Is this cool with you?

bobbym · 2014-01-31 22:07:52

Hi;

Okay, take your time, I will wait.

gAr · 2014-01-31 23:32:22

Hi bobbym,

I think these must be right, finally!

1)

where 'n_a' is any of the number of cards available of digit 'a' and 'h' is the number of cards greater than 'a'.

2)

3)

4)

For (9,9,7),

And the expected sum of the highest three, using the above equations:

bobbym · 2014-02-01 01:27:57

Hi;

H = 24, how would you phrase that? Cards less then a?

gAr · 2014-02-01 01:35:49

Hi,

'h' is the number of cards having face value > 'a'

For the example, a=7 and 'h' includes all 8's, 9's and 10's: h=4+4+16

bobbym · 2014-02-01 01:45:48

Very good! I am checking the last one now and you have an important result!

Could you please explain what f\goes into what for your formula 4).

The example is (7,7,9)

gAr · 2014-02-01 01:59:22

Yeah, but took quite a while to correct a mistake in my program!

For (7,7,9),
a=7, b=9, h=24, n7=n9=4

bobbym · 2014-02-01 02:00:21

Hi;

I will run it through your fourth formula.

gAr · 2014-02-01 02:12:07

Okay.

bobbym · 2014-02-01 02:12:56

Hi;

Did you see the top part of post #2030?

gAr · 2014-02-01 02:27:03

Hi,

Yes, the top part of my reply was refering to my program for calculating the expectation.
I saw that was what you actually wanted!

Also saw that it was already asked in "help me", good question!

Would you like me to post my code in "computer math" ?

bobbym · 2014-02-01 02:29:51

I saw that was what you actually wanted!

You read the future.

http://www.mathisfunforum.com/viewtopic.php?id=13145

gAr · 2014-02-01 02:41:42

You read the future.

Nope, math.se!

Yes, I was talking about that thread.

bobbym · 2014-02-01 02:45:07

That was me. Why the heck did you not post in there?

gAr · 2014-02-01 02:58:28

I have forgotten my login credentials there, had registered once a long time ago.
Never mind, you post the answers there you now know.

We can easily extend the formula for any number of picks. But more cases if we need sum of 'n' highest cards, with n>3. I wonder if the cases can be eliminated altogether!

bobbym · 2014-02-01 03:01:08

They do not get those answers. They belong to you and it is your choice whether or not to share them.

I have been working on using order statistics for the problem but have not been successful.

gAr · 2014-02-01 03:10:04

I don't mind you sharing the answer there.

The 10's have a different probability, that's the difficulty we have here.
Otherwise, we might have had a better answer.

bobbym · 2014-02-01 03:18:35

I am hazy on this whole idea so it might be wrong but there is a distribution called the Empirical Distribution which handles that.

gAr · 2014-02-01 03:21:50

Okay, I'll check that.
Taking a break now, see you later.

bobbym · 2014-02-01 03:24:49

Okay, and thanks for coming in.

gAr · 2014-02-03 18:18:27

Here's a formula for probability of the order statistic:

E.g. For the probability that 6th highest number is 7 among 8 selected, we have:

I don't know a formula for joint distribution yet.

The literature on these look stupid without any example.

bobbym · 2014-02-03 20:55:40

Hi gAr;

I have had much trouble with the order statistic of an empirical distribution like these. What literature are you looking at?

gAr · 2014-02-03 21:09:04

Hi,

I had not tried order statistics of discrete distributions before, the formulas in the program had Vandermonde's identity in it.

Literature, whatever I could find online.
I tried the formula in wikipedia, but couldn't understand what to make of f(x) and F(x).

I also looked at "A first course on order statistics", doesn't have a single numerical example!

bobbym · 2014-02-03 21:13:11

I think I remember that book, I had to throw it away for that very reason.

gAr · 2014-02-03 21:16:54

If we can get a formula for joint distribution, our job for the expected sum will be done!

bobbym · 2014-02-03 21:28:03

That has been difficult for me. Mathematica has a command to do all these type problems but when I try to have the command work on an empirical distribution like this one it fails. This has been the major problem, I can not get exact answers and must rely on simulations which are not close enough.

Math Is Fun Forum

#2026 2014-01-31 22:07:52

Re: Is this cool with you?

#2027 2014-01-31 23:32:22

Re: Is this cool with you?

#2028 2014-02-01 01:27:57

Re: Is this cool with you?

#2029 2014-02-01 01:35:49

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