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 λ is non-numeric.
2. x<0 or λ<=0
The probability density function  of an exponential distribution is: f(x;λ)={λe^-λx   ,   x>=0
                                                                               0      ,   x<0
                                                                                  or  f(x;λ)= λ e^-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.

== EXPONDIST is to model the time between events.

X or Lambda must be a numeric value in this function. Otherwise it shows error.

If x is less than 0, or Lambda less than or equal to zero, EXPONDIST shows error value.

AVEDEV (N1, N2...) Where N1, N 2 ...   are positive integers. Let’s see an example

EXPONDIST(x, Lambda, cum)

B

0.5

15

=EXPONDIST (B2, B3, TRUE) is 0.9994

=EXPONDIST (0.5, 15, FALSE) is 0.0083