gamma </math> and is convex.
-#As <math>T\to \infty </math>, <math>f(T)\to 0</math>.
-<br>
-{{one parameter exp distribution}}