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Full-Text Articles in Mathematics
Length Bias Estimation Of Small Businesses Lifetime, Simeng Li
Length Bias Estimation Of Small Businesses Lifetime, Simeng Li
Honors Theses
Small businesses, particularly restaurants, play a crucial role in the economy by generating employment opportunities, boosting tourism, and contributing to the local economy. However, accurately estimating their lifetimes can be challenging due to the presence of length bias, which occurs when the likelihood of sampling any particular restaurant's closure is influenced by its duration in operation. To address the issue, this study conducts goodness-of-fit tests on exponential/gamma family distributions and employs the Kaplan-Meier method to more accurately estimate the average lifetime of restaurants in Carytown. By providing insights into the challenges of estimating the lifetimes of small businesses, this study …
Detecting Trends And Patterns In Reliability Data Over Time Using Exponentially Weighted Moving-Averages, Harry F. Martz, Paul H. Kvam
Detecting Trends And Patterns In Reliability Data Over Time Using Exponentially Weighted Moving-Averages, Harry F. Martz, Paul H. Kvam
Department of Math & Statistics Faculty Publications
A simple, easy-to-use graphical method is presented for use in determining if there is any statistically significant trend or pattern over time in an underlying Poisson event rate of occurrence or binomial failure on demand probability. The method is based on the combined use of both an exponentially weighted moving-average (EWMA) and a Shewhart chart. Two nuclear power plant examples are introduced and used to illustrate the method. The false alarm probability and power when using the combined procedure are also determined for both cases using Monte Carlo simulation. The results indicate that the combined procedure is quite effective in …