# Bootstrap Censored Weibull Mixture for censoring threshold selection and standard error of the quantile estimates

### Description

Similarly as in `bootstrapCMLE`

, We will bootstrap the data set to obtain the MSE and SE of the quantile estimate under a certain subjective censoring threshold. Warning: The computation burden of this function is extremely heavy.

### Usage

1 2 | ```
bootstrapCenWbMix(dat, qInt = 0.05, canSet = c(0.5, 0.7, 1), B = 1000,
iniVec = NULL, randSeed = NULL, conCr = 1e-06, nIter = 1000)
``` |

### Arguments

`dat` |
The complect data set. See |

`qInt` |
Quantile of interest. See |

`canSet` |
Candidate set of thresholds. See |

`B` |
Number of bootstrap replicates |

`iniVec` |
A vector of length 6*length( |

`randSeed` |
See |

`conCr` |
Same as in |

`nIter` |
Same as in |

### Details

The EM algorithm for Weibull mixture is extremely senstive to the initial value, so the user should always try to find proper initial values for each threshold and data set.

The initial values in the argument are for the original data set. The EM algorithm for the original data set will be first carried out from these initial values. If they succesfully converged, the EM algorithm for the bootstrap data sets will start from the estimates of the original data set in the previous step. Otherwise, the EM algorithm will start from the initial value in the arguements. Although we could not gurantee the "global" maximum can be reached for each bootstrap replicate under this scheme, our simulation shown that it works reasonably well.

Similarly as `bootstrapCMLE`

, the main calculation of this function is done in C.

### Value

`results` |
A matrix of length( |

`parameters` |
A matrix of length( |

`bQEst` |
A matrix of B-by-length( |

### Note

Please report the numerical problems and inconvenience when using this function to the author.

### Author(s)

Yang (Seagle) Liu <yang.liu@stat.ubc.ca>

### References

Liu Y. (2012). Lower Quantile Estimation of Wood Strength Data. *Master Thesis, Department of Statistics, UBC.* Downloadable here.

### See Also

`bootstrapCMLE`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
###
mmix = rbind(c(0.7, 5, 7),c(0.3, 15, 6))
vmix = c(mmix) #A vector version of the paramters
set.seed(1)
y <- sort(simWbMix(100, mmix)) #Generate Data
#Run the EM for 70% Type II censoring
mix70 <- emCenWbMix.T2(y[1:70], 100, iniParam=vmix, useC=TRUE)
#Run the EM for the complete data set
mix100<- emCenWbMix.T2(y, 100, iniParam=vmix, useC=TRUE)
#Use bootstrap with the previous estimates as initials
bootstrapCenWbMix(y, canSet=c(0.7, 1),
iniVec=c(c(mix70$estimates), c(mix100$estimates)), B=5,randSeed=1)
#Or use the "true" value as the initials.
bootstrapCenWbMix(y, canSet=c(0.7, 1), iniVec=c(vmix, vmix), B=5,randSeed=1)
#B=5 is just for illustration. It should be at least 1000.
``` |

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