Empirical Cumulative Distribution Function for Random Number Generation
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Solution Overview
Problem
In large data sets, especially those generated by statistical analysis, the lack of accessible testing data leads to inaccurate or misleading performance testing results due to the exponential increase in complexity and data size, making it challenging to generate reliable testing data.
Innovation Solution
A computer-implemented method generates random numbers distributed by a population distribution using an empirical cumulative distribution function, allowing for the creation of approximation random numbers that can be used in testing processes even when original data is unavailable, by constructing an empirical cumulative distribution function from random samples and generating a second random number that approximates the first random number drawn from the population.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If random samples are collected from a population to generate testing data, then testing data becomes available for performance testing, but the complexity and data size increase exponentially with the number of variables
Solution Approach 1:
The patent extracts only the essential distribution characteristics from the population data by constructing an empirical cumulative distribution function (ECDF). Instead of working with the complete complex dataset containing all variables and relationships, the ECDF captures the fundamental statistical properties needed for generating representative testing data, thereby reducing complexity while maintaining reliability
Solution Approach 2:
The patent transforms the complex multivariate population data into a simplified univariate representation through the ECDF parameterization. By changing the data representation from raw multivariate samples to cumulative distribution parameters, the system maintains the essential statistical characteristics while dramatically reducing data complexity and size for testing purposes
2Reliability
If the quantity of variables in a data set is increased to improve testing coverage, then testing comprehensiveness improves, but data size and relationship complexity increase exponentially
Solution Approach 1:
The patent creates synthetic copies of population data characteristics through the ECDF model. Instead of collecting and storing large quantities of actual population data or generating exhaustive test cases with many variables, the ECDF provides a compact model that can generate unlimited representative testing data copies, maintaining comprehensiveness while minimizing data size
Solution Approach 2:
The patent performs preliminary analysis of the population to construct the ECDF before generating testing data. This preliminary action captures all necessary distribution information in advance, allowing subsequent testing data generation to proceed with minimal data storage requirements while maintaining comprehensive coverage of population characteristics
Data Source
AI summary
The disclosure relates to technology for generating random numbers that are distributed by the population distribution. An empirical cumulative distribution function is constructed from random samples of the population, and a first random number is generated that is uniformly distributed over a first interval. A second interval in the empirical cumulative distribution function is found such that a range of values of the second interval cover the first random number. A second random number is then generated as an approximation to the random number drawn from the population, where the second random number is employed as part of a testing process.