# Maximum time interval error

## Formula

Maximum time interval error

\[Mtie(\tau)=\operatorname{max}_{1\leq k\leq N-n}\left(\operatorname{max}_{k\leq t\leq k+n}(x_t)-\operatorname{min}_{k\leq t\leq k+n}(x_t)\right)\]

## Doc String

`AllanDeviations.mtie`

— Method.mtie(data, rate; [frequency=false], [overlapping=true], [taus=Octave]) Calculates the maximal time interval error

**parameters:**

`<data>`

: The data array to calculate the deviation from either as as phases or frequencies.`<rate>`

: The rate of the data given.`[frequency]`

: True if`data`

contains frequency data otherwise (default) phase data is assumed.`[overlapping]`

: True (default) to calculate overlapping deviation, false otherwise.`[taus]`

: Taus to calculate the deviation at. This can either be an AllanTauDescriptor type`AllTaus, Decadade, HalfDecade, Octave, HalfOctave, QuarterOctave`

, an array of taus to calculate at, a float number to build a custom log-scale on or an integer to build a specific number of log spaced points.

**returns: named tupple (tau, deviation, error, count)**

`tau`

: Taus which where used.`deviation`

: Deviations calculated.`error`

: Respective errors.`count`

: Number of contributing terms for each deviation.

## Possible issues

`mtie`

in itself needs a great amount of computations and can be very slow for big taus with many data points. When computations need too much time, consider reducing the number of taus and/or especially using smaller taus.- Mtie can be called with a non-overlapping calculation. This throws a warning because it is unusual to use but nevertheless faster.