Manuals/calci/EXPONDIST

EXPONDIST(X,Lambda,Cumulative)

$X$ is the value of the function.
$Lambda(\lambda )$ is the value of the rate parameter.
is the logical value like TRUE or FALSE.
- EXPONDIST(), returns the exponential distribution.

Description

This function gives the Exponential Distribution. This distribution is used to model the time until something happens in the process.
This describes the time between events in a Poisson process i.e, a process in which events occur continuously and independently at a constant average rate.
For e.g Time between successive vehicles arrivals at a workshop.
Exponential distribution is the only continuous memoryless random distribution. It is a continuous analog of the Geometric distribution.
In $EXPONDIST(X,Lambda,Cumulative)$ , $X$ is the value of the function, $Lambda$ is called rate parameter and $Cumulative$ is either TRUE or FALSE.
This function will give the Cumulative Distribution Function when $Cumulative$ is TRUE, otherwise it will give the Probability Density Function , when $Cumulative$ is FALSE.
Suppose we are not giving the $Cumulative$ value, by default it will consider the $Cumulative$ value is FALSE.
This function will give the error result when

1.  $X$  or  $Lambda$  is non-numeric.
2.  $X<0$  or  $Lambda\leq 0$

The Probability Density Function of an Exponential Distribution is: $f(x,\lambda )={\begin{cases}\lambda e^{-\lambda x}&,x\geq 0\\0&,x<0\end{cases}}$ or

f(x;\lambda )=\lambda e^{-\lambda x}.H(x)

where $\lambda$ is the rate parameter and $H(x)$ is the Heaviside step function
This function is valid only on the interval [0,infinity].

The Cumulative Distribution Function is : $F(x,\lambda )={\begin{cases}1-e^{-\lambda x}&,x\geq 0\\0&,x<0\end{cases}}$ or

F(x,\lambda )=1-e^{-\lambda x}.H(x)

ZOS

The syntax is to calculate EXPONDIST in ZOS is .
- where $X$ is the value of the function
- $Lambda$ is the value of the rate parameter
- $Cumulative$ is the logical value like TRUE or FALSE.
For e.g.,EXPONDIST(11..12,2.3..3.3..0.4,FALSE)

Exponential Distribution

Examples

Question : If jobs arrive at an average of 15 seconds, $\lambda =5$ per minute, what is the probability of waiting 30 seconds, i.e 0.5 min? Here $\lambda =5$ and $x=0.5$