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Self-weighted random sampling is a method of selecting a sample from a population where each individual has an equal chance of being selected, but the probability of selection is proportional to their weight or size.

In self-weighted random sampling, each individual in the population is assigned a weight or size, which represents their importance or contribution to the population. The probability of selecting an individual for the sample is proportional to their weight or size, so that individuals with higher weights or sizes are more likely to be selected.

To implement self-weighted random sampling, we first assign weights or sizes to each individual in the population. We then calculate the total weight or size of the population, and divide each individual's weight or size by the total weight or size to obtain their probability of selection. We can then use a random number generator to select individuals for the sample, using their probabilities of selection as weights.

Self-weighted random sampling is useful when we want to ensure that our sample is representative of the population in terms of some characteristic that is related to weight or size. For example, if we are studying the effect of income on health outcomes, we might assign weights to individuals based on their income, and use self-weighted random sampling to select a sample that is representative of the income distribution in the population.

Overall, self-weighted random sampling is a powerful tool for selecting representative samples from populations, and can be used in a wide range of applications in statistics and data analysis.

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