PrecisionCalc
xl
Precision
Get Your Numbers Right

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:

• Exactly 36 pieces of junk mail (very low probability)
• Exactly 23 pieces of junk mail (low probability)
• Up to a maximum of 26 pieces of junk mail (high probability)
• Up to a maximum of 32 pieces of junk mail (very high probability)

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

• xlPrecision results are returned as text that look like numbers, not as values that Excel recognizes as numbers. This is because Excel would truncate the results to 15 significant digits if it recognized them as numbers.

• target_num and average_num can accept both numbers and text.

• target_num and average_num accept text up to 32,767 characters long.

• maximum_significant_digits is ignored if it is higher than the maximum significant digits allowed by the edition of xlPrecision.

• Use maximum_significant_digits to increase calculation speed where desired. The lower the number used, the faster the calculation.

• You can use the results of xlPrecision functions as the operands in other xlPrecision formulas without losing any precision, but using them as operands in Excel's arithmetic functions will truncate them to 15 significant digits.

• If the return value is so large that it has more than 32,767 characters to the left of the decimal, then xlPrecision is of course unable to return a correct value and instead returns "#VALUE!". Note, that's a vastly larger number than Excel can return without xlPrecision. Excel itself can only return or recognize a number with no more than 308 digits to the left of the decimal.

• The 32,767 SD edition can only provide a maximum of 32,767 total characters, including all formatting characters such as decimal, leading hyphen or parentheses for negatives, and thousands separators. As a result, it can only return the maximum 32,767 significant digits when the result is an unformatted positive integer. This is due to Excel's limitation of 32,767 characters in a cell. In all cases, the 32,767 SD edition will give you as many significant digits as possible with the formatting you have chosen.

• Depending on how many significant digits the edition of xlPrecision provides, the result may be too long to conveniently view. You can view the full result by right-clicking the cell and choosing Format Cells | Alignment | Wrap Text, and widening the column to the width of the screen. An easy way to view the full result without changing column widths or wrapping text is to right-click the cell, choose Copy, and then paste into Notepad or a word processor.

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.