Difference between revisions of "Manuals/calci/EXPONDIST"
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2. x<0 or λ<=0 | 2. x<0 or λ<=0 | ||
The probability density function of an exponential distribution is: | The probability density function of an exponential distribution is: | ||
− | <math>f(x;λ)=λe^{-λx} | + | <math>f(x;λ)=λe^{-λx} , x\ge0 </math> |
:<math> =0 , x<0</math> | :<math> =0 , x<0</math> | ||
or | or |
Revision as of 23:26, 28 November 2013
EXPONDIST(x,Lambda,cum)
- is the value of the function
- is the value of the rate parameter
- 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: Failed to parse (syntax error): {\displaystyle f(x;λ)=λe^{-λx} , x\ge0 }
or
- 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 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
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.