Rnz - Revision history

Ray Chason: Quote the code as it stands in 5.0.0; distribution and usage have not changed

2026-06-02T03:04:05Z

Quote the code as it stands in 5.0.0; distribution and usage have not changed

Cathartes: /* Cumulative distribution function */ fill in integration constants. I probably did it correctly since it all adds up to 1 at the end.

2022-12-09T05:58:57Z

‎Cumulative distribution function: fill in integration constants. I probably did it correctly since it all adds up to 1 at the end.

Cathartes: /* Mathematical analysis */ add a section for the cumulative distribution function, because that would be useful. I still need to calculate the constants of integration.

2022-12-09T04:55:49Z

‎Mathematical analysis: add a section for the cumulative distribution function, because that would be useful. I still need to calculate the constants of integration.

Cathartes: clarify that "most probable" means mode, not mean. also don't need 6 significant digits for the mean in the text

2022-12-09T04:20:00Z

clarify that "most probable" means mode, not mean. also don't need 6 significant digits for the mean in the text

Actual-nh: Text didn't match what rest of article said

2021-06-17T02:05:11Z

Text didn't match what rest of article said

Bcode: /* Mathematical analysis */ syntax highlighting

2012-11-29T17:00:13Z

‎Mathematical analysis: syntax highlighting

Ray Chason: This really ought to be linked to Wikipedia

2011-07-01T11:10:04Z

This really ought to be linked to Wikipedia

99.239.146.253: cat

2011-05-29T21:11:43Z

cat

169.231.28.38: changed a link

2011-05-07T19:24:48Z

changed a link

Ray Chason: Categories

2011-02-01T23:56:41Z

@@ Line 17: / Line 17: @@
 rnz produces such a bizarre distribution that it is hard to tell what the original programmer had in mind.  It's quite possible that it was meant to be some distribution with Z in the name, but its construction doesn't seem to suggest one.
-The code is quoted below, with some cleanup for readability:
+The code is quoted below:
 <syntaxhighlight lang="c">
 int
-rnz(i)
+rnz(int i)
+{
-        register long x = i;
+    long x = (long) i;
-        register long tmp = 1000;
+    long tmp = 1000L;
-        tmp += rn2(1000);
+    tmp += rn2(1000);
-        tmp *= rne(4);
+    tmp *= rne(4);
-        if (rn2(2)) { x *= tmp; x /= 1000; }
+    if (rn2(2)) {
-         else { x *= 1000; x /= tmp; }
+        x *= tmp;
-        return((int)x);
+        x /= 1000;
 }</syntaxhighlight>
@@ Line 334: / Line 338: @@
 The standard deviation of rnz(x), then, is 1.04424x, or 365.483 for an ordinary prayer timeout. (Actually, it is 365.344, so the error introduced by treating Z as continuous is quite small.)
-{{nethack-343}}
+{{nethack-500}}
 [[Category:Random number functions]]

@@ Line 139: / Line 139: @@
 |<math>\frac{1}{10}</math> to <math>\frac{1}{8}</math>||<math>-\frac{x^{-1}}{2560}+\frac{1}{256}</math>
 |-
-|<math>\frac{1}{8}</math> to <math>\frac{1}{6}</math>||<math>-\frac{19x^{-1}}{10240}+C</math>
+|<math>\frac{1}{8}</math> to <math>\frac{1}{6}</math>||<math>-\frac{19x^{-1}}{10240}+\frac{1}{64}</math>
 |-
-|<math>\frac{1}{6}</math> to <math>\frac{1}{5}</math>||<math>-\frac{99x^{-1}}{10240}+C</math>
+|<math>\frac{1}{6}</math> to <math>\frac{1}{5}</math>||<math>-\frac{99x^{-1}}{10240}+\frac{1}{16}</math>
 |-
-|<math>\frac{1}{5}</math> to <math>\frac{1}{4}</math>||<math>-\frac{19x^{-1}}{2048}+C</math>
+|<math>\frac{1}{5}</math> to <math>\frac{1}{4}</math>||<math>-\frac{19x^{-1}}{2048}+\frac{31}{512}</math>
 |-
-|<math>\frac{1}{4}</math> to <math>\frac{1}{3}</math>||<math>-\frac{7x^{-1}}{128}+C</math>
+|<math>\frac{1}{4}</math> to <math>\frac{1}{3}</math>||<math>-\frac{7x^{-1}}{128}+\frac{31}{128}</math>
 |-
-|<math>\frac{1}{3}</math> to <math>\frac{1}{2}</math>||<math>-\frac{3x^{-1}}{64}+C</math>
+|<math>\frac{1}{3}</math> to <math>\frac{1}{2}</math>||<math>-\frac{3x^{-1}}{64}+\frac{7}{32}</math>
 |-
-|<math>\frac{1}{2}</math> to <math>1</math>||<math>-\frac{3x^{-1}}{8}+C</math>
+|<math>\frac{1}{2}</math> to <math>1</math>||<math>-\frac{3x^{-1}}{8}+\frac{7}{8}</math>
 |-
-|<math>1</math> to <math>2</math>||<math>\frac{3x}{8}+C</math>
+|<math>1</math> to <math>2</math>||<math>\frac{3x}{8}+\frac{1}{8}</math>
 |-
-|<math>2</math> to <math>3</math>||<math>\frac{3x}{64}+C</math>
+|<math>2</math> to <math>3</math>||<math>\frac{3x}{64}+\frac{25}{32}</math>
 |-
-|<math>3</math> to <math>4</math>||<math>\frac{7x}{128}+C</math>
+|<math>3</math> to <math>4</math>||<math>\frac{7x}{128}+\frac{97}{128}</math>
 |-
-|<math>4</math> to <math>5</math>||<math>\frac{19x}{2048}+C</math>
+|<math>4</math> to <math>5</math>||<math>\frac{19x}{2048}+\frac{481}{512}</math>
 |-
-|<math>5</math> to <math>6</math>||<math>\frac{99x}{10240}+C</math>
+|<math>5</math> to <math>6</math>||<math>\frac{99x}{10240}+\frac{15}{16}</math>
 |-
-|<math>6</math> to <math>8</math>||<math>\frac{19x}{10240}+C</math>
+|<math>6</math> to <math>8</math>||<math>\frac{19x}{10240}+\frac{63}{64}</math>
 |-
-|<math>8</math> to <math>10</math>||<math>\frac{x}{2560}+C</math>
+|<math>8</math> to <math>10</math>||<math>\frac{x}{2560}+\frac{255}{256}</math>
 |}

← Older revision		Revision as of 04:55, 9 December 2022
Line 129:		Line 129:

	This random variable, multiplied by the parameter '''i''', is the return value of rnz.		This random variable, multiplied by the parameter '''i''', is the return value of rnz.
		+
		+	=== Cumulative distribution function ===
		+
		+	The integral of the probability density function, which contains the probability that the result will be less than ''x'':
		+
		+	{\| class="wikitable"
		+	!Range!!Distribution
		+	\|-
		+	\|<math>\frac{1}{10}</math> to <math>\frac{1}{8}</math>\|\|<math>-\frac{x^{-1}}{2560}+\frac{1}{256}</math>
		+	\|-
		+	\|<math>\frac{1}{8}</math> to <math>\frac{1}{6}</math>\|\|<math>-\frac{19x^{-1}}{10240}+C</math>
		+	\|-
		+	\|<math>\frac{1}{6}</math> to <math>\frac{1}{5}</math>\|\|<math>-\frac{99x^{-1}}{10240}+C</math>
		+	\|-
		+	\|<math>\frac{1}{5}</math> to <math>\frac{1}{4}</math>\|\|<math>-\frac{19x^{-1}}{2048}+C</math>
		+	\|-
		+	\|<math>\frac{1}{4}</math> to <math>\frac{1}{3}</math>\|\|<math>-\frac{7x^{-1}}{128}+C</math>
		+	\|-
		+	\|<math>\frac{1}{3}</math> to <math>\frac{1}{2}</math>\|\|<math>-\frac{3x^{-1}}{64}+C</math>
		+	\|-
		+	\|<math>\frac{1}{2}</math> to <math>1</math>\|\|<math>-\frac{3x^{-1}}{8}+C</math>
		+	\|-
		+	\|<math>1</math> to <math>2</math>\|\|<math>\frac{3x}{8}+C</math>
		+	\|-
		+	\|<math>2</math> to <math>3</math>\|\|<math>\frac{3x}{64}+C</math>
		+	\|-
		+	\|<math>3</math> to <math>4</math>\|\|<math>\frac{7x}{128}+C</math>
		+	\|-
		+	\|<math>4</math> to <math>5</math>\|\|<math>\frac{19x}{2048}+C</math>
		+	\|-
		+	\|<math>5</math> to <math>6</math>\|\|<math>\frac{99x}{10240}+C</math>
		+	\|-
		+	\|<math>6</math> to <math>8</math>\|\|<math>\frac{19x}{10240}+C</math>
		+	\|-
		+	\|<math>8</math> to <math>10</math>\|\|<math>\frac{x}{2560}+C</math>
		+	\|}

	=== Mean ===		=== Mean ===

@@ Line 3: / Line 3: @@
 '''rnz''' is a function that generates a random number with a distribution that is meant to peak at a given value and trail off at larger values.  A call of rnz(350), for example, gives the base [[prayer timeout]] and will often return a number close to 350, sometimes a number somewhat less or somewhat more than 350, and rarely a number much greater or much less than 350.
-The most probable outcome turns out not to be the given parameter, but 1.29815 times that number, as can be seen in the graph to the right.
+The most probable outcome (the mode of the distribution) turns out not to be the given parameter, but half of that number, as can be seen in the graph to the right.  The mean outcome, on the other hand, is about 1.30 times the given parameter.
 rnz is used for the following purposes:

@@ Line 3: / Line 3: @@
 '''rnz''' is a function that generates a random number with a distribution that is meant to peak at a given value and trail off at larger values.  A call of rnz(350), for example, gives the base [[prayer timeout]] and will often return a number close to 350, sometimes a number somewhat less or somewhat more than 350, and rarely a number much greater or much less than 350.
-The most probable outcome turns out not to be the given parameter, but half of that number, as can be seen in the graph to the right.
+The most probable outcome turns out not to be the given parameter, but 1.29815 times that number, as can be seen in the graph to the right.
 rnz is used for the following purposes:

@@ Line 1: / Line 1: @@
 {{DISPLAYTITLE:rnz}}
-{{randomvariable|name=rnz(x)|graph=Rnz100.svg|caption=Probability density function of a call of rnz(100).|distribution=unique|mean=approx. 1.29815x|stddev=approx. 1.04424x}}
+{{randomvariable|name=rnz(x)|graph=Rnz100.svg|caption=[[wikipedia:Probability density function|Probability density function]] of a call of rnz(100).|distribution=unique|mean=approx. 1.29815x|stddev=approx. 1.04424x}}
 '''rnz''' is a function that generates a random number with a distribution that is meant to peak at a given value and trail off at larger values.  A call of rnz(350), for example, gives the base [[prayer timeout]] and will often return a number close to 350, sometimes a number somewhat less or somewhat more than 350, and rarely a number much greater or much less than 350.

← Older revision		Revision as of 21:11, 29 May 2011
Line 299:		Line 299:

	{{nethack-343}}		{{nethack-343}}
−	~~[[Category:Game mechanics]]~~
−	~~[[Category:Annotations]]~~
	[[Category:Random number functions]]		[[Category:Random number functions]]

@@ Line 11: / Line 11: @@
 * rnz(10) (or rnz(25) when first building a [[level]]) plays a part in determining when a [[corpse]] disintegrates.
-* A number of rnz calls are used in determining the [[prayer]] timeout.  In particular, the timeout after successful prayer is rnz(350), with a penalty of rnz(1000) added if you are [[crowning|crowned]] or have killed the [[Wizard of Yendor]].  If you have killed the Wizard and are also crowned, the penalty is doubled.
+* A number of rnz calls are used in determining the [[prayer timeout]].  In particular, the timeout after successful prayer is rnz(350), with a penalty of rnz(1000) added if you are [[crowning|crowned]] or have killed the [[Wizard of Yendor]].  If you have killed the Wizard and are also crowned, the penalty is doubled.
 == Mathematical analysis ==

← Older revision		Revision as of 23:56, 1 February 2011
Line 300:		Line 300:
	{{nethack-343}}		{{nethack-343}}
	[[Category:Game mechanics]]		[[Category:Game mechanics]]
		+	[[Category:Annotations]]
		+	[[Category:Random number functions]]