Sample generation method and system for digital simulation processes
View Patent ↗A method for generating a set of random numbers with statistics represented by a cumulative density function includes generating a set of uniformly spaced samples between an upper limit and a lower limit. Each of the uniformly spaced samples are then mapped to a corresponding value on a cumulative density function curve. The set of uniformly spaced samples are then scrambled to randomize the samples. Companding may also be incorporated in the sample generation process.
1. A computer for generating and analyzing random sample values, the computer comprising a processor and a memory having instructions for performing steps comprising the steps of:
generating a set of numbers {R}, the set of numbers {R} having evenly spaced values between an upper numerical limit and a lower numerical limit;
mapping each one of the generated set of numbers {R} to a corresponding mapped number to form a mapped generated set of numbers {X};
scrambling the order of the mapped generated set of numbers {X} in a substantially random manner to form a random set of sample values; and
utilizing the random set of sample values to form a histogram-type output; and
presenting the output on a display for statistical analysis.
2. The computer of claim 1 , wherein the instructions for generating a set of numbers {R} having equally spaced values between the upper numerical limit and the lower numerical limit comprises the step of generating a monotonically ordered set of numbers between the upper numerical limit and the lower numerical limit.
3. The computer of claim 2 , wherein the generated set of numbers {R} is uniformly distributed.
4. The computer of claim 3 , wherein:
the memory includes a lookup table mapping a set {Y} to the mapped generated set of numbers {X}; and
the step of mapping each one of the generated set of numbers {R} to a corresponding mapped number to form the mapped generated set of numbers {X} comprises the steps of
comparing a first number R 1 of the generated set of numbers {R} to the set {Y} to find the nearest value of the set {Y} to the first number R 1 ;
mapping the first number R 1 to a first random sample value X 1 of the random set of sample values {X} corresponding to the nearest value of the set {Y} to the first number R 1 ;
comparing a successive number R k+1 of the generated set of numbers {R} to a subset of the set {Y} to find the nearest value of the set {Y} to the successive number R k+1 ; and
mapping the successive number R k+1 to a second random sample value X k+1 of the random set of sample values {X} corresponding to the nearest value of the set {Y} to the first number R k+1 .
5. The computer of claim 4 , wherein the subset of the set {Y} consists of values of {Y} that are smaller or equal to the nearest value of the set {Y} to the first number R 1 .
6. The computer of claim 5 , wherein the subset of the set {Y} consists of the first value of {Y} found to be less than R 1 .
7. A program storage device, readable by a computer, tangibly embodying at least one program of instructions executable by the computer to perform method steps of for generating and analyzing random sample values, the method steps comprising the steps of:
generating a set of numbers {R}, the set of numbers {R} having evenly spaced values between an upper numerical limit and a lower numerical limit;
mapping each one of the generated set of numbers {R} to a corresponding mapped number to form a mapped generated set of numbers {X};
scrambling the order of the mapped generated set of numbers {X} in a substantially random manner to form a random set of sample values; and
utilizing the random set of sample values to form a histogram-type output; and
presenting the output on a display for statistical analysis.
8. The program storage device of claim 7 , wherein the method steps for generating a set of numbers {R} having equally spaced values between the upper numerical limit and the lower numerical limit comprises the method step of generating a monotonically ordered set of numbers between the upper numerical limit and the lower numerical limit.
9. The program storage device of claim 8 , wherein the generated set of numbers {R} is uniformly distributed.
10. The program storage device of claim 9 , wherein:
the computer includes a memory having a lookup table mapping a set {Y} to the mapped generated set of numbers {X}; and
the method step of mapping each one of the generated set of numbers {R} to a corresponding mapped number to form the mapped generated set of numbers {X} comprises the method steps of:
comparing a first number R 1 of the generated set of numbers {R} to the set {Y} to find the nearest value of the set {Y} to the first number R 1 ;
mapping the first number R 1 to a first random sample value X 1 of the random set of sample values {X} corresponding to the nearest value of the set {Y} to the first number R 1 ;
comparing a successive number R k+1 of the generated set of numbers {R} to a subset of the set {Y} to find the nearest value of the set {Y} to the successive number R k+1 ; and
mapping the successive number R k+1 to a second random sample value X k+1 of the random set of sample values {X} corresponding to the nearest value of the set {Y} to the first number R k+1 .
11. The program storage device of claim 10 , wherein the subset of the set {Y} consists of values of {Y} that are smaller or equal to the nearest value of the set {Y} to the first number R 1 .
12. The program storage device of claim 11 , wherein the subset of the set {Y} consists of the first value of {Y} found to be less than R 1 .