Boots – shoes – and leggings
Patent
1997-01-13
1998-07-21
Trammell, James P.
Boots, shoes, and leggings
364517, 36472419, 367135, G01S 1500
Patent
active
057842973
ABSTRACT:
A method for finding a probability density function (PDF) and its statistical moments for an arbitrary exponential function of the form g(x)=.alpha.x.sup.m e.sup.-.beta.x.spsp.n,0<x<.infin., where .alpha., .beta., n>0, m>-1 are real constants in one-dimensional distributions and g(x.sub.1,x.sub.2, . . . ,x.sub.l) in the hyperplane. Non-linear regression analyses are performed on the data distribution and a root-mean-square (RMS) is calculated and recorded for each solution set until convergence. The basis function is reconstructed from the estimates in the final solution set and a PDF is obtained. The moment generating function (MGF), which characterizes any statistical moment of the distribution, is obtained using a novel function derived by the inventors and the mean and variance are obtained in standard fashion. Simple hypotheses about the behavior of such functional forms may be tested statistically once the empirical least squares methods have identified an applicable model derived from actual measurements.
REFERENCES:
patent: 5537368 (1996-07-01), O'Brien et al.
F.J.O'Brien et al., "The Moi Formula for Improper Exponential Definite Inrals", Perceptual and Motor Skills, 79, pp. 1123-1127, 1994.
P.J. hoel et al., Introduction to Probability Theory, Houghton-Mifflin (Boston), 1971.
F. J. O'Brien, et al., "A Method for Deriving Probability Distributions with Gamma Functions", NUWC-NPT Technical Report, TR 10,474, Jan. 16, 1996 .
Bates Bruce J.
Nguyen Chung T.
O'Brien, Jr. Francis J.
Gauthier Robert W.
Kaminis Shah
Lall Prithvi C.
McGowan Michael J.
The United States of America as represented by the Secretary of
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