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;λ)= λe^-λ 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 :F(x,λ)={1-e^-λ x, x>=0

                                     $0,x<0$
or                                     :F(x,λ)=1-e^-λ x.H(x). 

• The mean or expected value of the exponential distribution is: E[x]=1/ λ.
• The variance of the exponential distribution is:Var[x]=1/ λ^2.