Template:One parameter exp distribution: Difference between revisions

Latest revision as of 07:33, 10 August 2012

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-===The One-Parameter Exponential Distribution===
+#REDIRECT [[The Exponential Distribution]]
-The one-parameter exponential <math>pdf</math> is obtained by setting <math>\gamma =0</math>, and is given by:
-::<math> \begin{align}f(t)= & \lambda {{e}^{-\lambda t}}=\frac{1}{m}{{e}^{-\tfrac{1}{m}t}},
-  & T\ge 0, \lambda >0,m>0
-\end{align}
-</math>
-where:
-This distribution requires the knowledge of only one parameter, <math>\lambda </math>, for its application. Some of the characteristics of the one-parameter exponential distribution are [[Appendix: Weibull References|
-[19]]]:
-:#The location parameter, <math>\gamma </math>, is zero.
-:#The scale parameter is <math>\tfrac{1}{\lambda }=m</math>.
-:#As <math>\lambda </math> is decreased in value, the distribution is stretched out to the right, and as <math>\lambda </math> is increased, the distribution is pushed toward the origin.
-:#This distribution has no shape parameter as it has only one shape, i.e. the exponential, and the only parameter it has is the failure rate, <math>\lambda </math>.
-:#The distribution starts at <math>t=0</math> at the level of <math>f(t=0)=\lambda </math> and decreases thereafter exponentially and monotonically as <math>t</math> increases, and is convex.
-:#As <math>t\to \infty </math> , <math>f(t)\to 0</math>.
-:#The <math>pdf</math> can be thought of as a special case of the Weibull <math>pdf</math> with <math>\gamma =0</math>  and <math>\beta =1</math>.