Wikipedia:Reference desk/Archives/Mathematics/2013 April 14

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

April 14

Calculating Stock Dividends

I don't want the answer, I just wanna know how to do a problem like this (I changed the numbers):

Acme Inc declared and issued a 80 percent stock dividend. The company has 884,000 shares authorized and 177,800 shares outstanding. The par value of the stock is $15 per share and the market value is 95 dollars per share. What is the general journal entry gonna look like? I know it has common stock and retained earnings as the two entries.

What do I multiply/divide? I can't get a straight answer elsewhere. Thanks. --131.156.211.13 (talk) 00:12, 14 April 2013 (UTC)

We are not licensed accountants, and cannot give accounting advice here. Sławomir Biały (talk) 00:23, 14 April 2013 (UTC)

It's for a class on accounting, nothing involving actual accounting. My book mentions nothing of this so I'm having trouble. Could you at least link me to a webpage that discusses this concept if no one can talk about it?--131.156.211.13 (talk) 00:34, 14 April 2013 (UTC)

This seems relevant, though I don't know if it answers your specific question: http://www.accountingcoach.com/online-accounting-course/17Xpg05.html What I don't understand is how a stock dividend of 80% (4 shares for every 5 held, as I see it) can apply when 80% of (884000 - 177800) exceeds the 177800 available.←86.186.142.172 (talk) 11:17, 14 April 2013 (UTC)

Mann Whitney U function

Is there a functional, non-computational description of the U-function? I can only find procedural descriptions but none using math-style functions and symbols. 93.132.160.155 (talk) 10:30, 14 April 2013 (UTC)

I'm a little confused by the use of the term "non-computational". From context, I presume you meant "algebraic, rather than algorithmic" as opposed to "conceptual". Please correct me if I'm wrong. Our article Mann–Whitney U effectively gives one, under method two:

$\min \left(\sum _{i\in A}R_{i}-{N_{A}(N_{A}+1) \over 2},\sum _{i\in B}R_{i}-{N_{B}(N_{B}+1) \over 2}\right)$

Where A and B are the two classes the data is split into, N_X is the number of observations in class X, and R_i is the rank of entry i. - Also note that there are several definitions running around for the Mann–Whitney/Mann–Whitney–Wilcoxon/Wilcoxon/Wilcoxon–Mann–Whitney test, each doing effectively the same thing, but with slightly different calculated statistics and critical values. -- 71.35.98.29 (talk) 18:50, 14 April 2013 (UTC)

Yes that's the way I meant it. But in the above formula, all the magic is hidden inside the $R_{i}$. Is it possible to break that open? 95.112.217.255 (talk) 08:32, 15 April 2013 (UTC)

I think perhaps you have to step back a little. You rank the observations by sticking the observations of both samples together, sorting all the values, and saying 1 for the first 2 for the second etc. The numbers you get out of that are the ranks you add up for each sample. Dmcq (talk) 08:56, 15 April 2013 (UTC)

Yes I know the algorithm. My question is how to put that prose description of what to do into some math-style formula. 95.112.217.255 (talk) 10:12, 15 April 2013 (UTC)

Well one can stick the conditions under the summation signs but I think Iverson brackets are easier here. For method 1 and denoting the values and samples as $v_{1i}\in S_{1},v_{2j}\in S_{2}$ one could say:

$U_{1}=\sum _{v_{1i}\in S_{1}}\sum _{v_{2j}\in S_{2}}[v_{2j}<v_{1i}]+{\frac {1}{2}}[v_{2j}=v_{1i}]$

this hides how one would normally do it because it doesn't say 'sort' anywhere. Dmcq (talk) 13:03, 15 April 2013 (UTC)

Thanks, that's what I was looking for! 95.112.217.255 (talk) 14:13, 15 April 2013 (UTC)