142:
regression). Now, if during regression there are points, the groupings of which, tend to be bent (i.e., when non-linear) and not arranged randomly above or below the regression line, then a folded-normal distribution would result. Thus the HND can be understood as arising in situations which are generally FND's. Now the text prior version specified that the HND is a ND folded at a (ND) mean of zero. And whereas that is absolutely true in a mathematical sense, it is also not as robust as the FND explanation. It was also confusing as after folding the (ND) mean is no longer zero (and the HND mean was not specified, well, maybe not, see below.).
74:
53:
22:
146:
why it is used. However, the reciprocal is used in the rest of the article. Should theta be propagated throughout the article? I have left it half-way, making only the minimum changes I though needed, but look forward to comments. I do not understand the
Expected value given. Can someone demonstrate this to me, please?
145:
Now, I would request discussion of several things here. The
Mathematica reference uses theta, the reciprocal of the mean which has been left out of the development of this article. I have gotten used to theta and its advantage of not blowing up and degenerating during regression, which is, I think,
141:
The PDF for the half-normal distribution (HND) was missing, so put it in. Also, the physical situation in which an HND arises, is for example when magnitudes and not signed distances occur (e.g., residuals during regression), and when there is no organized bias (e.g., no bent-line residuals during
208:
Further, I have included the pdf under the alternative parametrization (to mirror the normal distribution page), and to ensure the latter parts of the article (which I have not edited) follow on logically - instead of switching parametrization part way through the page
216:
Neither parametrization should be preferred, since they are both considered standard in different settings (as is discussed on the normal distribution page, so perhaps a link back to that section could be
124:
240:
Small comment: I'm finding that the given maxlik estimator isn't correct. Maybe it's something to do with this discussion about parametrisation, and inconsistency with R. I will look into it.
185:
was the mean of the half-normal and ***not*** the mean of the normal distribution being folded (which I have called X). I hope my edit has slightly clarified this (though potentially adding
183:
203:
165:, the parametrization of the half-normal you added used its own mean. Specifically, it was not immediately clear, given the link to the folded-normal page, that
279:
114:
284:
274:
90:
255:
81:
58:
223:
The derivation of the expected value follows from the integral-substitution method (as indicated in the article already).
33:
151:
21:
251:
162:
147:
39:
247:
73:
52:
243:
227:
89:
on
Knowledge. If you would like to participate, please visit the project page, where you can join
231:
168:
188:
268:
259:
235:
155:
86:
220:
So the theta should not, in my opinion, be propagated through the article.
15:
191:
171:
85:, a collaborative effort to improve the coverage of
197:
177:
8:
19:
241:
47:
190:
170:
205:as a subscript would be more explicit).
49:
7:
79:This article is within the scope of
38:It is of interest to the following
280:Low-importance Statistics articles
14:
99:Knowledge:WikiProject Statistics
72:
51:
20:
285:WikiProject Statistics articles
275:Start-Class Statistics articles
119:This article has been rated as
102:Template:WikiProject Statistics
260:19:30, 26 September 2023 (UTC)
1:
156:01:40, 19 December 2011 (UTC)
93:and see a list of open tasks.
236:15:15, 25 January 2012 (UTC)
301:
118:
67:
46:
199:
179:
82:WikiProject Statistics
28:This article is rated
200:
180:
189:
178:{\displaystyle \mu }
169:
105:Statistics articles
195:
175:
34:content assessment
262:
246:comment added by
198:{\displaystyle y}
139:
138:
135:
134:
131:
130:
292:
204:
202:
201:
196:
184:
182:
181:
176:
125:importance scale
107:
106:
103:
100:
97:
76:
69:
68:
63:
55:
48:
31:
25:
24:
16:
300:
299:
295:
294:
293:
291:
290:
289:
265:
264:
187:
186:
167:
166:
161:In response to
104:
101:
98:
95:
94:
61:
32:on Knowledge's
29:
12:
11:
5:
298:
296:
288:
287:
282:
277:
267:
266:
225:
224:
221:
218:
194:
174:
163:CarlWesolowski
160:
148:CarlWesolowski
137:
136:
133:
132:
129:
128:
121:Low-importance
117:
111:
110:
108:
91:the discussion
77:
65:
64:
62:Low‑importance
56:
44:
43:
37:
26:
13:
10:
9:
6:
4:
3:
2:
297:
286:
283:
281:
278:
276:
273:
272:
270:
263:
261:
257:
253:
249:
245:
238:
237:
233:
229:
222:
219:
215:
214:
213:
212:Discussion:
210:
206:
192:
172:
164:
158:
157:
153:
149:
143:
126:
122:
116:
113:
112:
109:
92:
88:
84:
83:
78:
75:
71:
70:
66:
60:
57:
54:
50:
45:
41:
35:
27:
23:
18:
17:
248:Simon Pedley
242:— Preceding
239:
226:
211:
207:
159:
144:
140:
120:
80:
40:WikiProjects
30:Start-class
269:Categories
96:Statistics
87:statistics
59:Statistics
256:contribs
244:unsigned
228:Srw1138
217:added).
123:on the
36:scale.
252:talk
232:talk
152:talk
115:Low
271::
258:)
254:•
234:)
173:μ
154:)
250:(
230:(
193:y
150:(
127:.
42::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
