formula for pyramid distribution? For Google Sheets

[smking204]

I've got a doozy for y'all. I want to create a formula that will return a random integer according to a pyramid distribution.

For example, A1 might serve as my input, which is itself a randomized integer, let's call it 24 for now. In B1, then, I want my pyramid formula, which will return a new integer that is + or - 50% of the input, but weighted toward the middle (12 and 36 would each have one chance of appearing, 13 and 35 would each have two chances, 14 and 34 would each have 3, and so on).

The formula needs to be 1) dependent on the variable input, and 2) able to be retooled for a different percentage

WAY too much math for me, but I hope to get some responses to dissect and get a little better at this sort of thing. Thanks a ton!

 

[smking204]

I tweaked the normal distribution formula so that it limits the results to +/- 50%. It works, but the endpoints will be a bit higher than expected (see the graph below). I experimented with changing the size of the standard deviation. I originally used a divisor of 2 which made the endpoints significantly higher. I used a divisor of 3, which made the endpoints about what you'd want, but it made the rest of the values drop off much quicker too. I think a divisor of 2.5 is about the best compromise.

Book1 (version 1).xlsb
	A	B	C	D	E
1	0	Midpoint	Range		Random #
2	0	24	50%		25
3	0
4	0
5	0
6	0
7	0
8	0
9	0
10	0
11	0
12	25	.........................
13	11	...........
14	29	.............................
15	39	.......................................
16	50	..................................................
17	56	........................................................
18	89	.........................................................................................
19	111	...............................................................................................................
20	115	...................................................................................................................
21	140	............................................................................................................................................
22	154	..........................................................................................................................................................
23	200	........................................................................................................................................................................................................
24	168	........................................................................................................................................................................
25	153	.........................................................................................................................................................
26	132	....................................................................................................................................
27	116	....................................................................................................................
28	109	.............................................................................................................
29	78	..............................................................................
30	73	.........................................................................
31	39	.......................................
32	40	........................................
33	25	.........................
34	24	........................
35	9	.........
36	15	...............
37	0
End

Cell Formulas
Range	Formula
E2	E2	=MEDIAN(INT(NORM.INV(RAND(),B2,B2*C2/2.5)),INT(B2-B2*C2),ROUNDUP(B2+B2*C2,0))
B12:B37	B12	=REPT(".",A12)

As far as I know, all these functions exist in Google Sheets, although with slightly different names (NORM.INV --> NORMINV). I hope it works for you, but if not, you'll have to find someone else to step in. Good luck!

You're a good man, Eric! Thanks so much, I'll be parsing through this and your earlier responses, they've been super helpful.