Spread cost with skewed normal distribution

[JontyO]

Hi all.

Using Office 365
I have a formula to apply a normal distribution to costs over time, but I have two problems.
1. I would like to skew the distribution either to the left or to the right by specifying a value other than the mean, by placing a variable percentage of the duration (K4) so the peak is for example at 65% of the duration, rather than 50%. (Less than 50% is skewed to the left, and greater than 50% is to the right, but happy to use any alternative equivalent). I tried this using the product of the duration and the %, but then the total distributed costs did not match the total to be distributed.
2. This formula also requires the start and finish dates have to be on the first of the month. (Cells G4 and H4, with columns R to BQ including all days of that month) I would like to be able to start the item on any day, and then apply part of the costs for that month.

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Row 2

OWNER

PACKAGE

DESCRIPTION

CURR

BUDGET

START

FINISH

REM DURATION

DIST' CURVE

PEAK (AT % DUR)

STD DEV

CHECK SUM

COMMITTED

ACTUAL

ESTIMATE AT COMPLETION

ESTIMATE TO COMPLETE

Mar-23​

Apr-23​

May-23​

Jun-23​

Jul-23​

Aug-23​

Sep-23​

Row 3

Row 4

Company

911100

Item Description

AUD

23,233,287

Apr-23

May-27

50.0​

Normal

65%

16​

Ok

-

-

23,233,287

23,233,287

-

203,451

223,441

244,438

266,365

289,129

312,615

S4 Formula

=+IF(AND($J4="Linear",S$2>=$G4,S$2<=$H4),$Q4/$I4,0)+IF(AND($J4="Normal",S$2>=$G4,S$2<=$H4),(NORM.DIST((YEAR(S$2)-YEAR($G4))*12+MONTH(S$2)-MONTH($G4)+1,$I4/2,$L4,TRUE)-NORM.DIST((YEAR(S$2)-YEAR($G4))*12+MONTH(S$2)-MONTH($G4),$I4/2,$L4,TRUE))/(1-2*NORM.DIST(0,$I4/2,$L4,TRUE))*$Q4,0)

Thanks in advance.