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### Generate multivariate distributions of lognormal and normal distribution in python

Strategy: Calculate the normal mean and variance for the lognormal variables, then simulate the normal variables and calculate $e^\cdot$. An AR-process with diagonal $\phi$ and noise cov $C_a$ will ...
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### Generate multivariate distributions of lognormal and normal distribution in python

To generate random numbers from correlated distributions where two are lognormal and one is normal, and then extend it to an AR(1) process, you can follow these steps: Step 1: Define Parameters and ...
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### Sign of correlation between $y$ and $\hat{y}$ with and without intercept

For simple linear regression (with an intercept) you have $\hat \beta_1=\frac{\sum (x_i-\bar x)(y_i-\bar y)}{\sum (x_i-\bar x)^2}=\frac{s_y}{s_x}r_{x,y}$ and, since $s_x >0$ and $s_y > 0$, this ...
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### Models for fully correlated data

Your question includes aspects of basic longitudinal data analysis, time-series analysis, and multi-state time-to-event analysis. Each of those is complicated enough; combining them can be even ...
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### Spearman vs. Pearson for an evenly distributed variable. Can I just choose the coefficent with the stronger correlation?

Have you read about Anscombe's quartet? Get that data and compute the Spearman's r and also Kendall's tau; the results are interesting. Bivariate correlation analysis is quite limited and can be ...

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