Stats-Projects

This project was co-authored by Heather Johnston and Youngwoo Kwon $$ \gdef{\boldphi}{\boldsymbol{\phi}} $$ Introduction COVID-19, or Coronavirus Disease 2019, was declared a pandemic by the World Health Organization on March 11, 2020. The disease originated in December 2019 in China and quickly spread around the world. Compared with the previous epidemics like Ebola and SARS, COVID-19 has a relatively low mortality rate, but spreads faster with numerous mildly symptomatic cases. In response to the spread of COVID-19, governments and institutions have implemented a variety of policies such as social distancing, masks requirements, stay-at-home orders, and travel restrictions to limit or prevent person-to-person interactions. ...

$$ \gdef{\boldphi}{\boldsymbol{\phi}} \gdef{\xmin}{x_{\text{min}}} \gdef{\gammaone} {\Gamma_{\alpha}^{\prime} (1-\alpha, \lambda \xmin)} \gdef{\gammatwo}{\Gamma_{\alpha}^{\prime \prime} (1-\alpha, \lambda \xmin)} \gdef{\gammazero}{\Gamma (1-\alpha, \lambda \xmin)} $$ Introduction The power-law distribution is of the form \( f(x) \propto x^{-\alpha} \), where \( \alpha \) is called the scaling parameter. It models many natural phenomena like acoustic attenuation, Curie–Von Schweidler law, neuronal avalanches, and others. As \( x \to 0 \), \( f(x) \) diverges out of bounds. Hence, we gdefine \( \xmin \) as a lower bound for the support of the distribution function \( f(x) \). Using this, the power-law density function can be written as ...

Calyampudi Radhakrishna Rao (కల్యంపూడి రాధాకృష్ణారావు) is a legendary mathematician and statistician who has made pioneering contributions to various fields such as information theory, estimation, inference, multivariate analysis, and orthogonal arrays. His groundbreaking work has had a profound impact on not only statistics but also economics, genetics, anthropology, geology, national planning, demography, biometry, and medicine. In April 2023, he received the International Prize in Statistics, also known as the Nobel Prize for Statistics, for his dedication to the field. ...

This is not really stats project but it is pretty cool The Dirichlet Function The Dirichlet function is one of the easiest functions to define. It’s literally, $$ \gdef{\boldphi}{\boldsymbol{\phi}} $$ $$ \begin{aligned} f(x)&=\left\{ \begin{array}{ll} 1, & \text{if } x \text{ is rational} \\ 0, & \text{if } x \text{ is not rational} \end{array} \right. \end{aligned} $$ or using the symbols from number theory/set theory that almost no one remembers, ...

Photograph credits: Vulkan Olmez Introduction In the last two decades, there have been significant developments in understanding the anatomy of the brain for mental illnesses like Major Depressive Disorder, Anxiety Disorder, Bipolar Disorder, Schizophrenia, Personality Disorder, etc. Most of these disorders, along with alcohol and drug abuse are studied together to analyze the possible coexistence and the quantification of the correlation. One such study by Muester, et. al[1], estimates high rates of co-occurring mental illnesses and substance use disorders at around 50%. While studying the psychiatric and pharmacological aspects of such disorders is very important for treating, studying the environmental and genetic predispositions of a mental illness can help regulate and mitigate its effect at an early stage. ...