Scilab Function

samplef - sample with replacement from a population and frequences of his values.

### Calling Sequence

  `s = samplef(n,X,f,orient)`

### Parameters

- `n` : positive integer (size of sample)
- `X` : matrix. Samples will be extracted from this matrix
- `f` : positive integer matrix with same type than X. It indicates frequences of corresponding values of X.
- `orient` : Optional parameter. Admissible values are 1, 2, 'r' or 'c'
- `s` : vector or matrix containing sample

### Description

This function gives s, a vector of lenght n. It contains a sample of n extractions, with replacement, from the vector (or matrix) X, each element counted with the frequence given by the corresponding value in vector f.

s=samplef(n,X,f) (or s=samplef(n,X,f,'*')) returns a vector s whose values are a random sample of n values from X, each value with a probability to be sampled proportional to the corresponding value of f, extracted with replacement, from X. f must have same lenght than X.

s=samplef(n,X,f,'r') (or, equivalently, s=samplef(n,X,f,1)) returns a matrix of type size(X,'r')xn. It contains a random sample of n rows from X, each row with a probability to be sampled proportional to the corresponding value of f, extracted with replacement, from the rows of X. The lenght of f must be equal to the number of rows of X.

s=samplef(n,X,f,'c') (or, equivalently, s=samplef(n,X,f,2)) returns a matrix of type nxsize(X,'c'). It contains a random sample of n columns from X, each column with a probability to be sampled proportional to the corresponding value of f, extracted with replacement, from the columns of X. The lenght of f must be equal to the number of columns of X.

### Examples

       a=[3 7 9;22 4 2]
       f1=[10 1 1 1 1 1]
       f2=[10 1 1]
       f3=[1 ; 15]
       s=samplef(15,a,f1)
       s=samplef(15,a,f2,'r')
       s=samplef(15,a,f3,'c')

### See Also

`sample` , `samwr` ,

### Author

Carlos Klimann