population variance वाक्य
उदाहरण वाक्य
मोबाइल
- If the random variable X represents samples generated by a continuous distribution with probability density function f ( x ), then the population variance is given by
- In other words, the expected value of the uncorrected sample variance does not equal the population variance " ? " 2, unless multiplied by a normalization factor.
- Where " S " 1 2 and " S " 2 2 are the usual unbiased ( Bessel-corrected ) estimates of the two population variances.
- For example, when " n " = 1 the variance of a single observation about the sample mean ( itself ) is obviously zero regardless of the population variance.
- Notice that the unknown population variance ? 2 does not appear in " T ", since it was in both the numerator and the denominator, so it canceled.
- When Rochelle became a founding member of the Western Sun, the NCIC began shifting members trying to keep together a conference that was built of schools with inordinately large population variances.
- Hence \ scriptstyle \ sigma _ y ^ 2 gives an estimate of the population variance that is biased by a factor of \ frac { n-1 } { n }.
- For example, robust estimators of scale are used to estimate the population variance or population standard deviation, generally by multiplying by a scale factor to make it an scale parameter : estimation.
- For example, the MAD of a sample from a standard Cauchy distribution is an estimator of the population MAD, which in this case is 1, whereas the population variance does not exist.
- Suppose it were known that the two population variances are equal, and samples of sizes " n " 1 and " n " 2 are taken from the two populations:
- Multiplying the standard sample variance as computed in that fashion by ( equivalently, using instead of in the estimator's formula ) corrects for this, and gives an unbiased estimator of the population variance.
- Now a question arises : is the estimate of the population variance that arises in this way using the sample mean " always " smaller than what we would get if we used the population mean?
- That is why the sum of squares of the deviations from the " sample " mean is too small to give an unbiased estimate of the population variance when the average of those squares is found.
- For example, consider again the estimation of an unknown population variance & sigma; 2 of a Normal distribution with unknown mean, where it is desired to optimise " c " in the expected loss function
- However, if the population variances are equal, or if the samples are rather small and the population variances can be assumed to be approximately equal, it is more accurate to use Student's t-test,.
- However, if the population variances are equal, or if the samples are rather small and the population variances can be assumed to be approximately equal, it is more accurate to use Student's t-test,.
- In other situations, it makes more sense to think of a robust measure of scale as an estimator of its own expected value, interpreted as an alternative to the population variance or standard deviation as a measure of scale.
- It is true that on average it underestimates the population variance, but to call it a serious error is nonsense : sometimes biased estimators perform better-- indeed in some cases " far " better-- than unbiased ones.
- If the " biased sample variance " ( the second central moment of the sample, which is a downward-biased estimate of the population variance ) is used to compute an estimate of the population's standard deviation, the result is
- For example, the square root of the unbiased estimator of the population variance is " not " a mean-unbiased estimator of the population standard deviation : the square root of the unbiased sample variance, the corrected sample standard deviation, is biased.
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