population variance वाक्य
उदाहरण वाक्य
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- Thirdly, Bessel's correction is only necessary when the population mean is unknown, and one is estimating " both " population mean " and " population variance from a given sample set, using the sample mean to estimate the population mean.
- When estimating a scale parameter, using a trimmed estimator as a robust measures of scale, such as to estimate the population variance or population standard deviation, one generally must multiply by a scale factor to make it an unbiased consistent estimator; see scale parameter : estimation.
- When estimating a scale parameter, such as when using an L-estimator as a robust measures of scale, such as to estimate the population variance or population standard deviation, one generally must multiply by a scale factor to make it an unbiased consistent estimator; see scale parameter : estimation.
- For example, dividing the IQR by 2 \ sqrt { 2 } \ operatorname { erf } ^ {-1 } ( 1 / 2 ) \ approx 1.349 ( using the error function ) makes it an unbiased, consistent estimator for the population variance if the data follow a normal distribution.
- Further, mean-unbiasedness is not preserved under non-linear transformations, though median-unbiasedness is ( see effect of transformations ); for example, the sample variance is an unbiased estimator for the population variance, but its square root, the sample standard deviation, is a biased estimator for the population standard deviation.
- The simplest estimators for population mean and population variance are simply the mean and variance of the sample, the "'sample mean "'and "'( uncorrected ) sample variance "' these are consistent estimators ( they converge to the correct value as the number of samples increases ), but can be improved.
- When estimating the population variance and standard deviation of a sample where the population mean is unknown, the sample variance estimated as the " mean " of the squared deviations of sample values from their mean ( that is, using a multiplicative factor ) is a biased estimator of the population variance, and for the average sample underestimates it.
- When estimating the population variance and standard deviation of a sample where the population mean is unknown, the sample variance estimated as the " mean " of the squared deviations of sample values from their mean ( that is, using a multiplicative factor ) is a biased estimator of the population variance, and for the average sample underestimates it.
- Firstly, while the sample variance ( using Bessel's correction ) is an unbiased estimate of the population variance, its square root, the sample standard deviation, is a " biased " estimate of the population standard deviation; because the square root is a concave function, the bias is downward, by Jensen's inequality.
- Where df " t " is the degrees of freedom " n " 1 of the estimate of the population variance of the dependent variable, and df " e " is the degrees of freedom " n " " p " 1 of the estimate of the underlying population error variance.
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