The function `icfit`

calculates the NPMLE of a distribution for interval censored data using an E-M algorithm
with polishing and checking the Kuhn-Tucker conditions (see `icfit`

help details).
It allows functions for the initfit option in order to calculate the starting value of the distribution in the E-M algorithm.
Because `icfit`

checks the Kuhn-Tucker conditions, we can try functions without doing extensive quality control,
since if the starting distribution is not close to the true NPMLE the only downside is a slower convergence. But if the
initfit function is the true NPMLE then convergence happens on the first iteration. Functions must input 5 objects, L,R, Lin, Rin,
and A, but need not use all of them.

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`L` |
numeric vector of left endpoints of censoring interval (equivalent to first element of Surv when type='interval2', see |

`R` |
numeric vector of right endpoints of censoring interval (equivalent to second element of Surv function when type='interval2', see |

`Lin` |
logical vector, should L be included in the interval? (see |

`Rin` |
logical vector, should R be included in the interval? (see |

`A` |
clique matrix |

`max.inner` |
see |

`max.outer` |
see |

`tol` |
see either |

`maxiter` |
see |

In order to work correctly within `icfit`

the function should output a list with at least a 'pf' element
giving the estimated mass of the distribution for a series of intervals.
Further, if an 'intmap' element is included (describing the series of intervals) it will be used by `icfit`

.

The function `initcomputeMLE`

outputs an icfit object with 'pf' and 'intmap' values and some other values
defined in the help for `computeMLE`

.

The function `initEMICM`

outputs an icsurv object with a 'pf' element but no 'intmap' element, in addition to
some other values defined in the help for `EMICM`

.

Here we define pf and intmap:

`pf` |
vector of estimated probabilities of the distribution |

`intmap` |
2 by k matrix, where the ith column defines an interval corresponding to the probability, pf[i] |

In rare cases the `computeMLE`

function (and hence the `initcomputeMLE`

function) can cause R to crash
(at least for version 0.1-3 of the `MLEcens`

package).

The wrappers for the functions were written by M. Fay, but the real work are the calculation engines:

The calculation engine for `initcomputeMLE`

is `computeMLE`

and was written by Marloes Maathuis, with
part of the code for the optimization step is adapted from code that was written by Piet Groeneboom.

The calculation engine for `initEMICM`

is `EMICM`

and was written by Alain Vandal and Robert Gentleman

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