Manuals/calci/EXPONDIST

EXPONDIST(x,lambda,cumulative)

• $x$ is the value of the function
• $lambda(\lambda )$ is the value of the rate parameter
• $cumulative$ is the logical value like TRUE or FALSE

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 Section

• The syntax is to calculate EXPONDIST in ZOS is $(x,lambda,cumulative)$.
  • 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 $x=0.5$

• =EXPONDIST(0.5,5,TRUE) = 0.917915001
• =EXPONDIST(5,3,TRUE) = 0.999999694
• =EXPONDIST(0.4,2,FALSE) = 0.898657928"

See Also

• GAMMADIST
• POISSONDISTRIBUTION

References

• Exponential Distribution