Weibull++ Standard Folio Data 1P-Exponential

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 * valign="middle" |Standard Folio Data 1P-Exponential
 * valign="middle" | Weibull++
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 * valign="middle" | Weibull++
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The One-Parameter Exponential Distribution
The one-parameter exponential $$pdf$$ is obtained by setting $$\gamma =0$$, and is given by:

$$ \begin{align}f(t)= & \lambda {{e}^{-\lambda t}}=\frac{1}{m}{{e}^{-\tfrac{1}{m}t}}, & t\ge 0, \lambda >0,m>0 \end{align} $$

where:

This distribution requires the knowledge of only one parameter, $$\lambda $$, for its application. Some of the characteristics of the one-parameter exponential distribution are [19]:
 * 1) The location parameter, $$\gamma $$, is zero.
 * 2) The scale parameter is $$\tfrac{1}{\lambda }=m$$.
 * 3) As $$\lambda $$ is decreased in value, the distribution is stretched out to the right, and as $$\lambda $$ is increased, the distribution is pushed toward the origin.
 * 4) 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, $$\lambda $$.
 * 5) The distribution starts at $$t=0$$ at the level of $$f(t=0)=\lambda $$ and decreases thereafter exponentially and monotonically as $$t$$ increases, and is convex.
 * 6) As $$t\to \infty $$, $$f(t)\to 0$$.
 * 7) The $$pdf$$ can be thought of as a special case of the Weibull $$pdf$$ with $$\gamma =0$$ and $$\beta =1$$.


 * valign="middle" | Exponential Distribution
 * valign="middle" | See Examples...
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 * valign="middle" | See Examples...
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