ean 128 barcode excel Expected normal frequency distribution function xnf in Software

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Expected normal frequency distribution function xnf
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/* Expected Normal Frequency Distribution Function xnf */ /* 6-6 */ DECLARE xnf(number of categories); scalefactor = f/(sd*25066283); /* 25066283 = sqrt(2*pi) */ shapefactor = -05/sd**2; DO i = 1 TO number of categories; category center value = base + (icn-05)*size of category; xnf(icn) = scalefactor*EXP(shapefactor* (category center value-xbar) **2); END; The observed frequencies at fx(i) can be compared with the values xnf(i) generated by this function If a distribution is approximately normal, many useful estimation rules can be applied In le design, it is often desirable to estimate how often a certain limit will be exceeded; for a distribution which is approximately normal, the cumulative area of the normal curve beyond the limit provides the desired estimate Table 6-7 lists some of these values in terms of t, the di erence between the mean and the limit as a ratio of the standard deviation,
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Table 6-7
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Normal one-tail probabilities
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t 0 025 050 075 100 125 150 175 200 225 250 275 300 400 500 p(value > limit) 0500 0401 0309 0227 0159 0106 0067 0040 0023 0012 0006 0003 0001 3 0000 03 0000 000 7
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limit = mean+ t or t = (limit-mean)/sd
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Sec 6-1
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Statistical Methods
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Infrequent Events Table 6-7 shows that events of value greater than the mean+3
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are quite rare Applying these values to Example 6-2, we rst tabulate the frequencies We obtain a mean of 9405 records per cylinder with a of 542 It takes t = +473 to exceed the cylinder capacity of 1197 For a normal distribution this is expected to happen less than once in a million cases (Table 6-7), but the distribution of bills per cylinder was not quite normal, due to seasonal variations In practice one over ow was found in 100 cylinders, as shown earlier in Example 6-1 Even when data is truly normally distributed, rare events can, of course, still happen; in fact, the high activity rates in data-processing systems can cause rare events to occur with annoying regularity When the normal distribution was introduced, the statement was made that distributions, when summed, become more normal This phenomenon is known as the the central limit theorem In the example which follows that rule will be applied to the problem of packing records into blocks for the tree-structured le evaluated in Chap 4-4-1, Example 48(1b) In order to pack xed-length records e ectively into one block, the capability of a block in terms of record segments was computed
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Block Over ow Due to Record Variability
nblock = y 1 =
B P R+P
A certain number of characters per block remained unused We will name this excess G and nd that G = B P nblock (R + P ) 6-3
These les are designed to always place nblock entries into a block, so that G < R The le-space usage for xed-length records was most e cient if G = 0 If the records are actually of variable length, the distribution of R has to be described A normal distribution may be a reasonable assumption if the average length is su ciently greater than the standard deviation; otherwise, record-length distributions tend to be of the Poisson type To make a choice, it is best to look at a histogram When assuming normality, the distribution is determined by the value of the mean record length, Rbar, and the standard deviation,
Example 6-3
Fixed space allocation per record
In Ex 4-8, case 1b, we had xed length records with the following parameters: B = 1000, R = 180, and P = 4, so that nblock = 5 and the excess per record was G = 1000 5 180 6 4 = 76 R/2 Now we take variable length records that are still on the average 180 characters long, and have a small standard deviation of 20 characters We allocate all the space in the block to the ve records (G = 0), providing (B P )/nblock P = 195 characters of space for each record The parameter t of Table 6-7 de nes the space between mean and limit in terms of the : t = (195 180)/20 = 075 From Table 6-7 we nd that 227% of the records will not t into their allotted space In Example 6-4 we try to do better by using buckets
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