# Predictive value of the maximum likelihood estimator of the number of contributors to a DNA mixture

### Description

The `PV`

function implements the predictive value of the maximum likelihood estimator of the number of contributors to a DNA
mixture

### Usage

1 | ```
PV(mat, prior)
``` |

### Arguments

`mat` |
matrix giving the estimates of the conditional probabilities that the maximum likelihood estimator classifies a given stain as a mixture of i contributors given that there are k contributor(s) to the stain. Estimates i must be given in columns for each possible value of the number of contributors given in rows. |

`prior` |
numeric vector giving the prior probabilities of encountering a mixture of i contributors. |

### Value

Vector of the predictive values

### Author(s)

Hinda Haned <contact@hindahaned.info>

### References

Haned H., Pene L., Sauvage F., Pontier D., The predictive value of the maximum likelihood estimator of the number of contributors to a DNA mixture, submitted, 2010.

### See Also

maximum likelihood estimator `likestim`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
# the following examples reproduce some of the calculations appearing
# in the article cited above, for illustrative purpose, the maximum
#number of contributors is set here to 5
#matcondi: Table 2 in Haned et al. (2010)
matcondi<-matrix(c(1,rep(0,4),0,0.998,0.005,0,0,0,0.002,0.937,0.067,0,0,0,0.058,
0.805,0.131,rep(0,3),0.127,0.662,rep(0,3),0.001,0.207),ncol=6)
#prior defined by a forensic expert (Table 3 in Haned et al., 2010)
prior1<-c(0.45,0.04,0.30,0.15,0.06)
#uniform prior, for each mixture type, the probability of occurrence is 1/5,
#5 being the threshold for the number of contributors
prior2<-c(rep(1/5,5))
#predictive values for prior1
PV(matcondi,prior1)
#for prior2
PV(matcondi, prior2)
``` |