clear all
close all
len=[30 14 38 19 43 13 13 24 7 27 26 19 22 13 15 17 20 7 19 18 10 35 20 29 25 25 30 ...
    28 30 32 30 24 34 29 35 21 30 15 18 16 25 17 20 15 27 15 26 11 35 15 33 17 25 34 ...
    17 32 20 33 20 21 25 30 28 13 15 9 13 7 12 13 14 16 19 8 12 16 13 15 12 10 11];

Y=len;
%sort(len)
[m,n]=size(Y);
y=zeros(1,7);
for i=1:n
    for j=1:6
        if len(:,i)<=6.5+j*5&len(:,i)>6.5+(j-1)*5
            y(j)=y(j)+1;
        end  
    end
        if len(:,i)<=43.5&len(:,i)>36.5
            y(7)=y(7)+1
    end
end
x=9:5:39;
k=8;
fenbu=y;
fenbu=fenbu(1:k-1);
figure('color',[1 1 1]);bar(fenbu);
y=fenbu/sum(fenbu)/5;
stem(y);
set(gca,'Xtick',[]);
figure;
plot(x,y,'*');
hold on;
c=[2,2];
[p1,resnorm1]=lsqcurvefit('duishuzhengtai',c,x,y);
[p2,resnorm2]=lsqcurvefit('stu',c,x,y)
x=0:0.05:50;
plot(x,duishuzhengtai(p1,x));
hold on;
plot(x,stu(p2,x),'r');
%求pnormi
pnorm=[p2(2) p2(1)];
pnormi=zeros(1,k-1);
pnormi(1)=normcdf(11.5,pnorm(1),pnorm(2));
for i=2:6
pnormi(i)=normcdf(11.5+(i-1)*5,pnorm(1),pnorm(2))-normcdf(11.5+(i-2)*5,pnorm(1),pnorm(2));
end
pnormi(7)=1-normcdf(11.5+(7-2)*5,pnorm(1),pnorm(2));
pnormi;
sum(pnormi);
%求fi^2/nPi=fipinorm
fipinorm=zeros(1,k-1);
fipinorm(1)=fenbu(1)^2/n/pnormi(1);
for i=2:k-1
    fipinorm(i)=fenbu(i)^2/n/pnormi(i);
end
fipinorm
xnorm=sum(fipinorm)-n
%求plogni
plogn=[p1(2) p1(1)];
plogni=zeros(1,k-1);
plogni(1)=logncdf(11.5,plogn(1),plogn(2))
for i=2:6
plogni(i)=logncdf(11.5+(i-1)*5,plogn(1),plogn(2))-logncdf(11.5+(i-2)*5,plogn(1),plogn(2));
end
plogni(7)=1-logncdf(11.5+(7-2)*5,plogn(1),plogn(2));
plogni;
sum(plogni);
%求fi^2/nPi=fipilogn
fipilogn=zeros(1,k-1);
fipilogn(1)=fenbu(1)^2/n/plogni(1);
for i=2:k-1
    fipilogn(i)=fenbu(i)^2/n/plogni(i);
end
fipilogn
xlogn=sum(fipilogn)-n

%求X^2(k-r-1）；
r=2;
k=8;
alfa=0.05;
v=k-r-1;
x=chi2inv(1-alfa,v)