Description Usage Arguments Details Value References Examples

Estimates the pairwise overlap matrix for a Manly mixture by simulating samples based on user-specified parameters.

1 | ```
Manly.overlap(tau, Mu, S, la, N = 1000)
``` |

`la ` |
matrix of transformation parameters (K x p) |

`tau ` |
vector of mixing proportions (length K) |

`Mu ` |
matrix of mean vectors (K x p) |

`S ` |
array of covariance matrices (p x p x K) |

`N ` |
number of samples simulated |

Estimates the pairwise overlap matrix for a Manly mixture. Overlap is defined as sum of two misclassification probabilities.

`OmegaMap` |
matrix of misclassification probabilities (K x K); OmegaMap[i,j] is the probability that X coming from the i-th component is classified to the j-th component. |

`BarOmega` |
value of average overlap. |

`MaxOmega` |
value of maximum overlap. |

Maitra, R. and Melnykov, V. (2010) “Simulating data to study performance of finite mixture modeling and clustering algorithms”, *Journal of Computational and Graphical Statistics*, 2:19, 354-376.

Melnykov, V., Chen, W.-C., and Maitra, R. (2012) “MixSim: An R Package for Simulating Data to Study Performance of Clustering Algorithms”, *Journal of Statistical Software*, 51:12, 1-25.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
set.seed(123)
#sets the number of components, dimensionality and sample size
K <- 3
p <- 2
#sets the mixture parameters
tau <- c(0.25, 0.3, 0.45)
Mu <- matrix(c(4.5,4,5,7,8,5.5),3)
la <- matrix(c(0.2,0.5,0.3,0.25,0.35,0.4),3)
S <- array(NA, dim = c(p,p,K))
S[,,1] <- matrix(c(0.4,0,0,0.4),2)
S[,,2] <- matrix(c(1,-0.2,-0.2,0.6),2)
S[,,3] <- matrix(c(2,-1,-1,2),2)
#computes the overlap
A <- Manly.overlap(tau, Mu, S, la)
print(A)
``` |

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