Methods Used in Both Pathways: | Ordinal Variables: | Continuous Variables: | Continuous-Ordinal Pairs: | Overview of Correlation Method 1: | Simulation Process: | Overview of Correlation Method 2: | References

Example: Mixture of 2 Normal Distributions | Step 1: Obtain the standardized cumulants | Step 2: Simulate the variable | Step 3: Determine if the constants generate a valid PDF | Step 4: Select a critical value | Step 5: Calculate the cumulative probability for the simulated variable up to $1 - \alpha$ | Step 6: Plot graphs | References

Examples | Step 1: Obtain the distributional parameters | Step 2: Check the parameter inputs | Step 3: Calculate the lower skurtosis bounds for the continuous variables | Simulation using Correlation Method 1: | Step 4: Verify the target correlation matrix falls within the feasible correlation bounds | Step 5: Generate the variables | Step 6: Summarize the results numerically and Step 7: Summarize the results graphically | Simulation using Correlation Method 2: | References

Error Loop | Correlation Bounds | Some general methods for determining correlation boundaries: | The Generate, Sort, and Correlate (GSC) Algorithm: | The Frechet-Hoeffding Correlation Bounds: | Methods Used in Both Pathways: | Correlation Method 1: | Correlation Method 2: | References

Expected Cumulants of Continuous Mixture Variables | Extension to more than two component distributions: | Approximate Correlations for Continuous Mixture Variables: | Correlation between continuous mixture variables M1 and M2: | Correlation between continuous mixture variable M1 or M2 and other random variable Y: | References

References

Benefits of this package: | Comparison to other R packages: | Barbiero & Ferrari's (2015) GenOrd | Amatya & Demirtas' (2016) MultiOrd | Leisch, Kaiser, & Hornik's (2010) orddata | Demirtas, Nordgren, & Allozi's (2017) PoisBinOrdNonNor | References

Methods Used in Both Pathways: | Ordinal Variables: | Continuous Variables: | Continuous-Ordinal Pairs: | Overview of Correlation Method 1: | Simulation Process: | Overview of Correlation Method 2: | References

Example | Step 1: Obtain the standardized cumulants | Step 2: Simulate the variable | Step 3: Determine if the constants generate a valid power method pdf | Step 4: Select a critical value | Step 5: Solve for $\Large z'$ | Step 6: Calculate $\Large \Phi(z')$ | Step 7: Plot graphs | Calculate descriptive statistics. | References

Simulation Functions: | Power Method Constants Functions: | Data Description (Summary) Functions: | Lower Kurtosis Boundary Functions: | Correlation Validation Functions: | Intermediate Correlation Functions: | Error Loop Functions: | Graphing Functions: | Additional Helper Functions: | References

Example | Step 1: Set up the distributions and obtain the standardized cumulants | Step 2: Calculate the lower kurtosis bounds for the continuous variables | Correlation Method 1 | Step 3: Verify the target correlation matrix falls within the feasible correlation bounds | Step 4: Generate the variables | Step 5: Summarize the results numerically | Step 6: Summarize the results graphically | Correlation Method 2 | References

Example | Step 1) Find the theoretical standardized cumulants for each distribution. | Step 2) Use the cumulants to find the constants for each distribution. | Step 3) Look at results to see which distributions still have invalid power method pdfs | Step 4) Look at constants and sixth cumulant corrections | Step 5) Simulate distributions | References

References