Question about a formula

[Arhowk]

Im making a random item generator and a key trait of the generator would be to scale the values that it puts out to a graph

so lets say you have 3 numbers

number A is the minimum, 20
number B is the maximum, 100
number C determines the rarity of numberB to numberC. If number C is 0.5, than number A will show up twice as much as number B. If number C is 2, than number B will show up twice as much as number A. (This also applies to all numbers inbetween, e.g. 60 will show up 1.5x as much as number A)

 

[muzzel]

Whats the question?

 

[Arhowk]

Whats the question?

how would i do whats stated in the top....

when generated randomly, (min) shows up (weight)x more than max and (min+max/2) shows up (weight/2) more than max and every number inbetween follows the same scheme

 

[muzzel]

Ok, this can be solved in a more general way.

Assume you have a probability density function (pdf) f that specifies your distribution. Then you can calculate the cumulative distribution function (cdf) F by integrating f (analytically).
F(u) = integrate f from -infinity to u
For x being uniformly distributed reals between 0 and 1 (use GetRandomReal native) F^-1(x) will return values distributed by the distribution specified by f. (F^-1 is the inverse of F, calculate it analytically).

Looks like this then:

All you need to do is write down the pdf for your problem with A,B,C as parameters (in your case a linear function, normalized to have an integral of 1).

 

[Arhowk]

Ok, this can be solved in a more general way.

Assume you have a probability density function (pdf) f that specifies your distribution. Then you can calculate the cumulative distribution function (cdf) F by integrating f (analytically).
F(u) = integrate f from -infinity to u
For x being uniformly distributed reals between 0 and 1 (use GetRandomReal native) F^-1(x) will return values distributed by the distribution specified by f. (F^-1 is the inverse of F, calculate it analytically).

Looks like this then:

All you need to do is write down the pdf for your problem with A,B,C as parameters (in your case a linear function, normalized to have an integral of 1).

Thanks for trying, but im 15 and trying to understand what you said but i really have no idea. Ill try a few google searches, but...

 

[gorillabull]

haha you can use weights, each number a,b and c is a weight so for example a = 2 b = 9 and c = 8 then you add all the weights together and divide each weight by that number to get a percentage

a+b+c = 19
2/19 = 10%
9/19 = 47%
8/19 = 42%

this way all the values are dependent on each other

 

[Arhowk]

haha you can use weights, each number a,b and c is a weight so for example a = 2 b = 9 and c = 8 then you add all the weights together and divide each weight by that number to get a percentage

a+b+c = 19
2/19 = 10%
9/19 = 47%
8/19 = 42%

this way all the values are dependent on each other

hm.. i must not be explaining myself properly

I don't want to select from a few pre-selected numbers, i want to get ANY number from the GetRandomInt function, but weigh it so that one side shows up more frequently than the others. Your method would work if there was a few pre-determined numbers, but there isn't.

(also, theres only one weight value that determines the scaling of the GetRandom)

 

[muzzel]

ok il go a little more into detail:

I.
Write down the pdf f for your problem. The pdf simply tells you what the chances are to get a specific observation (the random variable equals the specific value). In order to find the pdf we write down our necessities:
1. For your needs you need a stepwise defined function, in the interval [A, B] it is a linear function, outside of that interval it is 0.
Lets say the chance to get the number A is a, and the chance to get the number B is b.
So f(A) = a, f(B) = b
2. Then you want b = a*C. (thats how you defined the parameter C)
3. A function is a pdf if and only if the integral is 1 (the area under the function has to be 1). The area under a linear function is defined as:
area = (a+b)/2 * (B-A)
so we have the necessity
(a+b)/2*(B-A) = 1

This gives us:
a = 2/(C+1) * 1/(B-A)
b = (2-2/(C+1)) * 1/(B-A)

A linear function that interpolates the points (A, a) and (B, b) is
f(x) = (b-a)/(B-A) * x + (B*a - b*A)/(B-A)
and using the formulas for a and b:
f(x) = -2*(A*C - B - C*x + x)/((C+1)*(A-B)^2)
(on the interval [A, B], everywhere else f(x) is 0).
f(x) =

Example: Lets use A = 20, B = 100, C = 0.5. Then we get
f(x) =

which looks like this:

II.
We have to integrate the pdf f(x) to get the cdf F(x).
F'(x) =

(with constant == 0)
But since we have a stepwise function we need to adjust the bounds:
F(x) = F'(x) - F'(A), if A <= x <= B (this case is the interesting one)
F(x) = 0, if x < A
F(x) = F'(B) - F'(A), if x > B

III.
Invert the cdf to calculateF^-1(x). We use
F(x) = F'(x) - F'(A), since this area gets mapped to [0, 1] of the inverse.
F(x) =

=

The inverse is
F^-1(x) =

=

Use uniformly distributed random numbers in the interval of [0, 1] as input.

 

[Arhowk]

ok il go a little more into detail:

....

trying to understand what you said but i really have no idea

 

[Xonok]

....

I have a fitting curve. Without the math overkill.

Set i to random int between 1 and 100
set it to random between 1 and i
This basically does what you want, as the chance to get 0 is twice as much as for 100.
For every cycle that you add the chance increases.
Example
set i = random(1,100) //1% chance for every number
set i = random(1,i) //2% chance for 1 and 0.5% chance for 100
set i = random(1,i) //3% chance for 1 and 0.(3) for 100
set i = random(1,i) //4% and 0.25%
etc

 

[deathismyfriend]

Wow thts a nice easy solution xonok I may use this in my map at some point.

 

[Arhowk]

I have a fitting curve. Without the math overkill.

Set i to random int between 1 and 100
set it to random between 1 and i
This basically does what you want, as the chance to get 0 is twice as much as for 100.
For every cycle that you add the chance increases.
Example
set i = random(1,100) //1% chance for every number
set i = random(1,i) //2% chance for 1 and 0.5% chance for 100
set i = random(1,i) //3% chance for 1 and 0.(3) for 100
set i = random(1,i) //4% and 0.25%
etc

That makes sense! Ty

e/ would this work? (need to test it)

                real r = weight;
                real result = max;
                real nextResult;
                real r2;
                boolean invert = false;
                if(r < 1)
                {
                    invert = true;
                    r = 1 / r;
                }
                for(r >= 1)
                {
                    r = r - 1;
                    result = GetRandomReal(1, result);
                }
                if(r < 1)
                {
                    nextResult = GetRandomReal(1, result);
                    r2 = result - nextResult;
                    r2 = nextResult + (result / r);
                    result = r2;
                }
                if(invert)
                {
                    result = 0.5 - (result - 0.5)
                {

 

[Xonok]

That makes sense! Ty

e/ would this work? (need to test it)

                real r = weight;
                real result = max;
                real nextResult;
                real r2;
                boolean invert = false;
                if(r < 1)
                {
                    invert = true;
                    r = 1 / r;
                }
                for(r >= 1)
                {
                    r = r - 1;
                    result = GetRandomReal(1, result);
                }
                if(r < 1)
                {
                    nextResult = GetRandomReal(1, result);
                    r2 = result - nextResult;
                    r2 = nextResult + (result / r);
                    result = r2;
                }
                if(invert)
                {
                    result = 0.5 - (result - 0.5)
                {

I don't understand much of this and it doesn't look like JASS to me.
Can you explain what you wanted it to do?

 

[Arhowk]

I don't understand much of this and it doesn't look like JASS to me.
Can you explain what you wanted it to do?

its zinc... read post # 10

 

[Xonok]

its zinc... read post # 10

#10 is my own and it's easier than this.

Basically I don't understand zinc, only vanilla JASS and sometimes vJASS.

I get it that you combined it with weights, but how exactly I don't understand.

 

[Arhowk]

#10 is my own and it's easier than this.

Basically I don't understand zinc, only vanilla JASS and sometimes vJASS.

I get it that you combined it with weights, but how exactly I don't understand.

just ignore the {, replace the } with "endif" or "endloop"

its quite simple, it just loops through it untill the weight is >0<1 than gets another variable and adds on however much weight was lost... (so if it was a 25 than the next was a 15 an leftover weight was 0.5 it would end up to be 20)

                local real r = weight;
                local real result = max;
                local real nextResult;
                local real r2;
                local boolean invert = false;
                if r < 1 then
                    set invert = true;
                    set r = 1 / r;
                endif
                loop
                    exitwhen r >= 1
                    set r = r - 1;
                    set result = GetRandomReal(1, result);
                endloop
                if r < 1 then
                    set nextResult = GetRandomReal(1, result);
                    set r2 = result - nextResult;
                    set r2 = nextResult + (result / r);
                    set result = r2;
                endif
                if invert then
                    set result = 0.5 - (result - 0.5)
                endif

 

[Xonok]

just ignore the {, replace the } with "endif" or "endloop"

its quite simple, it just loops through it untill the weight is >0<1 than gets another variable and adds on however much weight was lost... (so if it was a 25 than the next was a 15 an leftover weight was 0.5 it would end up to be 20)

                local real r = weight;
                local real result = max;
                local real nextResult;
                local real r2;
                local boolean invert = false;
                if r < 1 then
                    set invert = true;
                    set r = 1 / r;
                endif
                loop
                    exitwhen r >= 1
                    set r = r - 1;
                    set result = GetRandomReal(1, result);
                endloop
                if r < 1 then
                    set nextResult = GetRandomReal(1, result);
                    set r2 = result - nextResult;
                    set r2 = nextResult + (result / r);
                    set result = r2;
                endif
                if invert then
                    set result = 0.5 - (result - 0.5)
                endif

I understand every piece separately, but not how it all comes together. Math is not my strong side.
That's why I avoid using JASS in my explanations.