Manuals/calci/EXPONDIST

EXPONDIST(x,Lambda,cum)

• $x$ is the value of the function
• $lambda$ is the value of the rate parameter
• $cu$ is the logical value like TRUE or FALSE

Description

• This function gives the exponential distribution. This distribution 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.
• In EXPONDIST(x, lambda,cu), xis the value of the function, lambda is called rate parameter and cu(cumulative) is the TRUE or FALSE. *This function will give the cumulative distribution function , when cu is TRUE,otherwise it will give the probability density function , when cu is FALSE.
• Suppose we are not giving the cu value, by default it will consider the cu 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

$f(x,\lambda )=\lambda e^{-\lambda x},x\geq 0$

$=0,x<0$

or

Failed to parse (syntax error): {\displaystyle f(x;\lambda)= λe^{-\lambda x} .H(x)}

• where λ 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 : Failed to parse (syntax error): {\displaystyle F(x;\lambda)={1-e^{-\lambda x}, x\ge 0}

$0,x<0$

or

F(x,λ)=1-e^{-\lambda x}.H(x).

• The mean or expected value of the exponential distribution is: 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 E[x]=\frac{1}{ λ}}
• The variance of the exponential distribution is: $Var[x]={\frac {1}{\lambda ^{2}}}$.