changing the frequency distribution with out the changing the shape of the disti

#1
i have frequency table of wind speeds from a measurement site and now i want to use that wind speed frequency table to find out wind speed at a neighboring site who's mean is 1.02 times the mean of site i am measuring from. So how should change the frequency distribution to make sure the shape remains similar but the mean would be different.

i am stumped because the frequency table needs to sum up to 100% and i can't really linearly multiple a factor to the frequency distribution table:confused:
 

Dason

Ambassador to the humans
#2
Adding a constant to all data values shifts the distribution by the amount of the constant - which has the effect of increasing the mean by the amount of the constant you added.

Multiplying all data values by a constant spreads out (or shrinks) the data but also has the effect of making the mean become the old mean times the constant.
 

Dason

Ambassador to the humans
#3
Adding a constant to all data values shifts the distribution by the amount of the constant - which has the effect of increasing the mean by the amount of the constant you added.

Multiplying all data values by a constant spreads out (or shrinks) the data but also has the effect of making the mean become the old mean times the constant.
 

BGM

TS Contributor
#4
There are just too many ways to transform the data to achieve the mean requirement, and it depends on how do you define "shapes remain similar"

- Scaling by a constant factor larger than 1 will makes the curve looks flatter.

- Add a positive constant will shift the whole curve horizontally to the right while keeping the exact shape (which is the only way to keep the exact shape, and thats why Dason point it out in the above post). Note that if the lower bound of the support of the original distribution is 0, then the new distribution will be bounded away from 0 which may not be desirable in the model.

- You may have other parametric assumptions, e.g. assuming the distribution following a Weibull distribution. Then by adjusting the parameters, you may achieve the mean adjustment while having the same family of distribution. But again it depends on your requirement.
 
#5
Thanks, and sorry for the delay in the follow up question somehow i am not getting the email reminder when someone replies. To be clear I understand changing the data but i want to directly change the frequency distribution for different mean so that i don't need to work on the data every time i want to change the frequency distribution like you mentioned above for Wiebull distribution we can change the scale parameter for the mean and not worry about the underlying data once we find the shape and scale of the distribution but i want to use the frequency distribution table rather than weibull distribution. Please let me know if the question makes sense.
 

BGM

TS Contributor
#6
First of all windspeed should be modeled as a continuous variable. In real life, all measurements all discrete due to the precision of the measuring instrument (and actually this could led to a philosophical debate on this topic so I do not go further). Continuous distribution can give you a more elegant, easy way to handle the data. Once you have a continuous model, you can always obtain the discrete counterpart by truncating the support into different intervals, just like what you do in producing a histogram.

And actually I am not exactly sure the question you asked. Sorry if it is off-topic.