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.
  • 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 $(X,Lambda,Cumulative)$.
  • 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lambda =5} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x=0.5}

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

Related Videos

Exponential Probability

See Also

• GAMMADIST
• POISSONDISTRIBUTION

References

• Exponential Distribution

• List of Main Z Functions

• Z3 home