You've made an error with the CDF. You need to add a row in the table, having no number but a CDF of zero, then the CDF for the number six will be exactly one. So the range used in your formulas becomes G3:G8. With the values used as at present, you are skewing the distribution towards the higher dice totals.
Hi Ross. While the CDF may appear to be incorrect (as CDFs typically end at one), it will give you the correct distribution without being skewed. Because I am using an approximate match and matching to the next lowest value, anything from 0 to 0.1667 matches to a roll of 1 and anything from 0.8333 to 1 matches to a roll of 6. If you build those same formulas and run a data table to simulate 1,000 dice rolls, you should see about 1/6th (16.67%) in each category (some variation due to sampling error).
Hi Pradeep. While it's true that CDFs will accumulate until they equal 1, in this case the last step occurs going from 0.83 to 1. Since we are using an approximate matching function, we have to choose whether to look for the next bigger or next smaller item. I chose to find the next smaller item, so I set up the CDF at using the lower side of each step, hence stopping at 0.83. It could have been set up to use the top side of each step, in which case the steps would have started at 0.17 instead of 0 and would then end at 1. Either set up will work.
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Your explanations are amazing! Thank you!
You've made an error with the CDF. You need to add a row in the table, having no number but a CDF of zero, then the CDF for the number six will be exactly one. So the range used in your formulas becomes G3:G8. With the values used as at present, you are skewing the distribution towards the higher dice totals.
Hi Ross. While the CDF may appear to be incorrect (as CDFs typically end at one), it will give you the correct distribution without being skewed. Because I am using an approximate match and matching to the next lowest value, anything from 0 to 0.1667 matches to a roll of 1 and anything from 0.8333 to 1 matches to a roll of 6. If you build those same formulas and run a data table to simulate 1,000 dice rolls, you should see about 1/6th (16.67%) in each category (some variation due to sampling error).
Thanks for the tutor and i am having difficulty on using monte carlo for production line optimization any idea.
would you mind and share the excel sheet?
You can download it at www.davidclaytonbrown.com/excel-resources
@@docbrownexcels thank you Brown, well explained, I've requested access as well for the file, appreciate if you could share with me.
The CDF should've been cumulated to 1 and not 0.83.
Hi Pradeep. While it's true that CDFs will accumulate until they equal 1, in this case the last step occurs going from 0.83 to 1. Since we are using an approximate matching function, we have to choose whether to look for the next bigger or next smaller item. I chose to find the next smaller item, so I set up the CDF at using the lower side of each step, hence stopping at 0.83. It could have been set up to use the top side of each step, in which case the steps would have started at 0.17 instead of 0 and would then end at 1. Either set up will work.
@@docbrownexcels. I just felt If am missing anything there. Glad you replied. Thanks for the explanation.