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Cauchy.m
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Cauchy.m
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classdef Cauchy < dContinuous
properties(SetAccess = protected)
location, scale,
OneOverPi, OneOverPiScale
end
methods (Static)
function Reals = ParmsToReals(Parms,~)
Reals = [Parms(1) NumTrans.GT2Real(eps,Parms(2))];
end
function Parms = RealsToParms(Reals,~)
Parms = [Reals(1) NumTrans.Real2GT(eps,Reals(2))];
end
end
methods
function obj=Cauchy(varargin)
obj=obj@dContinuous('Cauchy');
obj.ParmTypes = 'rr';
obj.DefaultParmCodes = 'rr';
obj.NDistParms = 2;
obj.OneOverPi = 1 / pi;
obj.CDFNearlyZero = 0.001; % Cut off more than usual of infinite tails
obj.CDFNearlyOne = 1 - obj.CDFNearlyZero;
obj.IntegralPDFXmuNAbsTol = 100*obj.IntegralPDFXmuNAbsTol; % For integrating PDF
obj.IntegralPDFXmuNRelTol = 100*obj.IntegralPDFXmuNRelTol;
switch nargin
case 0
case 2
ResetParms(obj,[varargin{:}]);
otherwise
ME = MException('Cauchy:Constructor', ...
'Cauchy constructor needs 0 or 2 arguments.');
throw(ME);
end
end
function []=ResetParms(obj,newparmvalues)
ClearBeforeResetParmsC(obj);
obj.location = newparmvalues(1);
obj.scale = newparmvalues(2);
ReInit(obj);
end
function PerturbParms(obj,ParmCodes)
% Perturb parameter values a little bit, e.g., prior to estimation attempts for testing.
newloc = ifelse(ParmCodes(1)=='f', obj.location, 1.1*obj.location);
newscale = ifelse(ParmCodes(2)=='f', obj.scale, 0.9*obj.scale);
obj.ResetParms([newloc newscale]);
end
function []=ReInit(obj)
assert(obj.scale>0,'Cauchy scale must be > 0.');
obj.OneOverPiScale = obj.OneOverPi / obj.scale;
obj.Initialized = true;
obj.LowerBound = InverseCDF(obj,obj.CDFNearlyZero);
obj.UpperBound = InverseCDF(obj,obj.CDFNearlyOne);
if (obj.NameBuilding)
BuildMyName(obj);
end
end
function thispdf=PDF(obj,X)
if ~obj.Initialized
error(UninitializedError(obj));
end
thispdf=zeros(size(X));
InBounds = (X>=obj.LowerBound) & (X<=obj.UpperBound);
SqrDev = ( (X(InBounds) - obj.location) / obj.scale ).^2;
thispdf(InBounds) = obj.OneOverPiScale ./ (1 + SqrDev);
end
function thiscdf=CDF(obj,X)
if ~obj.Initialized
error(UninitializedError(obj));
end
thiscdf=zeros(size(X));
InBounds = (X>=obj.LowerBound) & (X<=obj.UpperBound);
ATanDev = atan( (X(InBounds) - obj.location) / obj.scale );
thiscdf(InBounds) = 0.5 + obj.OneOverPi * ATanDev;
thiscdf(X>obj.UpperBound) = 1;
end
function thisval=InverseCDF(obj,P)
% from Mathematica
if ~obj.Initialized
error(UninitializedError(obj));
end
assert(min(P)>=0&&max(P)<=1,'InverseCDF requires 0<=P<=1');
Ang = pi * (P - 0.5);
%SinAng = sin(Ang); % Note: Tan(x) = Sin(x) / Cos(x)
%CosAng = cos(Ang);
thisval = obj.location + obj.scale * tan(Ang);
end
% The following are theoretically correct but is not true for the bounded approximation being implemented.
%
% function thisval=MGF(obj,Theta)
% assert(obj.Initialized,UninitializedError(obj));
% thisval = NaN;
% end
%
% function thisval=RawMoment(obj,I)
% assert(obj.Initialized,UninitializedError(obj));
% if I == 0
% thisval = 1;
% else
% thisval = NaN;
% end
% end
%
% function thisval=CenMoment(obj,I );
% assert(obj.Initialized,UninitializedError(obj));
% if I == 0
% thisval = 1;
% else
% thisval = NaN;
% end
% end
%
% function thisval=EstimatesFromMoments(obj,PassMoments,ParmCodes)
% ME = MException('Cauchy:EstimatesFromMoments', ...
% 'Cauchy cannot estimate from moments because they do not exist.');
% throw(ME);
% end
end % methods
end % class Cauchy