Difference between revisions of "Manuals/calci/EXPONDIST"
Jump to navigation
Jump to search
| Line 8: | Line 8: | ||
*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. | *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. | *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 <math>EXPONDIST(x,lambda,cumulative)</math>, <math>x</math> is the value of the function, <math> lambda</math> is called rate parameter and <math>cumulative</math> is either TRUE or FALSE. | *In <math>EXPONDIST(x,lambda,cumulative)</math>, <math>x</math> is the value of the function, <math> lambda</math> is called rate parameter and <math>cumulative</math> is either TRUE or FALSE. | ||
*This function will give the Cumulative Distribution Function when <math>cumulative</math> is TRUE, otherwise it will give the Probability Density Function , when <math>cumulative</math> is FALSE. | *This function will give the Cumulative Distribution Function when <math>cumulative</math> is TRUE, otherwise it will give the Probability Density Function , when <math>cumulative</math> is FALSE. | ||
Revision as of 23:20, 8 June 2014
EXPONDIST(x,lambda,cumulative)
- 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} is the value of the function
- 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(\lambda)} is the value of the rate parameter
- 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 cumulative} is the logical value like TRUE or FALSE
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 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 EXPONDIST(x,lambda,cumulative)} , 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} is the value of the function, 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} is called rate parameter 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 cumulative} is either TRUE or FALSE.
- This function will give the Cumulative Distribution Function when 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 cumulative} is TRUE, otherwise it will give the Probability Density Function , when 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 cumulative} is FALSE.
- Suppose we are not giving the value, by default it will consider the 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 cumulative} value is FALSE.
- This function will give the error result when
value, by default it will consider the 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 cumulative}
value is FALSE.1. 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}
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 lambda}
is non-numeric.
2. 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}
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 lambda \le 0}
The Probability Density Function of an 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 f(x,\lambda)=\begin{cases} \lambda e^{-\lambda x} &, x \ge 0 \\ 0 &, x<0 \end{cases}} 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;\lambda)= \lambda e^{-\lambda x} .H(x)}
- where 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} is the rate parameter 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 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 (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,\lambda)=\begin{cases} 1-e^{-\lambda x} &, x \ge 0 \\ 0 &, x<0 \end{cases}} 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,\lambda)=1-e^{-\lambda x}.H(x)}
Examples
Question : If jobs arrive at an average of 15 seconds, 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} 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"