PrecisionCalc
xl
Precision
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xlpPOISSON

Finds the Poisson Distribution, with up to 32,767 significant digits of precision. Same as Excel's built-in POISSON function, but with high precision. Can return both cumulative and non-cumulative Poisson.

The Poisson Distribution is the probability that a certain number of events (non-cumulative Poisson), or up to a maximum number of events (cumulative Poisson), will occur during a certain period of time. Finding the Poisson Distribution requires that the average number of events for the time period is known.

For example, if you get an average of 25 pieces of junk mail per week, xlpPOISSON can find the probability that, in any given typical week, you will receive:

Poisson Distribution is appropriate for scenarios in which there is a very large number of possible events, where each possible event rarely occurs. For example, although you may receive an average of 25 pieces of junk mail per week, you only rarely receive one from ABC Corporation. (If you usually receive one piece of junk mail from Acme Corporation every week, then that piece of junk mail is not rare and should therefore be excluded from your Poisson Distribution calculation.)

Poisson Distribution is not appropriate for scenarios in which the number of possible events is similar to the average number of events -- or in other words, where all possible events usually occur. For example, if a faucet drips 10 times per minute, the probability that it will drip exactly 9, 10, or 11 times in any given typical minute is much higher than would be indicated by the Poisson Distribution, while the probability that it will drip any other number of times is much lower than would be indicated by the Poisson Distribution.

 

Syntax

xlpPOISSON(target_num,average_num,is_cumulative,exponential_notation,maximum_significant_digits,restrict_input_lengths)

target_num Required. The number of events (non-cumulative Poisson) or maximum number of events (cumulative Poisson) in a given period of time, for which to find the probability of occurrence.
average_num Required. The expected or average number of events in a given period of time.
is_cumulative Required. Determines whether to find the cumulative Poisson Distribution, or the non-cumulative Poisson Distribution.

If TRUE, returns the cumulative Poisson Distribution. If FALSE, returns the non-cumulative Poisson Distribution.

exponential_notation Optional. Determines whether result is formatted in exponential notation. Set to TRUE to format in exponential notation. FALSE by default.
maximum_significant_digits Optional. Determines the maximum number of significant digits to be returned. Default is 100, or the user's custom maximum set in the About box, or the maximum number allowed by the edition of xlPrecision, whichever is less.
restrict_input_lengths Optional. TRUE by default. See xlpPOWER for details.

Remarks

Examples

Formula Description
=xlpPOISSON(23,25,FALSE) The probability that exactly 23 events will occur during a period of time for which an average of 25 events occur.
=xlpPOISSON(26,25,TRUE) The probability that up to a maximum of 26 events will occur (anywhere from 0 to 26 events) during a period of time for which 25 events occur on average.
=xlpPOISSON(21,25,FALSE,TRUE) The probability that exactly 21 events will occur during a period of time for which an average of 25 events occur. The number is returned in exponential notation.
=xlpPOISSON(19,25,TRUE,,500) The probability that up to a maximum of 19 events will occur (anywhere from 0 to 19 events) during a period of time for which 25 events occur on average, with 500 significant digits.