Sample size and its role in Central Limit Theorem (CLT)

2018 ◽  
Author(s):  
Mohammad Rafiqul Islam
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Sample Size ◽  
Central Limit

Medical overpayment estimation: A Bayesian approach

2017 ◽  
Vol 17 (3) ◽  
pp. 196-222 ◽  
Author(s):  
Rasim M. Musal ◽  
Tahir Ekin
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Model Selection ◽  
Sample Size ◽  
Mixture Model ◽  
Central Limit ◽  
Bayesian Approach ◽  
Current Practice ◽  
Claims Data ◽  
Medical Claims

Overpayment estimation using a sample of audited medical claims is an often used method to determine recoupment amounts. The current practice based on central limit theorem may not be efficient for certain kinds of claims data, including skewed payment populations with partial overpayments. As an alternative, we propose a novel Bayesian inflated mixture model. We provide an analysis of the validity and efficiency of the model estimates for a number of payment populations and overpayment scenarios. In addition, learning about the parameters of the overpayment distribution with increasing sample size may provide insights for the medical investigators. We present a discussion of model selection and potential modelling extensions.

scholarly journals Central Limit Theorem and Its Applications in Determining Shoe Sizes of University Students

2019 ◽  
pp. 1-9
Author(s):  
Mbuba Morris Mwiti ◽  
Samson W. Wanyonyi ◽  
Davis Mwenda Marangu
Keyword(s):  
Standard Deviation ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
University Students ◽  
Sample Size ◽  
Central Limit ◽  
Research Paper ◽  
Shoe Size ◽  
The Central Limit Theorem ◽  
The University

The Central limit theorem is a very powerful tool in statistical inference and Mathematics in general, since it has numerous applications such as in topology and many other areas. For the case of probability theory, it states that, “given certain conditions, the sample mean of a sufficiently large number or iterates of independent random variables, each with a well-defined mean and well-defined variance, will be approximately normally distributed”. In the research paper, three different statements of our theorem (CLT) are given. This research paper has data regarding the shoe size and the gender of the of the university students. The paper is aimed at finding if the shoe sizes converges to a normal distribution as well as find the modal shoe size of university students and to apply the results of the central limit theorem to test the hypothesis if most university students put on shoe size seven. The Shoe sizes are typically treated as discretely distributed random variables, allowing the calculation of mean value and the standard deviation of the shoe sizes. The sample data which is used in this research paper belonged to different areas of Kibabii University which was divided into five strata. From two strata, a sample size of 74 respondents was drawn and from the remaining three strata, a sample of 73 students per stratum was drawn at random which totaled to a sample size of 367 respondents. By analyzing the data, using SPSS and Microsoft Excel, it was vivid that the shoe sizes are normally distributed with a well-defined mean and standard deviation. We also proved that most university students put on shoe size seven by testing our hypothesis using the p-value. The modal shoe size for university students was found to be seven since it had the highest frequency (97/367). This research was aimed at enlightening shoe investors, whose main market is the university students, on the shoe sizes that are on high demand among university students.

scholarly journals On the Markov Transition Kernels for First Passage Percolation on the Ladder

2011 ◽  
Vol 48 (02) ◽  
pp. 366-388 ◽  
Author(s):  
Eckhard Schlemm
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Asymptotic Variance ◽  
Almost Sure Convergence ◽  
First Passage Percolation ◽  
First Passage ◽  
Percolation Problem ◽  
Vertex Set ◽  
Step Transition

We consider the first passage percolation problem on the random graph with vertex set N x {0, 1}, edges joining vertices at a Euclidean distance equal to unity, and independent exponential edge weights. We provide a central limit theorem for the first passage times l n between the vertices (0, 0) and (n, 0), thus extending earlier results about the almost-sure convergence of l n / n as n → ∞. We use generating function techniques to compute the n-step transition kernels of a closely related Markov chain which can be used to explicitly calculate the asymptotic variance in the central limit theorem.

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