This demonstration provides a more comprehensive and practical example of how to simulate exponential random numbers in Julia. It covers both common methods, includes verification steps, and offers optional visualization to help you understand and trust the results. Remember to install the `Plots` package if you intend to use the histogram functionality.

Simulating Binomial Random Variables with Julia

The Law of Large Numbers (LLN) is a fundamental concept in probability and statistics. It essentially states that as the number of trials or observations increases, the average of the results will converge towards the expected value or true mean. In simpler terms, the more data you have, the more reliable your sample average becomes.

Week 5 - Using this lesson plan, students will have ample time to delve deep into the world of Monte Carlo simulations and gain hands-on experience with the Julia programming language.

This course provides an in-depth exploration of random number generation, sampling techniques, and simulation methods using Julia. Participants will learn how to generate random numbers from various distributions, perform statistical sampling, and design simulations to model real-world processes. The course combines theoretical concepts with practical implementation in Julia, making it suitable for students, researchers, and professionals in fields such as data science, statistics, and engineering.

QuantEcon

Stochastic Processes in Julia - Markov Chain Worked Example with Julia

Financial Mathematics With Julia

Chaining In Julia Programming

Julia, while not as mature as Python or R in terms of dedicated GIS packages, offers a growing ecosystem for geospatial analysis. This tutorial explores some key packages and their functionalities. It's important to note that the Julia GIS landscape is evolving, so staying updated with the latest developments is always recommended.

Cholesky Decomposition with Julia

The Tidier.jl Julia Package

NYCflights13 Worked Example with Julia

The NYC Flights 13 dataset in R is a popular resource for data analysis. It contains comprehensive information about all domestic flights departing from New York City airports (JFK, LGA, EWR) during the year 2013.

Julia provides excellent support for working with arbitrarily large integers, often called "big integers" or "bignums." This is incredibly useful when dealing with numbers that exceed the capacity of standard integer types (like `Int64`). This tutorial covers the basics of using big integers in Julia.

Carrying out model diagnostics for regression models in Julia can help you evaluate the performance and validity of your models.

Statistical Functions In Julia

Game Theory with Julia

The DataFrames.jl package in Julia is a powerful tool for working with tabular data, similar to data frames in R or Pandas in Python.

Introduction to Julia Syllabus

Concatenating Arrays in Julia

Demonstration of Paired t-test with Julia

Creating Confidence Intervals with Julia

Creating a Bland-Altman Plot with Julia

Generalized Linear Models with Julia

Using Mixed Models With Julia

Solving Polynomial Equations using Julia

Markov Chains with Julia

Creating Special Matrices with Julia

Linear Algebra Tutorial Sheet with Julia

The Sharpe Ratio is a widely used risk-adjusted performance metric in finance. It measures the excess return of an investment (or portfolio) compared to the risk-free rate per unit of volatility or standard deviation.

Correlation Analysis with Julia

Several Julia packages offer functionality for splitting datasets into training and testing sets.

The Julia Package Ecosystem

This tutorial provides a comprehensive introduction to hierarchical clustering in Julia. Experiment with different distance metrics and linkage methods to see how they affect the results. The dendrogram is an invaluable tool for understanding the hierarchical structure of your data. Remember to choose the method that best suits your data and the goals of your analysis.

This example provides a much more complete and practical demonstration of how to create and visualize Kaplan-Meier survival curves in Julia using the `SurvivalAnalysis` package.

Cox Proportional Hazard Model with Julia

The Nelson-Aalen analysis is a statistical method used in survival analysis to estimate the **cumulative hazard function**.

This exercise involves investigating the water holding capacity of soil in three different woodland areas by analyzing soil samples. The data provided includes the water holding capacity (in milliliters per gram) for each sample from Woodland A, B, and C. The task is to carry out a suitable analysis, such as calculating basic statistics (mean, standard deviation) and performing a one-way ANOVA to determine if there are significant differences between the three areas. The analysis will require making assumptions about the normality of data distribution, homogeneity of variance, and the independence of samples. The goal is to conclude whether the differences in water holding capacity between the woodland areas are statistically significant.

An overview of key distance measures in Julia

Linear Regression with Julia

Description of the Pima Diabetes Dataset

Worked example of Logistic Regression with Julia on the Pima Diabetes Dataset

The Sortino Index is a risk-adjusted return metric that measures the performance of an investment relative to the downside deviation, which is the standard deviation of returns below a specified minimum acceptable return (MAR). It is similar to the Sharpe ratio, but focuses only on downside risk rather than total volatility.

The Treynor Index is a risk-adjusted performance metric used to evaluate the performance of an investment portfolio, especially in comparison to a benchmark. It measures the excess return of an investment portfolio relative to the risk-free rate per unit of systematic risk.

Creating a Julia Function to compute the Geometric Mean of a dataset

In addition to calculating correlation coefficients, you may want to test the significance of the correlation. This is done using a correlation test, which evaluates whether the observed correlation is significantly different from zero. Here's how you can do correlation tests in Julia for Pearson, Spearman, and Kendall correlations.

Demonstration of the Chi Square Test with Julia

K-Means Clustering With Julia - K-means clustering is an unsupervised machine learning algorithm used to partition a dataset into a predefined number of clusters (K). It aims to group similar data points together by minimizing the distance between each data point and the centroid (center) of its assigned cluster

Weibull Distribution - Worked Example

This course provides a comprehensive introduction to probability distributions and their applications in statistical modeling and data analysis using the Julia programming language. Students will learn to understand, simulate, and apply various probability distributions, leveraging Julia's powerful computational capabilities. The course covers both theoretical concepts and practical implementations, ensuring students gain a solid foundation in probability and statistical computing.

The Weibull distribution is highly versatile and finds applications across various fields due to its flexibility in modeling different types of data.

This course introduces students to the principles and techniques of data analytics using Julia, with a special focus on the Tidier.jl package for data manipulation. Students will learn to manage, transform, and visualize data, as well as handle text and date operations effectively.

This course introduces students to the Julia programming language, focusing on its applications in statistical computing and data analysis. Students will learn how to leverage Julia's high-performance capabilities to perform complex statistical operations, data manipulation, visualization, and modelling.

This course provides an in-depth exploration of linear algebra concepts and techniques using the Julia programming language. Students will learn to apply Julia's high-performance capabilities to solve linear algebra problems, including matrix operations, vector spaces, eigenvalues, and more.

This course introduces students to numerical computing using the Julia programming language. It covers the fundamentals of numerical methods and how they are implemented in Julia for solving real-world scientific and engineering problems.

Set theory is fundamental in many areas of mathematics. Here are some short exercises related to set theory functions using Julia, suitable for students.

NCCU representative.