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INVERSE GAUSSIAN MOMENT ESTIMATESName:
Note that Dataplot supports two parameterizations of the inverse Gaussian distribution. The original parameterization of Tweedie has shape parameters \(\mu\) and \(\gamma\) (some references use \(\lambda\) for this parameter). The Chan parameterization has shape parameters \(\mu\) and \(\sigma\) where
This command returns estimates for \(\mu\), \(\sigma\), and \(\gamma\) so that estimates based on either parameterization can be obtained. The input array, say X, should contain the following values:
If one of the values is not available, then you can enter either CPUMIN or the statistic missing value. For example, if the skewness is not available, you can do one of the following:
LET CPUMIN = PROBVAL LET X(3) = CPUMIN or
LET X(3) = -9999 The following output vector, say Y, is returned:
Any of these moment estimates that cannot be computed will be set to CPUMIN. This can happen if certain summary statistics are not provided or if the equation solvers are not able to find a solution. The 3-parameter moment and modified moment estimates are computed using the codes provided on pages 360-361 of Cohen and Whitten.
<SUBSET/EXCEPT/FOR qualification> where <x> is the variable containing the summary statistics; <y> is a variable containing the inverse gaussian moment estimates; and where the <SUBSET/EXCEPT/FOR qualification> is optional and rarely used for this command.
. Purpose: Test INVERSE GAUSSIAN MOMENT ESTIMATES command . . Step 1: Read data . . Data from . . Cohen and Whitten (1988), "Parameter Estimation in . Reliability and Life Span Models", Dekker, p. 54. . serial read x 0.654 0.613 0.315 0.449 0.297 0.402 0.379 0.423 0.379 0.3235 0.269 0.740 0.418 0.412 0.494 0.416 0.338 0.392 0.484 0.265 end of data . let xmean = mean x let xsd = sd x let xmin = mini x let xskew = skew x let n = size x let z = data xmean xsd xskew xmin n . let y = inverse gaussian moment estimates z . let numdec = 5 . let locmom = y(1); let locmom = round(locmom,numdec) let mumom = y(2); let mumom = round(mumom,numdec) let sigmamom = y(3); let sigmamom = round(sigmamom,numdec) let gammamom = y(4); let gammamom = round(gammamom,numdec) let locmmom = y(5); let locmmom = round(locmmom,numdec) let mummom = y(6); let mummom = round(mummom,numdec) let sigmmmom = y(7); let sigmmmom = round(sigmmmom,numdec) let gammmmom = y(8); let gammmmom = round(gammmmom,numdec) . let xmean = round(xmean,numdec) let xsd = round(xsd,numdec) let xskew = round(xskew,numdec) let xmin = round(xmin,numdec) . print "Inverse Gaussian Parameter Estimates From Summary Data" print " " print " " print "Sample Mean: ^xmean" print "Sample SD: ^xsd" print "Sample Skewness: ^xskew" print "Sample Minimum: ^xmin" print "Sample Size: ^n" print " " print " " print "3-Parameter Inverse Gaussian Moment Estimates:" print "Location: ^locmom" print "Mu: ^mumom" print "Sigma: ^sigmamom" print "Gamma: ^gammamom" print " " print " " print "3-Parameter Inverse Gaussian Modified Moment Estimates:" print "Location: ^locmmom" print "Mu: ^mummom" print "Sigma: ^sigmmmom" print "Gamma: ^gammmmom"The following output is generated. Inverse Gaussian Parameter Estimates From Summary Data Sample Mean: 0.42313 Sample SD: 0.12528 Sample Skewness: 1.06732 Sample Minimum: 0.265 Sample Size: 20 3-Parameter Inverse Gaussian Moment Estimates: Location: 0.07099 Mu: 0.35213 Sigma: 0.12528 Gamma: 2.78197 3-Parameter Inverse Gaussian Modified Moment Estimates: Location: 0.12162 Mu: 0.30151 Sigma: 0.12528 Gamma: 1.74641
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Date created: 06/23/2014 |