PROGRAM FOR EVALUATION OF SIGNIFICANCE, CONFIDENCE INTERVALS AND LIMITS BY DIRECT CALCULATION OF PROBABILITIES

We propose a program which allows one to estimate significance, confidence intervals and limits, taking into account systematics and statistical uncertainties of variables described by Poisson distributions. The given program can be used for combining searches. The motivation of the direct probabilities calculations is determined by two reasons. Firstly, the tail of a Poisson distribution is heavier than that of a normal distribution. In the case of small probabilities the Gaussian approximation gives the wrong values of estimators. Secondly, the estimators which are constructed on the basis of the likelihood ratio often have poor statistical properties. In searches for new particles in high energy physics the tasks of the comparison of the possibilities of dif- ferent planned experiments and of the setting and combining of the results of running experiments are vitally important. The determination of the signif- icance of the results and the setting of confidence limits are related to these tasks.