Transform for one distribution to another

#1
Warning : Stats newbie

Okay if I have a distribution that the only thing I am sure of is that it is Gaussian/Normal and over time(actually a long time) ends up as a Gamma Function for which I know the parameters. Is there a way to determine what transform would have occurred to the Normal Function to arrive at the known Gamma Function Image 17-12-2021 at 15.44.jpeg and normal Image 17-12-2021 at 15.45.jpeg Or is it not going to occur because the power of exp are just not compatible. I know I can calculated the Coxbox transform to go from Gamma to Normal and could then look at it the inverse of the transform it gives me, but is there a better way to determine a transform that would go from Normal to known Gamma.
Same question but with johnson distribution rather than Gamma
Thanks in anticipation.
 

Dason

Ambassador to the humans
#2
I guess I'm not sure why you want to do this. Some details on that would be helpful in determining if what you're doing makes any sense or not or if there is something better you could do.

With that said...

So it's almost always possible to transform one continuous distribution to a different distribution. The main idea being we can always apply the CDF of the distribution at hand to an observation - this will transform things into a uniform distribution. We can also then apply an inverse CDF to a uniform distribution to get a draw from the distribution we used for the inverse CDF. In combining these things depending on certain properties being met we can essentially transform any distribution to any other distribution.
 
#3
I have a number of distributions that give good fits for a Gamma Distribution. I know from the physics that these distributions must have started out as normal/gaussian a long time previously. I would like to determine the transform function that would have occurred to change the initial distribution where all I know is it is normal and the final distribution Gamma. I know that a number of processes are at play and I have a number of final Gamma distributions for a number of characteristics and was hoping that by determining the different transformations for such distributions I can make some statements about what the processes are.
 

hlsmith

Less is more. Stay pure. Stay poor.
#4
So you have observed data, historic, and more current data from the same population but new observations and the distribution changed in the new observations. Is the new distribution more skewed or what context can you provide? Curious what we are discussing.
 
#5
So you have observed data, historic, and more current data from the same population but new observations and the distribution changed in the new observations. Is the new distribution more skewed or what context can you provide? Curious what we are discussing.
It is do with various galaxy characteristics, I know what the distributions of various characteristics are today. Research says current distributions are log normals. I am seeing Gamma and Johnson fits. Research papers modelling initial conditions for star formation etc assume things assume normal distributions. So I am assuming things were distributed normally in the distant past.
 

hlsmith

Less is more. Stay pure. Stay poor.
#6
Given the travel time of light and galactic distances, aren't all data in the past :)

Thanks for share!
 
#8
this question is too general
Okay if I have two PDF's is there a way of working out the transform function to go from one distribution to another. I can find lots of examples of how to arrive at a new PDF given a PDF and a transform function, but suppose I know the two PDF's and want the transform function.

Just being able to produce a differential equation for the transform function from the two PDF's would be useful.
 

Dason

Ambassador to the humans
#9
I mean I outlined that procedure already. You need the CDF and Inverse CDF but with some math you can get that from a PDF.