Sampling proportional to random size

Conference · Mon Jan 01 04:00:00 EST 1979

OSTI ID:6175467

Uppuluri, V R.R.; Patil, S A

Let X/sub 1/, X/sub 2/,...,X/sub N/ be N nonnegative i.i.d. random variables. Let Y/sub 1/ = X/sub ..cap alpha../ with probability X/sub ..cap alpha../(X/sub 1/ + ... + X/sub N/), ..cap alpha.. = 1,2...N. This is referred to as the first realization when sampling with probability proportional to size. Next Y/sub 1/ is deleted from X/sub 1/,X/sub 2/,...,X/sub N/ and other observation, Y/sub 2/, is made similarly. It is of interest to find the distributional properties of the sequence Y/sub 1/,Y/sub 2/,...,Y/sub n/ (n less than or equal to N). These properties are used by E. Barouch and G.M. Kaufman in order to estimate recoverable oil resources. The distributional properties of (Y/sub 1/,Y/sub 2/,...Y/sub n/) are presented for the case when X/sub ..cap alpha../ has a general distribution, and specialized for the case when X/sub ..cap alpha../ has a gamma distribution. The distributional properties of Y/sub n/ are also obtained given the immediate past y/sub n-1/; these results supplement the distributional properties of Y/sub n/ given y/sub 1/,y/sub 2/,...,y/sub n-1/.

• Research Organization: Union Carbide Corp., Oak Ridge, TN (USA). Computer Sciences Div.; Tennessee Technological Univ., Cookeville (USA). Dept. of Mathematics
• DOE Contract Number: W-7405-ENG-26
• OSTI ID: 6175467
• Report Number(s): CONF-790729-1
• Country of Publication: United States
• Language: English

Related Subjects

02 PETROLEUM
020100* -- Petroleum-- Reserves-- (-1989)
03 NATURAL GAS
030100 -- Natural Gas-- Reserves-- (-1989)
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ANALYTICAL SOLUTION
GEOLOGIC DEPOSITS
MATHEMATICAL MODELS
MATHEMATICS
NATURAL GAS DEPOSITS
PETROLEUM DEPOSITS
RANDOMNESS
RESOURCES
SAMPLING
STATISTICS