I have a homework assignment where I need to run 1000 simulations in excel using an exponential distribution. I'm not sure how to get excel to give me the data I need. This is the question (the first part, at least):
I've figured out how to use the exponential distribution formula in excel, but I can't get it to return any values greater than 1. I think it's just the nature of that function, but I can't figure out how to get Excel to display the simulated lifetimes of the components. Any help at all would be much appreciated.
with λ in cell N4, the formula =-1/$N$4*LN(1-RAND()) yields a random number from the exponential distribution with parameter λ
from http://www.tushar-mehta.com/publish_train/xl_vba_cases/0806%20generate%20random%20numbers.shtml
Related
I apologize if the title is a bit vague. I am trying to create a calculator that takes into account how much "scrap" I have, how much is needed to resmelt it, and how many bars recieved.
Currently using:
(=if((amtOwned/qtyToSmelt)<1,,rounddown((amtOwned/qtyToSmelt)*barsMade))
Table and Formula
The problem I am having is you MUST have the QTY to Smelt. But the value returned includes partial quantities.
Ex. 125 Bottle Caps should equal 4 Bars total. Yet it returns 5.
How can i make the formula only account for increments of the bars recieved?
Thank you for any help, again i apologize if this isn't that clear. Im not exactly sure how to express my need in this situation.
I have tried messing around with the syntax and where every argument sits, even this formula is the most recent iteration of what i thought would be needed.
EDIT: I have tried using the TRUNC function and this seems to be working as I need it to. The formula now is:
=TRUNC((AMTowned/AMTneeded),0)*barsRecieved
=TRUNC((136/50),0)*2 This is returning 2 bars instead of 3. Which is exactly what I need.
It appears this is working by truncating the number first then multiplying it. So, 1.5 becomes 1 before being multiplied. This was my guess after doing more research. I had been searching for a while before I posted this but am glad to have learned what I have in searching for this.
There is a tool for auditing formulas. To see it go to Formulas > Evaluate Formula.
So here is you formula =IF((E3/C3)<1,,ROUNDDOWN((E3/C3)*D3,0))
Have you tried the calculation on your regular calculator? To me it is doing what you would expect. (125/50)*2 = 5
Stata uses the method of quantile calculation called R-2 (https://en.wikipedia.org/wiki/Quantile), whereas Excel uses R-7 with percentile.inc function. My goal is to find a correct formula in Excel that would give results identical to ones in Stata with the R-2 method.
For now, I can see that percentile.inc matches Stata results only for odd and discrete samples (I am dealing with discrete samples). However, the issue occurs with even samples shown here
Conceptually, using percentile.inc in Excel does not seem to be correct since it is an R-7 method, even though it matches with the R-2 method for odd and discrete samples.
My question is what is the simplest formula that would be correct to use in Excel to match Stata percentile results?
So a fairly literal translation of R-2 into Excel for N=4 would look like this (assuming sorted data):
=(INDEX(A$2:A$5,CEILING(C2*4,1))+INDEX(A$2:A$5,FLOOR(C2*4+1,1)))/2
It does indeed go wrong if you try and put in a quantile of zero so that would have to be a special case as would a quantile of 1. I assume Stata gives the lowest and highest values in the set in these two cases?
A more dynamic formula with all the checking would look like this:
=IFS(OR(C2<0,C2>1),"Out of range",C2=0,A$2,C2=1,INDEX(A:A,COUNT(A:A)+1),TRUE,(INDEX(A$2:INDEX(A:A,COUNT(A:A)+1),CEILING(C2*COUNT(A:A),1))+INDEX(A$2:INDEX(A:A,COUNT(A:A)+1),FLOOR(C2*COUNT(A:A)+1,1)))/2)
although you could make it shorter using the Let construct in Microsoft 365.
It would probably be nice to implement this as function in VBA which would sort the data as well as returning the quantile value or of course you could do the sort in a Microsoft 365 formula as well:
=LET(N,COUNT(A:A),sortedRange,SORT(A$2:INDEX(A:A,N+1)),IFS(OR(C2<0,C2>1),"Out of range",C2=0,INDEX(sortedRange,1),C2=1,INDEX(sortedRange,N),TRUE,(INDEX(sortedRange,CEILING(C2*N,1))+INDEX(sortedRange,FLOOR(C2*N+1,1)))/2))
What I have attempted:
AVERAGEIF(B11:V11,">+MEDIAN(B11:V11)")
What I am trying to do:
I would like to take the average of the upper half of given data. Elaborating more. I would like to find a formula that will allow me to remove a given lower fence of outliers and dissect the data then given to me. I would greatly prefer to maintain this formula within one cell "not grabbing different results from formulas within multiple cells".
Update:
Following through I found the solution.. I think.
One thing I should have explained further:
The data coming in replicating a typical sqrt function.
What I wanted to achieve is to capture the mean of the "plateau" of the data.
The equation I used was:
=AVERAGEIF(B3:B62,(">"&+TRIMMEAN(B3:B62,0.8)),B3:B62)
This was something I just copied and pasted. of course "B3" and "B62" are significant only for my application.
My rough explanation of the equation:
TRIMMEAN will limit the AVERAGE to the top 20%(">")(0.8) of the data selected. So for my application, this SHOULD give me a rough mean of the "plateau" of the data i would like to find the mean for.
This formula calculates the Median() of the range, then AverageIf() uses the median and only grabs values that are greater than or equal to >= the median ~ giving you the average of the 'top-half' of your values.
AVERAGEIF(A1:A10,">="&MEDIAN(A1:A10))
Hope this help!
I want to produce 100 random numbers with normal distribution (with µ=10, σ=7) and then draw a quantity diagram for these numbers.
How can I produce random numbers with a specific distribution in Excel 2010?
One more question:
When I produce, for example, 20 random numbers with RANDBETWEEN(Bottom,Top), the numbers change every time the sheet recalculates. How can I keep this from happening?
Use the NORMINV function together with RAND():
=NORMINV(RAND(),10,7)
To keep your set of random values from changing, select all the values, copy them, and then paste (special) the values back into the same range.
Sample output (column A), 500 numbers generated with this formula:
IF you have excel 2007, you can use
=NORMSINV(RAND())*SD+MEAN
Because there was a big change in 2010 about excel's function
As #osknows said in a comment above (rather than an answer which is why I am adding this), the Analysis Pack includes Random Number Generation functions (e.g. NORM.DIST, NORM.INV) to generate a set of numbers. A good summary link is at http://www.bettersolutions.com/excel/EUN147/YI231420881.htm.
Rand() does generate a uniform distribution of random numbers between 0 and 1, but the norminv (or norm.inv) function is taking the uniform distributed Rand() as an input to generate the normally distributed sample set.
About the recalculation:
You can keep your set of random values from changing every time you make an adjustment, by adjusting the automatic recalculation, to: manual recalculate. (Re)calculations are then only done when you press F9. Or shift F9.
See this link (though for older excel version than the current 2013) for some info about it: https://support.office.com/en-us/article/Change-formula-recalculation-iteration-or-precision-73fc7dac-91cf-4d36-86e8-67124f6bcce4.
Take a look at the Wikipedia article on random numbers as it talks about using sampling techniques. You can find the equation for your normal distribution by plugging into this one
(equation via Wikipedia)
As for the second issue, go into Options under the circle Office icon, go to formulas, and change calculations to "Manual". That will maintain your sheet and not recalculate the formulas each time.
Another interesting way to do this is using the Box-Muller Method. This lets you generate a normal distribution with mean of 0 and standard deviation σ (or variance σ2) of 1 using two uniform random distributions between 0 and 1. Then you can take this Norm(0,1) distribution and scale it to whatever mean and standard deviation you want.
Here's the formula in excel for a normal(0, 1) distribution:
=SQRT(-2*LN( RAND()))*COS(2 * PI()*RAND())
Then use this formula to scale your normal distribution to mean 10 and standard deviation of 7:
Norm(µ=b, σ=a) = a*Norm(µ=0, σ2=1) + b
This would make the equation in Excel:
=7* SQRT(-2*LN( RAND()))*COS(2 * PI()*RAND()) + 10
You can read more about the math behind this Box-Muller Equation on en.Wikipedia
Note that this equation only works if you calculate the cosine function using radians.
The numbers generated by
=NORMINV(RAND(),10,7)
are uniformally distributed. If you want the numbers to be normally distributed, you will have to write a function I guess.
I'm sure this is the kind of problem other have solved many times before.
A group of people are going to do measurements (Home energy usage to be exact).
All of them will do that at different times and in different intervals.
So what I'll get from each person is a set of {date, value} pairs where there are dates missing in the set.
What I need is a complete set of {date, value} pairs where for each date withing the range a value is known (either measured or calculated).
I expect that a simple linear interpolation would suffice for this project.
If I assume that it must be done in Excel.
What is the best way to interpolate in such a dataset (so I have a value for every day) ?
Thanks.
NOTE: When these datasets are complete I'll determine the slope (i.e. usage per day) and from that we can start doing home-to-home comparisons.
ADDITIONAL INFO After first few suggestions:
I do not want to manually figure out where the holes are in my measurement set (too many incomplete measurement sets!!).
I'm looking for something (existing) automatic to do that for me.
So if my input is
{2009-06-01, 10}
{2009-06-03, 20}
{2009-06-06, 110}
Then I expect to automatically get
{2009-06-01, 10}
{2009-06-02, 15}
{2009-06-03, 20}
{2009-06-04, 50}
{2009-06-05, 80}
{2009-06-06, 110}
Yes, I can write software that does this. I am just hoping that someone already has a "ready to run" software (Excel) feature for this (rather generic) problem.
I came across this and was reluctant to use an add-in because it makes it tough to share the sheet with people who don't have the add-in installed.
My officemate designed a clean formula that is relatively compact (at the expensive of using a bit of magic).
Things to note:
The formula works by:
using the MATCH function to find the row in the inputs range just before the value being searched for (e.g. 3 is the value just before 3.5)
using OFFSETs to select the square of that line and the next (in light purple)
using FORECAST to build a linear interpolation using just those two points, and getting the result
This formula cannot do extrapolations; make sure that your search value is between the endpoints (I do this in the example below by having extreme values).
Not sure if this is too complicated for folks; but it had the benefit of being very portable (and simpler than many alternate solutions).
If you want to copy-paste the formula, it is:
=FORECAST(F3,OFFSET(inputs,MATCH(F3,inputs)-1,1,2,1),OFFSET(inputs,MATCH(F3,inputs)-1,0,2,1
(inputs being a named range)
There are two functions, LINEST and TREND, that you can try to see which gives you the better results. They both take sets of known Xs and Ys along with a new X value, and calculate a new Y value. The difference is that LINEST does a simple linear regression, while TREND will first try to find a curve that fits your data before doing the regression.
The easiest way to do it probably is as follows:
Download Excel add-on here: XlXtrFun™ Extra Functions for Microsoft Excel
Use function intepolate().
=Interpolate($A$1:$A$3,$B$1:$B$3,D1,FALSE,FALSE)
Columns A and B should contain your input, and column G should contain all your date values. Formula goes into the column E.
A nice graphical way to see how well your interpolated results fit:
Take your date,value pairs and graph them using the XY chart in Excel (not the Line chart). Right-click on the resulting line on the graph and click 'Add trendline'. There are lots of different options to choose which type of curve fitting is used. Then you can go to the properties of the newly created trendline and display the equation and the R-squared value.
Make sure that when you format the trendline Equation label, you set the numerical format to have a high degree of precision, so that all of the significant digits of the equation constants are displayed.
The answer above by YGA doesn't handle end of range cases where the desired X value is the same as the reference range's X value. Using the example given by YGA, the excel formula would return #DIV/0! error if an interpolated value at 9999 was asked for. This is obviously part of the reason why YGA added the extreme endpoints of 9999 and -9999 to the input data range, and then assumes that all forecasted values are between these two numbers. If such padding is undesired or not possible, another way to avoid a #DIV/0! error is to check for an exact input value match using the following formula:
=IF(ISNA(MATCH(F3,inputs,0)),FORECAST(F3,OFFSET(inputs,MATCH(F3,inputs)-1,1,2,1),OFFSET(inputs,MATCH(F3,inputs)-1,0,2,1)),OFFSET(inputs,MATCH(F3,inputs)-1,1,1,1))
where F3 is the value where interpolated results are wanted.
Note: I would have just added this as a comment to the original YGA post, but I don't have enough reputation points yet.
alternatively.
=INDEX(yVals,MATCH(J7,xVals,1))+(J7-MATCH(J7,xVals,1))*(INDEX(yVals,MATCH(J7,xVals,1)+1)-INDEX(yVals,MATCH(J7,xVals,1)))/(INDEX(xVals,MATCH(J7,xVals,1)+1)-MATCH(J7,xVals,1))
where j7 is the x value.
xvals is range of x values
yvals is range of y values
easier to put this into code.
You can find out which formula fits best your data, using Excel's "trend line" feature. Using that formula, you can calculate y for any x
Create linear scatter (XY) for it (Insert => Scatter);
Create Polynominal or Moving Average trend line, check "Display Equation on
chart" (right-click on series => Add Trend Line);
Copy the equation into cell and replace x's with your desired x value
On screenshot below A12:A16 holds x's, B12:B16 holds y's, and C12 contains formula that calculates y for any x.
I first posted an answer here, but later found this question