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# samplef

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

### Calling Sequence

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

### Arguments

- 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 length 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 length 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 length 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 length 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=[1 ; 15] f3=[10 1 1] s=samplef(15,a,f1) s=samplef(15,a,f2,'r') s=samplef(15,a,f3,'c')

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