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

= 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, NX is the number of observations in class X, and Ri 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)