最大似然估计方法估计幂律分布源码程序 - matlab金融统计

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标题：最大似然估计方法估计幂律分布源码程序
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所属分类: 金融统计资源类型：文件大小: 4.31 KB 上传时间: 2016-03-06 12:09:34 下载次数: 6 资源积分：1分提供者: 源码共享 20160306120850617

内容：
最大似然估计方法估计幂律分布源码程序，这个是用于拟合幂律分布的函数。函数使用最大似然估计方法估计幂律分布。经验证效果非常好。

vec = [];

sample = [];

xminx = [];

limit = [];

finite = false;

nosmall = false;

nowarn = false;

% parse command-line parameters; trap for bad input

i=1;

while i<=length(varargin),

argok = 1;

if ischar(varargin{i}),

switch varargin{i},

case 'range', vec = varargin{i+1}; i = i + 1;

case 'sample', sample = varargin{i+1}; i = i + 1;

case 'limit', limit = varargin{i+1}; i = i + 1;

case 'xmin', xminx = varargin{i+1}; i = i + 1;

case 'finite', finite = true;

case 'nowarn', nowarn = true;

case 'nosmall', nosmall = true;

otherwise, argok=0;

end

if ~argok,

disp(['(PLFIT) Ignoring invalid argument #' num2str(i+1)]);

end

i = i+1;

end

if ~isempty(vec) && (~isvector(vec) || min(vec)<=1),

fprintf('(PLFIT) Error: ''range'' argument must contain a vector; using default.\n');

vec = [];

end;

if ~isempty(sample) && (~isscalar(sample) || sample<2),

fprintf('(PLFIT) Error: ''sample'' argument must be a positive integer > 1; using default.\n');

sample = [];

end;

if ~isempty(limit) && (~isscalar(limit) || limit<min(x)),

fprintf('(PLFIT) Error: ''limit'' argument must be a positive value >= 1; using default.\n');

limit = [];

end;

if ~isempty(xminx) && (~isscalar(xminx) || xminx>=max(x)),

fprintf('(PLFIT) Error: ''xmin'' argument must be a positive value < max(x); using default behavior.\n');

xminx = [];

end;

% reshape input vector

x = reshape(x,numel(x),1);

% select method (discrete or continuous) for fitting

if isempty(setdiff(x,floor(x))), f_dattype = 'INTS';

elseif isreal(x), f_dattype = 'REAL';

else f_dattype = 'UNKN';

end;

if strcmp(f_dattype,'INTS') && min(x) > 1000 && length(x)>100,

f_dattype = 'REAL';

end;

% estimate xmin and alpha, accordingly

switch f_dattype,

case 'REAL',

xmins = unique(x);

xmins = xmins(1:end-1);

if ~isempty(xminx),

xmins = xmins(find(xmins>=xminx,1,'first'));

end;

if ~isempty(limit),

xmins(xmins>limit) = [];

end;

if ~isempty(sample),

xmins = xmins(unique(round(linspace(1,length(xmins),sample))));

end;

dat = zeros(size(xmins));

z = sort(x);

for xm=1:length(xmins)

xmin = xmins(xm);

z = z(z>=xmin);

n = length(z);

% estimate alpha using direct MLE

a = n ./ sum( log(z./xmin) );

if nosmall,

if (a-1)/sqrt(n) > 0.1

dat(xm:end) = [];

xm = length(xmins)+1;

break;

end;

% compute KS statistic

cx = (0:n-1)'./n;

cf = 1-(xmin./z).^a;

dat(xm) = max( abs(cf-cx) );

end;

D = min(dat);

xmin = xmins(find(dat<=D,1,'first'));

z = x(x>=xmin);

n = length(z);

alpha = 1 + n ./ sum( log(z./xmin) );

if finite, alpha = alpha*(n-1)/n+1/n; end; % finite-size correction

if n < 50 && ~finite && ~nowarn,

fprintf('(PLFIT) Warning: finite-size bias may be present.\n');

end;

L = n*log((alpha-1)/xmin) - alpha.*sum(log(z./xmin));

case 'INTS',

if isempty(vec),

vec = (1.50:0.01:3.50); % covers range of most practical

end; % scaling parameters

zvec = zeta(vec);

xmins = unique(x);

xmins = xmins(1:end-1);

if ~isempty(xminx),

xmins = xmins(find(xmins>=xminx,1,'first'));

end;

if ~isempty(limit),

limit = round(limit);

xmins(xmins>limit) = [];

end;

if ~isempty(sample),

xmins = xmins(unique(round(linspace(1,length(xmins),sample))));

end;

if isempty(xmins)

fprintf('(PLFIT) Error: x must contain at least two unique values.\n');

alpha = NaN; xmin = x(1); D = NaN;

return;

end;

xmax = max(x);

dat = zeros(length(xmins),2);

z = x;

fcatch = 0;

for xm=1:length(xmins)

xmin = xmins(xm);

z = z(z>=xmin);

n = length(z);

% estimate alpha via direct maximization of likelihood function

if fcatch==0

try

% vectorized version of numerical calculation

zdiff = sum( repmat((1:xmin-1)',1,length(vec)).^-repmat(vec,xmin-1,1) ,1);

L = -vec.*sum(log(z)) - n.*log(zvec - zdiff);

catch

% catch: force loop to default to iterative version for

% remainder of the search

fcatch = 1;

end;

if fcatch==1

% force iterative calculation (more memory efficient, but

% can be slower)

L = -Inf*ones(size(vec));

slogz = sum(log(z));

xminvec = (1:xmin-1);

for k=1:length(vec)

L(k) = -vec(k)*slogz - n*log(zvec(k) - sum(xminvec.^-vec(k)));

end

end;

[Y,I] = max(L);

% compute KS statistic

fit = cumsum((((xmin:xmax).^-vec(I)))./ (zvec(I) - sum((1:xmin-1).^-vec(I))));

cdi = cumsum(hist(z,xmin:xmax)./n);

dat(xm,:) = [max(abs( fit - cdi )) vec(I)];

end

% select the index for the minimum value of D

[D,I] = min(dat(:,1));

xmin = xmins(I);

z = x(x>=xmin);

n = length(z);

alpha = dat(I,2);

if finite, alpha = alpha*(n-1)/n+1/n; end; % finite-size correction

if n < 50 && ~finite && ~nowarn,

fprintf('(PLFIT) Warning: finite-size bias may be present.\n');

end;

L = -alpha*sum(log(z)) - n*log(zvec(find(vec<=alpha,1,'last')) - sum((1:xmin-1).^-alpha));

otherwise,

fprintf('(PLFIT) Error: x must contain only reals or only integers.\n');

alpha = [];

xmin = [];

L = [];

return;

文件列表（点击上边下载按钮，如果是垃圾文件请在下面评价差评或者投诉）:

最大似然估计方法估计幂律分布源码程序/
最大似然估计方法估计幂律分布源码程序/plfit.m
最大似然估计方法估计幂律分布源码程序/www.gusucode.com.txt
最大似然估计方法估计幂律分布源码程序/【谷速代码】-免费源码.url
最大似然估计方法估计幂律分布源码程序/内容简介.txt

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