i have generated random variable according to normal distribution in excel using technique of analysis toolpak
what i need to know is that why kurtois of this normal variable is not equal to 3? here excel formula for calculation of kurtois
=KURT(A2:A2001) and its corresponding value is equal to `0.14521546`
does it mean that 3 is only in case of infinity sample ? and for specific amount of sample range of amplitudes of kurtois varies between -1 and 1? here is also formula for calculation skewnes
=SKEW(A2:A2001)
-0.006510255
thanks in advance
Excel's KURT() function calculates excess kurtosis which is kurtosis-3.
Therefore it should be around 0 for a normally distributed random variable like in your case.
Related
I want to generate a single column of 6000 numbers with a normal distribution, with a mean of 30.15, standard deviation of 49.8, minium of -11.5, maximum 133.5.
I am a total newb at this so i tried to use the following formula in a cell and than just drag it down to cell 6000:
=NORMINV(RANDBETWEEN(-11.5,133.5)/100,30.15,49.8)
It returns a value but sometimes it returns #NUM! error. Thank you!
Unfortunately NORMINV expects a probability for the argument, which must be a value in the interval (0, 1). Any parameter outside that range will yield #NUM!.
What you're asking cannot be done directly with a normal distribution since that has no constraints on the minimum and maximum values.
One approach is to use a primary column to generate the normally distributed numbers, then filter out the ones you want in the adjacent column. But this will cause even the mean (let alone higher moments) to go off quite considerably due to your minimum and maximum values not being equidistant from the mean. You could get round this by recentering the distribution and adjusting afterwards.
I am looking for a function in excel that will allow me to generator left skewed data with the option of picking a mean and standard deviation.
E.g If I want to generate 5 numbers with SD 2 and mean 45 , it must be 43,44,45,46,47.
I would also like to be able to pick the upper and lower limit. I don't want 0,44,46,46,90
This isn't an Excel question (i.e. it has nothing to do with Excel).
I don't think there's a standard function in any application or language that will give you what you need, you're basically asking for someone to develop an algorithm for you. If you want to do this in Excel you need some VBA code..
I don't mind having a crack at the algorithm but you need to be more specific with your parameters..
are there always 5 numbers returned? (this simplifies it hugely)
do they have to be integers?
also the SD of 43,44,45,46,47 is 1.414 not 2, 2 is the variance
I have a mean value x and I want to model it into the future. I want to output a value of what it could be in 6 months. Assuming the value follows a normal distribution and we have the standard deviation how do I randomize the value x while following a normal distribution? I'm doing this in excel, but just understanding it would help too! Basically I want to produce numbers 68% of the time within 1 deviation, 95% of the time withing 2 deviation etc. etc.
You can use the excel function 'NORMINV' to convert a random input 'RAND()' to a normal distribution.
=NORMINV(RAND(),Mean,Std Dev)
i.e. if you repeat this many times, save and analyze the results, you'll see a bell curve over the input Mean value.
Does that get you started?
The tricky bit comes when you come up with the formula to predict what a value will be in the future using this.
I am trying to average a column of numbers, throwing out values a specific difference from MAX. The users will not be Excel experts, so I am trying to stay away from Array formulas so they can edit the difference number based on different conditions.
=AVERAGEIF(DM7:DM34,"=>Max(DM7:DM34)-3",DM7:DM34)
This returns a #Div/0, while the MAX portion alone returns the value I need.
I think what you may require is something like:
=AVERAGEIF(DM7:DM34,">="&MAX(DM7:DM34)-3)
You might achieve some added "comfort" by changing 3 in -3 to a cell reference where the difference number would be placed/changed.
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.