Template:Characteristics of the exponential distribution alta

Characteristics
The characteristics of the 1-parameter exponential distribution can be exemplified by examining its parameter, lambda ( λ ) and the effect lambda has on the pdf, reliability and failure rate functions.

Effects of λ on the pdf



 * The scale parameter is $$\tfrac{1}{\lambda }$$.
 * As λ is decreased in value, the distribution is stretched out to the right, and as λ 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). Its only parameter is the failure rate, λ.
 * The distribution starts at T = 0 at the level of f(T = 0) = λ . It decreases thereafter exponentially and monotonically as T increases, and it is convex.
 * As $$T\to \infty $$, $$f(T)\to 0$$.
 * This pdf can be thought of as a special case of the Weibull pdf with β = 1.



Effects of λ on the Reliability Function

 * The 1-parameter exponential reliability function starts at the value of 1 at T = 0 . It decreases thereafter monotonically and is convex.
 * As $$T\to \infty $$, $$R(T\to \infty )\to 0$$.

Effects of λ on the Failure Rate Function
The failure rate function for the exponential distribution is constant and equal to the parameter λ.