# provide examples of a research articles that have an infinite sample size as the population size

In research, the notion of an "infinite sample size" is often conceptual rather than literal. Researchers typically use a sufficiently large sample size that can approximate an infinite population, particularly in fields such as statistics, economics, and certain types of social science research.
Here are examples of theoretical contexts or methodologies in which researchers might treat sample sizes as effectively infinite:
1. **Statistical Models**:
- In many statistical models, particularly those that utilize non-parametric methods, researchers often assume an infinite population size when deriving results. An example is the use of the central limit theorem, which holds that, given a sufficiently large sample size (often approximated as infinity), the distribution of sample means will approximate a normal distribution. Articles discussing this theorem typically do not specify a finite sample but acknowledge its theoretical underpinnings.
2. **Population Genetics**:
- In population genetics, theoretical models sometimes assume that the population size is large enough to treat it as infinite when studying allele frequencies over many generations. An example of such a study might be "The Effect of Migration on the Genetic Structure of a Population" where models and simulations may operate under infinite population size assumptions to ignore sampling bias and streamline calculations.
3. **Queuing Theory**:
- Research articles in operations research or queuing theory can involve models assuming an infinite number of potential customers or arrivals. For instance, consider "Analysis of Infinite-Server Queuing Systems" in which the arrival process can be treated as having an infinite population of potential customers, leading to simplifications in the mathematical modeling.
4. **Epidemiological Models**:
- Certain epidemiological models, such as those dealing with disease spread in a large population (like SIR models), might be analyzed under the assumption of an infinite population size to derive foundational models for transmission dynamics. Articles like "Modeling Infectious Disease Dynamics: The Basic Reproduction Number and Its Relationship to the Spread of Illness" often reference infinite populations to illustrate theoretical outcomes.
5. **Game Theory and Economics**:
- In game theory, some models operate under the assumption of infinite players or agents. For instance, research articles exploring Nash Equilibrium in a continuum of players might treat the population as infinitely large to derive generalizable strategies without dealing with finitely bounded constraints.
If you're looking for specific articles, consider searching through databases such as JSTOR, Google Scholar, or PubMed using keywords related to the above contexts. Look for theoretical discussions that involve asymptotic behaviors, population genetics models, or statistical theory papers that reference large (or effectively infinite) sample sizes in their methodologies.