# R

## Neyman-Pearson and some other Uniformly Most Powerful Tests

Introduction Suppose data consisting of i.i.d. observations $$X^n=(X_1,X_2,\cdots,X_n)$$ are available from a distribution $$F(x,\theta),\,\theta\in\Theta\subset\mathbf{R}.$$ The exact value $$\theta$$ corresponding to the distribution that generated the observations is unknown. The problem is, using the available data $$X^n,$$ construct tests for making decisions on the possible value of unknown parameter $$\theta$$.

## Win Odds Confidence Intervals in R

Continuous distributions Mann-Whitney estimate for the win probability Consider two independent, continuous RVs (random variables) $$\xi$$ and $$\eta$$. The following probability is called the win probability of RV $$\eta$$ against the RV $$\xi$$

## Exponential Distribution

Introduction This is a short reminder of some simple properties of exponential distributions. The continuous random variable (RV) $$\xi$$ has an exponential distribution with the rate $$\lambda>0$$ if its CMD (cumulative distribution function) has the following form

## Dose-Response Curves in R

Introduction Abstract In clinical research the dose–response relationship is often non-linear, therefore advanced fitting models are needed to capture their behavior. The talk will concentrate on fitting non-linear parametric models to the dose–response data and will explain some specificities of this problem.