JOINT PROBABILITY CONCLUSIONS              

     THE JOINT PROBABILITY, P_j , IS THE PROBABILITY OF ALL PEAKS  CONSIDERED OCCURRING SIMULTANEOUSLY IN A SPECTRUM.  IT IS A MEASURE OF THE UNIQUENESS OF A SPECTRUM.  THE SMALLER THE P_j , THE MORE UNIQUE THE SPECTRUM.  FOR THE NIST DATABASE, Version 4, A P_j VALUE OF 0.000016 REPRESENTS A UNIQUE SPECTRUM.

UPPER LIMITS

1. P_j IS LESS THAN THE  SMALLEST INDIVIDUAL MASS OCCURRENCE PROBABILITY, p_i ,  IN A SPECTRUM.

                                                                          P_j < min (p_i)

2. P_j IS ALWAYS LESS THAN 0.17 FOR ANY FIVE PEAKS AND 0.07 FOR ANY TEN PEAKS.

                                                             P_j < 0.17 (n=5)

                                                   P_j < 0.07 (n=10)

LOWER LIMITS

3. P_j IS GREATER THAN THE PRODUCT OF THE INDIVIDUAL MASS PROBABILITIES IN THE SPECTRUM.   ALSO NO SINGLE MASS PROBABILITY, p_i , CAN BE HIGHER THAN 0.49 EXCEPT IN A BINARY ENCODED SPECTRUM.

                                                               P_j > (p₁ x p₂ x p₃ x ... p_n)

                                                         p_i < 0.49

BASE PEAKS

4.  NO BASE PEAK, P_base , WILL OCCUR WITH A PROBABILITY HIGHER THAN 0.057.

                                                                   P_base < 0.058

TYPICAL JOINT PROBABILITY

5. FOR A RANDOMLY PICKED SPECTRUM, CIS 1-ETHYL- 4-METHYL- CYCLOHEXANE,  THE UPPER LIMIT TO P_j IS 0.010 FOR THE FOUR HIGHEST INTENSITY PEAKS IN THE SPECTRUM AND THE LOWER LIMIT IS 0.0000002 .   THE ACTUAL P_j FOR THE FOUR PEAKS IS 0.00015 (NINE SPECTRA IN THE NIST V. 4 DATABASE).