(25) Poisson Distribution
12-23-2017, 06:39 PM
Post: #1
 SlideRule Senior Member Posts: 1,000 Joined: Dec 2013
(25) Poisson Distribution
extracted from Matematisk Institutt (MAR, 1977) Avd.C by Erling Sverdrup
[attachment=5471] [attachment=5472] [attachment=5473] [attachment=5474] [attachment=5475]
BEST!
SlideRule
12-24-2017, 12:20 PM (This post was last modified: 12-24-2017 12:58 PM by Dieter.)
Post: #2
 Dieter Senior Member Posts: 2,397 Joined: Dec 2013
RE: (25) Poisson Distribution
(12-23-2017 06:39 PM)SlideRule Wrote:  extracted from Matematisk Institutt (MAR, 1977) Avd.C by Erling Sverdrup

First of all: This seems to be the Erling Sverdrup who has an own article on Wikipedia:
Quote:Erling Sverdrup (23 February 1917 – 15 March 1994) was a Norwegian statistician and actuarial mathematician. He played an instrumental role in building up and modernising the fields of mathematical statistics and actuarial science in Norway, primarily at the Department of Mathematics at the University of Oslo but also via his links to Statistics Norway.

So "Matematisk Institutt" is the department of mathematics / math sciences at the university of Oslo. "Avd. C" is short for "avdeling C" which simply means "department C".

The idea of rescaling exp(-λ) to prevent underflow is nice, but the implementation of the first program leaves room for improvments. Forty years later, here is another version that implements the same idea and works with the exact threshold (ln 1E99) instead of 227.

Code:
01  STO 3 02  X<>Y 03  STO 2 04  EEX 05  9 06  9 07  LN 08  X>=Y? 09  X<>Y 10  CHS 11  e^x 12  STO 0 13  CLX 14  STO 1 15  STO 4 16  RCL 0 17  STO+1 18  RCL 3 19  RCL 4 20  x>=y? 21  GTO 29 22  1 23  STO+4 24  RCL 2 25  RCL 4 26  / 27  STOx0 28  GTO 16 29  EEX 30  9 31  9 32  LN 33  RCL 2 34  - 35  X>=0? 36  CLX 37  e^x 38  STOx0 39  STOx1 40  RCL 0 41  RCL 1

Input:  λ [ENTER] k
Output X: cumulative distribution function P(x≤k)
Output Y: probability mass function P(x=k)

Registers:
R0: PMF
R1: CDF
R2: λ
R3: k
R4: x=0...k

Example:

f [PRGM]  f [FIX] 4

4,68 [ENTER] 5
[R/S]  => 0,6719
[X↔Y] => 0,1736

240 [ENTER] 10
[R/S]  => 1,0717063 E–87
[X↔Y] => 1,0272443 E–87

450 [ENTER] 450
[R/S]  => 0,5125
[X↔Y] => 0,0188

Both results can also be recalled from R1 or R0 respectively.

Dieter
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