Parameter estimation and hypothesis verification - matlab

%--------------------------------------------------------------------------
%   The first 18 Chapter    Parameter estimation and hypothesis testing 
%--------------------------------------------------------------------------

%% examp18.2-1
%+++++++++++++++++++++++++ call normfit Function solving +++++++++++++++++++++++++++++++
x = [15.14  14.81  15.11  15.26  15.08  15.17  15.12  14.95  15.05  14.87];
[muhat,sigmahat,muci,sigmaci] = normfit(x,0.1)

%++++++++++++++++++++++++++++ call mle Function solving ++++++++++++++++++++++++++++++++
x = [15.14  14.81  15.11  15.26  15.08  15.17  15.12  14.95  15.05  14.87];
[mu_sigma,mu_sigma_ci] = mle(x,'distribution','norm','alpha',0.1)

%% examp18.2-2
x = [0.7917,0.8448,0.9802,0.8481,0.7627
        0.9013,0.9037,0.7399,0.7843,0.8424
        0.9842,0.7134,0.9959,0.6444,0.8362
        0.7651,0.9341,0.6515,0.7956,0.8733];
PdfFun = @(x,theta) theta*x.^(theta-1).*(x>0 & x<1);
[phat,pci] = mle(x(:),'pdf',PdfFun,'start',1)

%% examp18.3-1
%++++++++++++++++++++++++++++++++ Bilateral test ++++++++++++++++++++++++++++++++++
x = [97  102  105  112  99  103  102  94  100  95  105  98  102  100  103];
[h,p,muci,zval] = ztest(x,100,2,0.05)

%++++++++++++++++++++++++++++++++ One side test ++++++++++++++++++++++++++++++++++
x = [97  102  105  112  99  103  102  94  100  95  105  98  102  100  103];
[h,p,muci,zval] = ztest(x,100,2,0.05,'right')

%% examp18.3-2
x = [49.4  50.5  50.7  51.7  49.8  47.9  49.2  51.4  48.9];
[h,p,muci,stats] = ttest(x,50,0.05)

%% examp18.3-3
x = [20.1,  20.0,  19.3,  20.6,  20.2,  19.9,  20.0,  19.9,  19.1,  19.9];
y = [18.6,  19.1,  20.0,  20.0,  20.0,  19.7,  19.9,  19.6,  20.2];
alpha = 0.05;
tail = 'both';
vartype = 'equal';
[h,p,muci,stats] = ttest2(x,y,alpha,tail,vartype)

%% examp18.3-4
x = [49.4  50.5  50.7  51.7  49.8  47.9  49.2  51.4  48.9];
var0 = 1.5;
alpha = 0.05;
tail = 'both';
[h,p,varci,stats] = vartest(x,var0,alpha,tail)

%% examp18.3-5
x = [20.1,  20.0,  19.3,  20.6,  20.2,  19.9,  20.0,  19.9,  19.1,  19.9];
y = [18.6,  19.1,  20.0,  20.0,  20.0,  19.7,  19.9,  19.6,  20.2];
alpha = 0.05;
tail = 'both';
[h,p,varci,stats] = vartest2(x,y,alpha,tail)```

```css
muhat =

   15.0560


sigmahat =

    0.1397


muci =

   14.9750
   15.1370


sigmaci =

    0.1019
    0.2298


mu_sigma =

   15.0560    0.1325


mu_sigma_ci =

   14.9750    0.1019
   15.1370    0.2298


phat =

    5.1502


pci =

    2.8931
    7.4073


h =

     1


p =

    0.0282


muci =

  100.1212  102.1455


zval =

    2.1947


h =

     1


p =

    0.0141


muci =

  100.2839       Inf


zval =

    2.1947


h =

     0


p =

    0.8961


muci =

   48.9943   50.8945


stats = 

   That contains the following fields  struct:

    tstat: -0.1348
       df: 8
       sd: 1.2360


h =

     0


p =

    0.3191


muci =

   -0.2346    0.6791


stats = 

   That contains the following fields  struct:

    tstat: 1.0263
       df: 17
       sd: 0.4713


h =

     0


p =

    0.8383


varci =

    0.6970    5.6072


stats = 

   That contains the following fields  struct:

    chisqstat: 8.1481
           df: 8


h =

     0


p =

    0.5798


varci =

    0.1567    2.8001


stats = 

   That contains the following fields  struct:

    fstat: 0.6826
      df1: 9
      df2: 8