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Reservoir sampling is a family of randomized algorithms for choosing a simple random sample, without replacement, of k items from a population of unknown size n in a single pass over the items. The size of the population n is not known to the algorithm and is typically too large for all n items to fit into main memory. The population is ...
For example, if a teacher has a class arranged in 5 rows of 6 columns and she wants to take a random sample of 5 students she might pick one of the 6 columns at random. This would be an epsem sample but not all subsets of 5 pupils are equally likely here, as only the subsets that are arranged as a single column are eligible for selection.
In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of successes (random draws for which the object drawn has a specified feature) in draws, without replacement, from a finite population of size that contains exactly objects with that feature, wherein each draw is either a success or a failure.
Considering the centered sample mean in this case, the random sample original distribution function is replaced by a bootstrap random sample with function ^, and the probability distribution of ¯ is approximated by that of ¯, where = ^, which is the expectation corresponding to ^. [25]
A simple example is fitting a line in two dimensions to a set of observations. Assuming that this set contains both inliers, i.e., points which approximately can be fitted to a line, and outliers, points which cannot be fitted to this line, a simple least squares method for line fitting will generally produce a line with a bad fit to the data including inliers and outliers.
The best example of the plug-in principle, the bootstrapping method. Bootstrapping is a statistical method for estimating the sampling distribution of an estimator by sampling with replacement from the original sample, most often with the purpose of deriving robust estimates of standard errors and confidence intervals of a population parameter like a mean, median, proportion, odds ratio ...
Inverse transformation sampling takes uniform samples of a number between 0 and 1, interpreted as a probability, and then returns the smallest number such that () for the cumulative distribution function of a random variable. For example, imagine that is the standard normal distribution with mean zero and standard deviation one. The table below ...
Suppose marbles are drawn without replacement until the urn is empty. Let be the indicator random variable of the event that the -th marble drawn is red. Then {} =, …, + is an exchangeable sequence. This sequence cannot be extended to any longer exchangeable sequence.