matlab normspec叠加图

 p = normspec(specs,mu,sigma)

matlab自带的这个函数每次绘制都会打开一个新的句柄，无法绘制两个分布的叠加。在原函数基础上修改获得如下图类似的效果。

normspec两个分布叠加

 修改

function [p,h] = mynormspec(specs,mu,sigma,region,color)
%NORMSPEC Plots normal densit between specification limits.
%    NORMSPEC(SPECS) plots the standard normal density, shading the
%    portion inside the spec limits.  SPECS is a two element vector
%    containing the lower and upper specification limits.
%    Set SPECS(1)=-Inf if there is no lower limit, and SPECS(2)=Inf
%    if there is no upper limit. 
% 
%    NORMSPEC(SPECS,MU,SIGMA) shades the portion inside the spec limits of
%    a normal density with parameters MU and SIGMA.  The defaults are MU=0 and
%    SIGMA=1.
% 
%    NORMSPEC(SPECS,MU,SIGMA,REGION) shades either the portion 'inside' or
%    'outside' of the spec limits.  The default is REGION='inside'.
% 
%    [P] = NORMSPEC(...) returns the probability, P, of the shaded area.
%
%    [P,H] = NORMSPEC(...) returns a handle H to the line objects.
% 
%   Copyright 1993-2011 The MathWorks, Inc. 
%fill in default args
if nargin<2
    mu=0;
end
if nargin<3
    sigma=1;
end
if nargin<4
    region='inside';
end
%test for invalid args
if numel(specs) ~= 2 || ~isnumeric(specs),
    error(message('stats:normspec:BadSpecsSize'));
end
if max(size(mu)) > 1 || max(size(sigma)) > 1 ,
    error(message('stats:normspec:ScalarRequired'));
end
if ~strcmp(region,'inside') && ~strcmp(region,'outside')
    error(message('stats:normspec:BadRegion'));
end    
%swap the specs if they are reversed
lb = specs(1);
ub = specs(2);
if lb > ub
    lb = specs(2);
    ub = specs(1);
end
lbinf = isinf(lb);
ubinf = isinf(ub);
%continue checking for invalid args
if lbinf && ubinf
    error(message('stats:normspec:BadSpecsInfinite'));
end
%compute normal curve
prob = (0.0002:0.0004:0.9998)';
x = norminv(prob,mu,sigma);
y = normpdf(x,mu,sigma);
%compute p
if strcmp(region,'outside')
    if lbinf,
        p = normcdf(-ub,-mu,sigma); % P(t > ub)
    elseif ubinf,
        p = normcdf(lb,mu,sigma); % P(t < lb)
    else
        p = sum(normcdf([lb -ub],[mu -mu],sigma)); % P(t < lb) + Pr(t > ub)
    end
else
    if lbinf,
        p = normcdf(ub,mu,sigma); % P(t < ub)
    elseif ubinf,
        p = normcdf(-lb,-mu,sigma); % P(t > lb)
    else
        p = diff(normcdf([lb ub],mu,sigma)); % P(lb < t < ub)
    end
end
hh = plot(x,y,'black-');
xlims = 4*[specs(1) specs(2)];
%compute the endpoints of the spec limit lines and plot limit lines
%lower limit line goes up, and upper limit line goes down
pll =  [xlims(1);xlims(1)];
ypll = [0;eps];
if lbinf,
    ll =  pll;
    yll = ypll;
else
    ll =  [lb; lb];
    yll = [0; normpdf(lb,mu,sigma)];
end
pul =  [xlims(2);xlims(2)];
ypul = [eps;0];
if ubinf,
    ul =  pul;
    yul = ypul;
else
    ul  = [ub; ub];
    yul = [normpdf(ub,mu,sigma); 0];
end
%create title, draw spec lines, and shade area
switch region
    case 'inside'
        if ubinf
            str = sprintf('%s',getString(message('stats:normspec:ProbGTlb',num2str(p))));
            k = find(x > lb);
            hh1 = plot(ll,yll,'black-');
        elseif lbinf
            str = sprintf('%s',getString(message('stats:normspec:ProbLTub',num2str(p))));
            k = find(x < ub);
            hh1 = plot(ul,yul,'black-');
        else
            str = sprintf('%s',getString(message('stats:normspec:ProbBetweenBounds',num2str(p))));
            k = find(x > lb & x < ub);
            hh1 = plot(ll,yll,'black-',ul,yul,'black-');
        end
        xfill = [ll; x(k); ul];
        yfill = [yll; y(k); yul];
        fill(xfill,yfill,color);
    case 'outside'
        if ubinf
            str = sprintf('%s',getString(message('stats:normspec:ProbLTlb',num2str(p))));
            k1 = find(x < lb);
            k2=[];
            hh1 = plot(ll,yll,'black-');
        elseif lbinf
            str = sprintf('%s',getString(message('stats:normspec:ProbGTub',num2str(p))));
            k1=[];
            k2 = find(x > ub);
            hh1 = plot(ul,yul,'black-');
        else
            str = sprintf('%s',getString(message('stats:normspec:ProbOutsideBounds',num2str(p))));
            k1 = find(x < lb );
            k2=find(x > ub);
            hh1 = plot(ll,yll,'black-',ul,yul,'black-');
        end
        xfill = [pll;  x(k1); ll          ; ul;          x(k2); pul  ];
        yfill = [ypll; y(k1); flipud(yll) ; flipud(yul); y(k2); ypul ];
        fill(xfill,yfill,color);
    otherwise
        error(message('stats:normspec:BadRegion'));
end
%return line handles, if requested
if nargout > 1
    h = [hh; hh1];
end

　

绘制并手动修饰

figure
mynormspec([-inf, 3], 0, 1.5, 'outside', 'w')
hold on
mynormspec([3, 8], 0, 1.5, 'inside', 'b') % 表示[3, inf]
hold on
mynormspec([-10, 3], 4.5, 2, 'inside', 'r') % 表示[-inf, 3]
hold on
mynormspec([3, inf], 4.5, 2, 'outside', 'w')
xlim([-8, 13])
xlabel('x')
ylabel('PDF')

% 求对应的阴影面积
p1 = diff(normcdf([3, inf], 0, 1.5));
p2 = diff(normcdf([-inf, 3], 4.5, 2));