function?x?=?randp（NMalphab）
%?randp?generates?Pareto?random?variables.
%
%?created:?	Fri?Aug??8?1997?（c）?Matthew?Roughan
%?author:??	Matthew?Roughan?
%?email:???	matthew.roughan@adelaide.edu.au
%
%?This?function?generates?Pareto?random?variables?（of?type?I）
%????see?“Statistical?Distributions“?Evans?Hastings?and?Peacock?Wiley?1993
%????or??http://www.maths.adelaide.edu.au/matthew.roughan/probability_distrns/node6.html
%????or??http://en.wikipedia.org/wiki/Pareto_distribution
%
%?The?Pareto?distribution?is?a?classic?“heavy-tailed“?or?“power-law“?distribution.
%?It?has?distribution?function
%????F（x）?=?1?-?（b/x）^alpha?for?x>=b
%?and?density
%????f（x）?=?（alpha/b）?*?（b/x）^（alpha+1）?for?x>=b
%
%?Its?mean?is
%????E[X]?=?b?*?alpha/（alpha-1）?for?alpha>1
%?but?note?that?the?mean?is?infinite?for?alpha<=1
%
%?Its?variance?is?
%????Var（X）?=?b^2?*?alpha/[（alpha-1）^2*（alpha-2）]?for?alpha>1
%?but?note?that?the?variance?is?infinite?for?alpha<=2
%
%?Median
%????Med（X）?=?b?*?2^（1/alpha）
%
%?INPUTS:
%????（NM）?????size?of?output?matrix?of?random?variables
%????alpha>0???shape?parameter?of?Pareto?distribution
%????b>0???????location?（sometimes?called?scale）?parameter?of?Pareto?distribution
%?
%?OUTPUTS
%????x?????????an?（NM）?array?of?random?Pareto?distributed?numbers
%?????????????????range?of?x?=?[b?inf）
%?
%?Note?the?function?calls?“rand“?so?if?you?want?to?control?the?seed?use?rand（‘state‘?seed）.
%
%?Note?that?the?type?II?Pareto?is?just?shifted?so?that?x>=0?so?to?obtain?this?distribution
%?just?take
%?????????????x?=?randp（NMalphab）?-?b;
%

if?（alpha?<=?0）
??error（‘alpha?must?be?>?0‘）
end
if?（b?<=?0）
??error（‘b?must?be?>?0‘）
end
if?（N<1?|?ceil（N）?~=?N）
??error（‘N?must?be?a?positive?integer‘）
end
if?（M<1?|?ceil（M）?~=?M）
??error（‘M?must?be?a?positive?integer‘）
end

y?=?rand（NM）;
x?=?b*（1-y）.^（-1/alpha）;

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件????????1336??2009-08-03?01:56??license.txt
?????文件????????1838??2009-08-03?01:21??randp.m
?????文件?????????977??2009-08-03?01:48??randp_test.m
?????文件????????8042??2009-08-03?01:48??randp_test.png