Coverage Technical Report, Census of Population, 2016
9. Estimation

Estimation for the DCS, the RRC and the COS is covered in Section 6.2, Section 7.4 and Section 8.5, respectively. This section describes how the results of census coverage studies are combined to produce estimates of population undercoverage ( U MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaacaWGdbaaaa@3DE8@ ), population overcoverage ( O MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaacaWGdbaaaa@3DE8@ ) and population net undercoverage ( N MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaacaWGdbaaaa@3DE8@ ) in different domains. The impact of sampling errors on the quality of the estimates is also measured by an estimated standard error for each estimate. Reverse Record Check (RRC) results and census data are used to produce undercoverage estimates, while the Census Overcoverage Survey (COS) results estimate overcoverage. Net undercoverage is the difference between undercoverage and overcoverage. This section expands on how these estimates and the associated standard errors are calculated.

The following definitions are used:

C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaacaWGdbaaaa@3DE8@
=
published census count of the number of persons in the target population
U ^ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaaceWGvbGbaKaaaaa@3E0A@
=
undercoverage estimate
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=
estimated number of persons not included in C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaacaWGdbaaaa@3DE8@ who should have been included
O ^ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaaceWGpbGbaKaaaaa@3E04@
=
overcoverage estimate
This is an empty cell
=
estimated number of enumerations included in C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaacaWGdbaaaa@3DE8@ that should not have been included
N ^ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaaceWGobGbaKaaaaa@3E03@
=
net undercoverage estimate
This is an empty cell
=
estimated number of enumerations not included in C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaacaWGdbaaaa@3DE8@ that should have been included, less the number of enumerations included in C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaacaWGdbaaaa@3DE8@ who should not have been included
This is an empty cell
=
U ^ O ^ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaaceWGvbGbaKaacqGHsislceWGpbGb aKaaaaa@3FDB@
T ^ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaaceWGubGbaKaaaaa@3E09@
=
estimated number of persons in the census target population based on census enumerations and the estimate of population net undercoverage
This is an empty cell
=
C + N ^ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaacaWGdbGaey4kaSIabmOtayaajaaa aa@3FAD@
R ^ U MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaaceWGsbGbaKaadaWgaaWcbaGaamyv aaqabaaaaa@3F0D@
=
estimated undercoverage rate
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=
100 * U ^ T ^ = 100 * U ^ C + N ^ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaacaaIXaGaaGimaiaaicdacaGGQaWa aSaaaeaaceWGvbGbaKaaaeaaceWGubGbaKaaaaGaeyypa0JaaGymai aaicdacaaIWaGaaiOkamaalaaabaGabmyvayaajaaabaGaam4qaiab gUcaRiqad6eagaqcaaaaaaa@494A@
R ^ O MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaaceWGsbGbaKaadaWgaaWcbaGaam4t aaqabaaaaa@3F07@
=
estimated overcoverage rate
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=
100 * O ^ T ^ = 100 * O ^ C + N ^ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaacaaIXaGaaGimaiaaicdacaGGQaWa aSaaaeaaceWGpbGbaKaaaeaaceWGubGbaKaaaaGaeyypa0JaaGymai aaicdacaaIWaGaaiOkamaalaaabaGabm4tayaajaaabaGaam4qaiab gUcaRiqad6eagaqcaaaaaaa@493E@
R ^ N MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaaceWGsbGbaKaadaWgaaWcbaGaamOt aaqabaaaaa@3F06@
=
estimate of net undercoverage rate
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=
100 * N ^ T ^ = 100 * U ^ O ^ C + N ^ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaacaaIXaGaaGimaiaaicdacaGGQaWa aSaaaeaaceWGobGbaKaaaeaaceWGubGbaKaaaaGaeyypa0JaaGymai aaicdacaaIWaGaaiOkamaalaaabaGabmyvayaajaGaeyOeI0Iabm4t ayaajaaabaGaam4qaiabgUcaRiqad6eagaqcaaaaaaa@4B14@

U ^ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaaceWGvbGbaKaaaaa@3E0A@ is calculated using RRC results and census data, and O ^ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaaceWGvbGbaKaaaaa@3E0A@ is produced from the COS, as shown below:

Table 9.1
Components of the population coverage error estimates for Canada
Table summary
This table displays the results of Components of the population coverage error estimates for Canada. The information is grouped by Components (appearing as row headers), Number of
persons (appearing as column headers).
ComponentsTable 9.1 Note 1 Number of persons
Estimate of U 1,557,061
Estimate of O 707,335
Estimate of N 849,726
C 35,151,728
C + estimate of N 36,001,454

The estimated standard errors are defined as follows:

By definition, we have v ( U ^ ) = v ( M ^ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaacaWG2bGaaiikaiqadwfagaqcaiaa cMcacqGH9aqpcaWG2bWaaeWaaeaaceWGnbGbaKaaaiaawIcacaGLPa aaaaa@44CA@ (refer to Section 7.4.7).

v ( M ^ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaacaWG2bGaaiikaiqad2eagaqcaiaa cMcaaaa@4056@
=
estimated variance of M ^ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaaceWGnbGbaKaaaaa@3E02@ based on the RRC design
v ( O ^ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaacaWG2bGaaiikaiqad+eagaqcaiaa cMcaaaa@4058@
=
estimated variance of O ^ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaaceWGpbGbaKaaaaa@3E04@ based on the COS design

Therefore:

s e ( U ^ ) = v ( M ^ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaacaWGZbGaamyzaiaacIcaceWGvbGb aKaacaGGPaGaeyypa0ZaaOqaaeaacaWG2bGaaiikaiqad2eagaqcai aacMcaaSqaaaaaaaa@459C@

s e ( R ^ U ) = ( U ^ 2 + T ^ 2 2 U ^ T ^ T ^ 4 ) v ( M ^ ) + U ^ 2 T ^ 4 v ( O ^ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaacaWGZbGaamyzamaabmaabaGabmOu ayaajaWaaSbaaSqaaiaadwfaaeqaaaGccaGLOaGaayzkaaGaeyypa0 ZaaOaaaeaadaqadaqaamaalaaabaGabmyvayaajaWaaWbaaSqabeaa caaIYaaaaOGaey4kaSIabmivayaajaWaaWbaaSqabeaacaaIYaaaaO GaeyOeI0IaaGOmaiqadwfagaqcaiqadsfagaqcaaqaaiqadsfagaqc amaaCaaaleqabaGaaGinaaaaaaaakiaawIcacaGLPaaacaWG2bWaae WaaeaaceWGnbGbaKaaaiaawIcacaGLPaaacqGHRaWkdaWcaaqaaiqa dwfagaqcamaaCaaaleqabaGaaGOmaaaaaOqaaiqadsfagaqcamaaCa aaleqabaGaaGinaaaaaaGccaWG2bWaaeWaaeaaceWGpbGbaKaaaiaa wIcacaGLPaaaaSqabaaaaa@5AAC@

s e ( O ^ ) = v ( O ^ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaacaWGZbGaamyzamaabmaabaGabm4t ayaajaaacaGLOaGaayzkaaGaeyypa0ZaaOqaaeaacaWG2bGaaiikai qad+eagaqcaiaacMcaaSqaaaaaaaa@45C8@

s e ( R ^ O ) = ( O ^ 2 T ^ 4 ) v ( M ^ ) + ( U ^ 2 + T ^ 2 2 O ^ T ^ T ^ 4 ) v ( O ^ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaacaWGZbGaamyzamaabmaabaGabmOu ayaajaWaaSbaaSqaaiaad+eaaeqaaaGccaGLOaGaayzkaaGaeyypa0 ZaaOaaaeaadaqadaqaamaalaaabaGabm4tayaajaWaaWbaaSqabeaa caaIYaaaaaGcbaGabmivayaajaWaaWbaaSqabeaacaaI0aaaaaaaaO GaayjkaiaawMcaaiaadAhacaGGOaGabmytayaajaGaaiykaiabgUca RmaabmaabaWaaSaaaeaaceWGvbGbaKaadaahaaWcbeqaaiaaikdaaa GccqGHRaWkceWGubGbaKaadaahaaWcbeqaaiaaikdaaaGccqGHsisl caaIYaGabm4tayaajaGabmivayaajaaabaGabmivayaajaWaaWbaaS qabeaacaaI0aaaaaaaaOGaayjkaiaawMcaaiaadAhacaGGOaGabm4t ayaajaGaaiykaaWcbeaaaaa@5BC3@

s e ( N ^ ) = v ( M ^ ) + v ( O ^ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaacaWGZbGaamyzamaabmaabaGabmOt ayaajaaacaGLOaGaayzkaaGaeyypa0ZaaOqaaeaacaWG2bGaaiikai qad2eagaqcaiaacMcacqGHRaWkcaWG2bGaaiikaiqad+eagaqcaiaa cMcaaSqaaaaaaaa@49DF@

s e ( R ^ N ) = ( ( U ^ O ^ ) 2 + T ^ 2 2 ( U ^ O ^ ) T ^ 2 T ^ 4 ) [ v ( M ^ ) + v ( O ^ ) ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfKttLearuGrYvMBJHgitnMCPbhDG0evam XvP5wqSXMqHnxAJn0BKvguHDwzZbqegqvATv2CG4uz3bIuV1wyUbqe dmvETj2BSbqegm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8rrpk 0dbbf9q8WrFfeuY=Hhbbf9v8vrpy0dd9qqpae9q8qqvqFr0dXdHiVc =bYP0xH8peuj0lXxfrpe0=vqpeeaY=brpwe9Fve9Fve8meaacaGacm GadaWaaiqacaabaiaafaaakeaacaWGZbGaamyzamaabmaabaGabmOu ayaajaWaaSbaaSqaaiaad6eaaeqaaaGccaGLOaGaayzkaaGaeyypa0 ZaaOaaaeaadaqadaqaamaalaaabaGaaiikaiqadwfagaqcaiabgkHi Tiqad+eagaqcaiaacMcadaahaaWcbeqaaiaaikdaaaGccqGHRaWkce WGubGbaKaadaahaaWcbeqaaiaaikdaaaGccqGHsislcaaIYaGaaiik aiqadwfagaqcaiabgkHiTiqad+eagaqcaiaacMcaceWGubGbaKaada ahaaWcbeqaaiaaikdaaaaakeaaceWGubGbaKaadaahaaWcbeqaaiaa isdaaaaaaaGccaGLOaGaayzkaaWaamWaaeaacaWG2bGaaiikaiqad2 eagaqcaiaacMcacqGHRaWkcaWG2bGaaiikaiqad+eagaqcaiaacMca aiaawUfacaGLDbaaaSqabaaaaa@5FB3@

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