PROBABILITY & STATISTICS FUNCTIONS FOR MLAB

THE PURPOSE OF THE SOFTWARE TO BE DEVELOPED UNDER THIS SBIR PHASE I GRANT IS TO ENHANCE THE MLAB MATHEMATICAL MODELING PROGRAM BY PROVIDING FUNCTIONS IN FOUR AREAS: 1) STATISTICAL DISTRIBUTIONS, DENSITY FUNCTIONS, THE INVERSES OF THESE DISTRIBUTIONS, 2) RANDOM SAMPLES FROM SPECIFIED STATISTICAL DISTRIBUTIONS, 3) TESTS OF STATISTICAL HYPOTHESES IN CONNECTION WITH DATA, BOTH PARAMETRIC AND NON-PARAMETRIC, AND 4) MATHEMATICAL FUNCTIONS WITH STATISTICAL UTILITY. FUNCTIONS WILL ALSO BE PROVIDED WHICH APPLY TO A WIDE RANGE OF STATISTICAL COMPUTATIONS, INCLUDINGELEMENTARY STATISTICS, SURVIVAL ANALYSIS, AND STUDY DESIGN. ALL OF THESE FUNCTIONS WILL BE EMBEDDED IN THE MLAB SYSTEM, WHICH PROVIDES COMMANDS FOR INPUT FROM FILES AND THE KEYBOARD, SCALAR AND MATRIX COMPUTATION, CONVENIENT GRAPHICAL AND TABULAR OUTPUT, BOTH TO THE SCREEN AND TO HARD COPY, AND A POWERFUL PROGRAMMING LANGUAGE TO SUPPORT THE DEVELOPMENT OF APPLICATIONS WHICH USE THE STATISTICAL CAPABILITY. WHILE MANY OF THE STATISTICAL FUNCTIONS TO BE PROVIDED ARE AVAILABLE PIECEMEAL ELSEWHERE, THERE WILL BE SEVERAL WHICH WILL BE UNIQUE TO MLAB. HAVING ALL THESE FUNCTIONS TOGETHERIN THE MLAB ENVIRONMENT INCREASES THEIR UTILITY SYNERGISTICALLY. THE STATISTICAL FUNCTIONS WILL COMPLEMENT THE EXISTING MLAB CAPABILITIES IN CURVE-FITTING, LEADING TO A LEVEL OF INTEGRATED FUNCTIONALITY NOT AVAILABLE IN ANY EXISTING SYSTEM. IN ADDITION, THE CAPABILITIES OF MLAB WILL BE ENHANCED IN ORDER THAT THE USER MAY MAKE MORE EFFECTIVE USE OF THE STATISTICAL FUNCTIONS. THE NEW STATISTICAL FUNCTIONALITY WILL BE FULLY DOCUMENTED IN A REFERENCE MANUAL AND IN AN ON-LINE HYPERTEXT HELP SYSTEM. THE PURPOSE OF THE SOFTWARE TO BE DEVELOPED UNDER THIS SBIR PHASE I GRANT IS TO ENHANCE THE MLAB MATHEMATICAL MODELING PROGRAM BY PROVIDING FUNCTIONS IN FOUR AREAS: 1) STATISTICAL DISTRIBUTIONS, DENSITY FUNCTIONS, THE INVERSES OF THESE DISTRIBUTIONS, 2) RANDOM SAMPLES FROM SPECIFIED STATISTICAL DISTRIBUTIONS, 3) TESTS OF STATISTICAL HYPOTHESES IN CONNECTION WITH DATA, BOTH PARAMETRIC AND NON-PARAMETRIC, AND 4) MATHEMATICAL FUNCTIONS WITH STATISTICAL UTILITY. FUNCTIONS WILL ALSO BE PROVIDED WHICH APPLY TO A WIDE RANGE OF STATISTICAL COMPUTATIONS, INCLUDINGELEMENTARY STATISTICS, SURVIVAL ANALYSIS, AND STUDY DESIGN. ALL OF THESE FUNCTIONS WILL BE EMBEDDED IN THE MLAB SYSTEM, WHICH PROVIDES COMMANDS FOR INPUT FROM FILES AND THE KEYBOARD, SCALAR AND MATRIX COMPUTATION, CONVENIENT GRAPHICAL AND TABULAR OUTPUT, BOTH TO THE SCREEN AND TO HARD COPY, AND A POWERFUL PROGRAMMING LANGUAGE TO SUPPORT THE DEVELOPMENT OF APPLICATIONS WHICH USE THE STATISTICAL CAPABILITY. WHILE MANY OF THE STATISTICAL FUNCTIONS TO BE PROVIDED ARE AVAILABLE PIECEMEAL ELSEWHERE, THERE WILL BE SEVERAL WHICH WILL BE UNIQUE TO MLAB. HAVING ALL THESE FUNCTIONS TOGETHERIN THE MLAB ENVIRONMENT INCREASES THEIR UTILITY SYNERGISTICALLY. THE STATISTICAL FUNCTIONS WILL COMPLEMENT THE EXISTING MLAB CAPABILITIES IN CURVE-FITTING, LEADING TO A LEVEL OF INTEGRATED FUNCTIONALITY NOT AVAILABLE IN ANY EXISTING SYSTEM. IN ADDITION, THE CAPABILITIES OF MLAB WILL BE ENHANCED IN ORDER THAT THE USER MAY MAKE MORE EFFECTIVE USE OF THE STATISTICAL FUNCTIONS. THE NEW STATISTICAL FUNCTIONALITY WILL BE FULLY DOCUMENTED IN A REFERENCE MANUAL AND IN AN ON-LINE HYPERTEXT HELP SYSTEM.