Stata Tip 20: Generating Histogram Bin Variables

Contrast enhancement using histogram equalization with bin underflow and bin overflow

The histogram equalization (HE) is a widely used contrast enhancement method. But what is missing fromthe HE is a mechanism to control the rate of enhancement. The enhanced image always follows the uniform distribution. This paper presents a simple enhancement rate control mechanism for the HE. The gradient of the mapping function is controlled hy putting contraints on the probability density f...

Regression models for categorical dependent variables using Stata, 2nd Edition

Histogram bin width selection for time-dependent Poisson processes

In constructing a time histogram of the event sequences derived from a nonstationary point process, we wish to determine the bin width such that the mean squared error of the histogram from the underlying rate of occurrence is minimized. We find that the optimal bin widths obtained for a doubly stochastic Poisson process and a sinusoidally regulated Poisson process exhibit different scaling rel...

Linear regression model with histogram-valued variables

Histogram-valued variables are a particular kind of variables studied in Symbolic Data Analysis where to each entity under analysis corresponds a distribution that may be represented by a histogram or by a quantile function. Linear regression models for this type of data are necessarily more complex than a simple generalization of the classical model: the parameters cannot be negative; still th...

Chapter 4 : Generating Random Variables

Many of the methods in computational statistics require the ability to generate random variables from known probability distributions. This is at the heart of Monte Carlo simulation for statistical inference (Chapter 6), bootstrap and resampling methods (Chapters 6 and 7), Markov chain Monte Carlo techniques (Chapter 11), and the analysis of spatial point processes (Chapter 12). In addition, we...