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The construction of a well tuned probability distributions is illustrated insynthetic way, these probability distributions produce faithful realizations ofthe impact point distributions for particles in silicon strip detector. Theiruse for track fitting shows a drastic improvements of a factor two, for the lownoise case, and a factor three, for the high noise case, respect to thestandard approach. The tracks are well reconstructed even in presence of hitswith large errors, with a surprising effect of hit discarding. The applicationsillustrated are simulations of the PAMELA tracker, but other type of trackerscan be handled similarly. The probability distributions are calculated for thecenter of gravity algorithms, and they are very different from gaussianprobabilities. These differences are crucial to accurately reconstruct trackswith high error hits and to produce the effective discarding of the too noisyhits (outliers). The similarity of our distributions with the Cauchydistribution forced us to abandon the standard deviation for our comparisonsand instead use the full width at half maximum. A set of mathematicalapproaches must be developed for these applications, some of them are standardin wide sense, even if very complex. One is essential and, in its absence, allthe others are useless. Therefore, in this paper, we report the details of thiscritical approach. It extracts physical properties of the detectors, and allowsthe insertion of the functional dependence from the impact point in theprobability distributions. Other papers will be dedicated to the remainingparts.

Improvements of Track Fitting with Well Tuned Probability Distributions for Silicon Strip Detectors